About genemroz

genemroz · ‎01-27-2022

Thank you for your response. My particular use case would fall in the category of data visualization. I am using Proc Optmodel to optimize the pointing of multiple cameras so as to optimize sky coverage for the detection of meteors. I wish to visualize the field of view of the individual cameras at selected altitude levels. The shape of the FoV at any given altitude is a complex shape affected by lens distortion, atmospheric extinction and the presence of local obstructions (trees, buildings etc.) Proc Optmodel operates on a dataset that holds a 3d matrix of x,y,z cartesian coordinates of the interior of each possible field of view of each camera. It finds the optimal orientation of the cameras that covers the maximum volume of sky with at least 3-camera coverage. I was hoping to find the polygon described by the concave hull of the interior x,y coordinates of the optimal orientations at a selected z. Then I could use Gproject to transform the polygon from x,y and fixed z to Lat/Long and use Gmap in conjunction the SAS Annotate Facility to visualize the outline of the polygon of the optimal orientations over a map of the coverage region. I understand that concave hulls are not unique but I don't think that's very critical in this application as the shape of the perimeter is not terribly convoluted but is smoothly concave in some regions. I hope that's somewhat clear. Writing this response has sparked an idea in me to plot the interior points that I already have instead of trying to find the concave hull. I'll try this. Thanks for your interest, Gene

genemroz · ‎01-27-2022

Thanks, Rick, for your response and for the links. They are helpful. Unfortunately, I am not proficient with SAS/IML Programming. But this would be a great topic for a future Do Loop post. I hope you will consider it. Thanks again, Gene

genemroz · ‎01-26-2022

I have seen Rick Wicklin's blog entry on creating two-dimensional convex hulls. Is there a way within SAS to create two-dimensional concave hulls? Thanks in advance for any guidance you can provide, Gene

genemroz · ‎12-14-2021

Rob, The dataset of non-zero observations is 950,000 observations and 44MB. Much larger than the 5MB attachment limit. Is there another way to send it to you? Gene

genemroz · ‎12-14-2021

Rob, I tried the DECOMP option but it didn't help. I can post the code here but what's the best way for me to send the dataset to you? It has 4.25 million observations and is 200MB. Thanks for your offer to help, Gene

genemroz · ‎12-13-2021

Thanks, Rob, for pointing out my error. I fixed it and ran the code. Execution time was only a few seconds faster at 37 minutes and 10 seconds. The logfile is below. Do you see anything else that can be improved for better performance? Can you explain is happening under the hood when the Best Bound value creeps down at such small increments and so slowly? Thanks for your help, Gene 72 Proc Optmodel; 73 options fullstimer; 74 /* Read CoverageMatrix data into index sets*/ 75 set <str> stations; 76 read data work.station_id into stations=[station]; NOTE: There were 8 observations read from the data set WORK.STATION_ID. 77 78 set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>}; 79 80 set <str> ORIENTATION_STRING=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /; 81 set ORIENTATIONS = setof {s in orientation_string} 82 <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>; 83 put orientations=; ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>} 84 85 86 87 set <str> Targets; 88 read data work.targets into TARGETS=[target]; NOTE: There were 195228 observations read from the data set WORK.TARGETS. 89 num Matrix {stations, ORIENTATION_string, TARGETS}; 90 read data work.RoO_Matrix into [station orientation_string target] 91 Matrix=k; NOTE: There were 12494592 observations read from the data set WORK.ROO_MATRIX. 92 93 /* Set Constants*/ 94 /* optimal number of cameras covering each target*/ 95 %Let k=3; 96 num k=&k; SYMBOLGEN: Macro variable K resolves to 3 97 98 /*Declare Variables*/ 99 var CHI {stations, ORIENTATIONS} binary; 100 101 var IsTriplyCovered {TARGETS} binary; 102 impvar XIT{target in TARGETS}=sum{station in stations, <a,e> in 103 orientations} matrix[station, a||'/'||e, target] *Chi[station,a,e]; 104 105 /*Rob Pratt suggestion to improve execution time*/ 106 fix CHI['USL000',45,35]=1; 107 108 /* Declare Model*/ 109 max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t]; 110 111 /*Subject to Following Constraints*/ 112 con CHI_constraint {station in stations}: 113 sum{<a,e> in ORIENTATIONS}CHI[station,a,e] <=1; 114 115 con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t]; 116 117 set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a; 118 put AZIMUTHS=; AZIMUTHS={45,90,135,180,225,270,315,360} 119 set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45}; 120 put AZIMUTH_PAIRS=; AZIMUTH_PAIRS={<45,45>,<45,360>,<90,45>,<90,90>,<135,90>,<135,135>,<180,135>,<180,180>,<225,180>,<225,225>,<270,225>,<270,270>,<315, 270>,<315,315>,<360,315>,<360,360>} 121 122 con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}: 123 sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1; 124 /* expand; */ 125 126 /* Call Solver and Save Results:*/ 127 solve with milp/ heuristics=2 presolver=3 relobjgap=0.0; NOTE: Problem generation will use 2 threads. NOTE: The problem has 195292 variables (0 free, 1 fixed). NOTE: The problem uses 195228 implicit variables. NOTE: The problem has 195292 binary and 0 integer variables. NOTE: The problem has 195268 linear constraints (40 LE, 0 EQ, 195228 GE, 0 range). NOTE: The problem has 1142932 linear constraint coefficients. NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range). NOTE: The MILP presolver value AGGRESSIVE is applied. NOTE: The MILP presolver removed 192680 variables and 192689 constraints. NOTE: The MILP presolver removed 1107728 constraint coefficients. NOTE: The MILP presolver modified 801 constraint coefficients. NOTE: The presolved problem has 2612 variables, 2579 constraints, and 35204 constraint coefficients. NOTE: The MILP solver is called. NOTE: The parallel Branch and Cut algorithm is used. NOTE: The Branch and Cut algorithm is using up to 2 threads. Node Active Sols BestInteger BestBound Gap Time 0 1 3 23990.0000000 61138.0000000 60.76% 9 0 1 3 23990.0000000 39312.0000000 38.98% 9 0 1 3 23990.0000000 38127.7801515 37.08% 11 0 1 3 23990.0000000 37130.9544114 35.39% 11 0 1 3 23990.0000000 36692.3216045 34.62% 12 0 1 3 23990.0000000 36504.1395405 34.28% 12 0 1 3 23990.0000000 36420.4284890 34.13% 12 0 1 3 23990.0000000 36356.7490045 34.02% 13 0 1 3 23990.0000000 36274.3886694 33.87% 13 0 1 3 23990.0000000 36204.5574512 33.74% 13 0 1 3 23990.0000000 36137.2290216 33.61% 14 0 1 3 23990.0000000 36123.2972914 33.59% 14 0 1 3 23990.0000000 36119.0474640 33.58% 14 0 1 3 23990.0000000 36106.1955179 33.56% 15 0 1 3 23990.0000000 36097.8491496 33.54% 15 0 1 3 23990.0000000 36092.0621002 33.53% 15 0 1 3 23990.0000000 36084.1711840 33.52% 15 0 1 3 23990.0000000 36080.1799044 33.51% 16 NOTE: The MILP solver added 785 cuts with 4461 cut coefficients at the root. 1 2 3 23990.0000000 36080.1799044 33.51% 16 92 84 3 23990.0000000 35678.8140111 32.76% 20 200 187 3 23990.0000000 35438.1099578 32.30% 25 307 287 4 24330.0000000 35317.9985736 31.11% 27 347 325 5 24436.0000000 35299.0728640 30.77% 28 376 353 5 24436.0000000 35270.9243489 30.72% 30 498 465 5 24436.0000000 35179.5881591 30.54% 35 622 582 5 24436.0000000 35156.6853080 30.49% 40 747 1 5 24436.0000000 35019.6880171 30.22% 47 819 69 6 24522.0000000 35019.6880171 29.98% 50 820 70 6 24522.0000000 35019.6880171 29.98% 50 925 170 9 27481.0000000 35019.6880171 21.53% 53 935 175 9 27481.0000000 35019.6880171 21.53% 55 1037 274 9 27481.0000000 35019.6880171 21.53% 60 NOTE: The Decomposition algorithm is used. NOTE: The Decomposition algorithm time is 0.63 seconds. 1164 396 9 27481.0000000 34670.4366167 20.74% 65 1224 449 9 27481.0000000 34530.2041077 20.41% 70 1239 462 10 27492.0000000 34530.2041077 20.38% 71 1273 491 11 27500.0000000 34523.2661646 20.34% 73 1313 528 11 27500.0000000 34462.2905258 20.20% 75 1417 619 11 27500.0000000 34384.1242965 20.02% 80 1477 672 11 27500.0000000 34278.6085959 19.78% 85 1567 750 11 27500.0000000 34212.6188681 19.62% 90 1625 799 11 27500.0000000 34175.6139980 19.53% 95 1695 864 11 27500.0000000 34154.3283232 19.48% 100 1721 887 12 27503.0000000 34126.7849157 19.41% 100 1724 888 13 27505.0000000 34087.9161005 19.31% 100 1807 952 13 27505.0000000 33933.0291500 18.94% 105 1869 1002 13 27505.0000000 33881.4232385 18.82% 110 1927 1041 14 27512.0000000 33778.3581663 18.55% 114 1930 1043 14 27512.0000000 33762.8985315 18.51% 115 1975 1076 14 27512.0000000 33694.1238456 18.35% 120 2020 1107 14 27512.0000000 33640.0080999 18.22% 125 2021 1107 16 27545.0000000 33640.0080999 18.12% 125 2047 1125 16 27545.0000000 33606.3341194 18.04% 130 2073 1145 16 27545.0000000 33598.7736264 18.02% 135 2119 1182 16 27545.0000000 33566.4744542 17.94% 140 2163 1216 16 27545.0000000 33539.2577104 17.87% 145 2193 1240 16 27545.0000000 33527.8809774 17.84% 150 2221 1263 16 27545.0000000 33526.0634607 17.84% 155 2259 1291 16 27545.0000000 33457.3006099 17.67% 160 2291 1316 16 27545.0000000 33439.9249790 17.63% 165 2319 1336 17 27600.0000000 33401.0503735 17.37% 169 2321 1336 17 27600.0000000 33394.4530001 17.35% 171 2351 1361 17 27600.0000000 33369.3079313 17.29% 176 2383 1387 17 27600.0000000 33351.6920371 17.25% 180 2429 1418 19 28145.0000000 33318.7316262 15.53% 183 2463 1436 19 28145.0000000 33287.1613501 15.45% 185 2493 1453 19 28145.0000000 33196.4363181 15.22% 190 2528 1479 19 28145.0000000 33179.2226119 15.17% 195 2552 1497 19 28145.0000000 33138.2243498 15.07% 200 2580 1517 19 28145.0000000 33116.4226635 15.01% 205 2604 1524 19 28145.0000000 33078.0263628 14.91% 210 2630 1538 19 28145.0000000 33071.0639472 14.90% 215 2648 1547 19 28145.0000000 33057.6900363 14.86% 220 2684 1565 19 28145.0000000 33034.0598860 14.80% 225 2706 1581 19 28145.0000000 33018.3238359 14.76% 230 2736 1593 19 28145.0000000 32999.2147639 14.71% 235 2762 1616 19 28145.0000000 32991.2401113 14.69% 240 2786 1629 19 28145.0000000 32971.7655490 14.64% 245 2804 1640 19 28145.0000000 32954.8817894 14.60% 250 2828 1654 19 28145.0000000 32947.3818875 14.58% 255 2859 1675 19 28145.0000000 32937.1002699 14.55% 260 2885 1689 19 28145.0000000 32916.2067867 14.50% 265 2905 1696 19 28145.0000000 32886.9752917 14.42% 270 2935 1718 19 28145.0000000 32872.3261050 14.38% 275 2963 1737 19 28145.0000000 32862.0474192 14.35% 280 2991 1752 19 28145.0000000 32846.4084678 14.31% 285 3010 1767 19 28145.0000000 32833.6042658 14.28% 290 3032 1778 19 28145.0000000 32824.0539439 14.25% 295 3042 1778 19 28145.0000000 32812.0985895 14.22% 300 3070 1795 19 28145.0000000 32802.9313734 14.20% 305 3090 1796 19 28145.0000000 32776.4674619 14.13% 310 3116 1811 19 28145.0000000 32768.1291616 14.11% 315 3130 1818 19 28145.0000000 32765.6154429 14.10% 320 3144 1826 19 28145.0000000 32758.4546474 14.08% 325 3168 1839 19 28145.0000000 32738.1771688 14.03% 330 3186 1839 19 28145.0000000 32720.2593456 13.98% 335 3218 1860 19 28145.0000000 32703.9446058 13.94% 340 3244 1880 19 28145.0000000 32695.6508850 13.92% 345 3260 1883 19 28145.0000000 32681.5042359 13.88% 351 3273 1894 19 28145.0000000 32679.9761645 13.88% 355 3287 1897 19 28145.0000000 32664.5114888 13.84% 360 3313 1909 19 28145.0000000 32622.2162981 13.72% 365 3342 1935 19 28145.0000000 32606.8530471 13.68% 370 3354 1943 19 28145.0000000 32603.6748745 13.68% 375 3378 1962 19 28145.0000000 32594.4430060 13.65% 380 3392 1969 19 28145.0000000 32581.8484317 13.62% 385 3412 1976 19 28145.0000000 32570.4567912 13.59% 390 3440 1997 19 28145.0000000 32543.2918336 13.52% 395 3464 2005 19 28145.0000000 32529.5712123 13.48% 400 3480 2012 19 28145.0000000 32512.0159007 13.43% 406 3494 2014 19 28145.0000000 32498.1884249 13.40% 410 3508 2018 19 28145.0000000 32489.2116594 13.37% 415 3522 2018 19 28145.0000000 32472.6505570 13.33% 420 3548 2040 19 28145.0000000 32468.0946120 13.31% 425 3566 2046 19 28145.0000000 32453.9744347 13.28% 430 3584 2055 19 28145.0000000 32447.9099523 13.26% 435 3608 2064 19 28145.0000000 32429.8186704 13.21% 440 3624 2069 19 28145.0000000 32412.7257155 13.17% 445 3642 2077 19 28145.0000000 32399.0641145 13.13% 450 3660 2087 19 28145.0000000 32395.5001725 13.12% 455 3686 2103 19 28145.0000000 32381.8860548 13.08% 460 3710 2121 19 28145.0000000 32369.8393202 13.05% 465 3722 2127 19 28145.0000000 32362.2786409 13.03% 470 3742 2139 19 28145.0000000 32349.7596371 13.00% 475 3760 2141 19 28145.0000000 32323.3519976 12.93% 480 3774 2147 19 28145.0000000 32317.0238356 12.91% 485 3792 2155 19 28145.0000000 32304.2578449 12.88% 490 3808 2159 19 28145.0000000 32285.2578640 12.82% 495 3824 2168 19 28145.0000000 32281.3548247 12.81% 500 3846 2177 19 28145.0000000 32266.3143726 12.77% 505 3868 2187 19 28145.0000000 32253.2656199 12.74% 510 3888 2196 19 28145.0000000 32246.1066227 12.72% 515 3945 2224 19 28145.0000000 32210.8131186 12.62% 520 3967 2235 19 28145.0000000 32194.5390467 12.58% 525 3985 2240 19 28145.0000000 32180.8921155 12.54% 530 4011 2255 19 28145.0000000 32164.8927594 12.50% 535 4029 2258 19 28145.0000000 32133.1775338 12.41% 540 4048 2270 19 28145.0000000 32130.5662909 12.40% 545 4066 2273 19 28145.0000000 32124.7942211 12.39% 550 4089 2288 19 28145.0000000 32115.5910735 12.36% 555 4113 2300 19 28145.0000000 32110.6607619 12.35% 560 4137 2311 19 28145.0000000 32098.4243915 12.32% 565 4155 2315 19 28145.0000000 32080.6187936 12.27% 570 4181 2331 19 28145.0000000 32072.6683070 12.25% 575 4203 2342 19 28145.0000000 32063.4811472 12.22% 580 4217 2343 19 28145.0000000 32053.9412333 12.19% 585 4241 2357 19 28145.0000000 32051.8034044 12.19% 590 4257 2362 19 28145.0000000 32039.3685135 12.15% 595 4281 2371 19 28145.0000000 32032.3362767 12.14% 600 4301 2380 19 28145.0000000 32021.3018941 12.11% 605 4323 2386 19 28145.0000000 32007.5817268 12.07% 610 4345 2397 19 28145.0000000 31999.2190069 12.04% 615 4367 2410 19 28145.0000000 31998.7399175 12.04% 620 4391 2419 19 28145.0000000 31986.1735671 12.01% 625 4413 2435 19 28145.0000000 31979.9174940 11.99% 630 4427 2435 19 28145.0000000 31957.0406653 11.93% 635 4449 2445 19 28145.0000000 31944.5725237 11.89% 640 4465 2448 19 28145.0000000 31931.8700111 11.86% 645 4483 2450 19 28145.0000000 31917.3537133 11.82% 650 4497 2454 19 28145.0000000 31903.3508142 11.78% 655 4515 2458 19 28145.0000000 31898.5707476 11.77% 660 4533 2471 19 28145.0000000 31892.4111173 11.75% 665 4547 2475 19 28145.0000000 31876.6885913 11.71% 670 4583 2490 19 28145.0000000 31869.1311284 11.69% 675 4599 2499 19 28145.0000000 31862.7031547 11.67% 680 4617 2504 19 28145.0000000 31850.8973269 11.64% 685 4633 2511 19 28145.0000000 31843.6541359 11.62% 690 4651 2521 19 28145.0000000 31835.3270751 11.59% 695 4663 2525 19 28145.0000000 31817.6557916 11.54% 700 4685 2529 19 28145.0000000 31805.1312837 11.51% 705 4703 2530 19 28145.0000000 31794.8589187 11.48% 710 4723 2532 19 28145.0000000 31777.4954324 11.43% 715 4739 2540 19 28145.0000000 31775.4585865 11.43% 720 4751 2545 19 28145.0000000 31765.8162203 11.40% 725 4814 2572 19 28145.0000000 31761.6654875 11.39% 731 4827 2576 19 28145.0000000 31744.7172772 11.34% 735 4841 2584 19 28145.0000000 31742.6475725 11.33% 740 4861 2594 19 28145.0000000 31716.7215296 11.26% 745 4879 2595 19 28145.0000000 31703.7362426 11.22% 750 4899 2600 19 28145.0000000 31687.6507539 11.18% 755 4919 2605 19 28145.0000000 31681.4975952 11.16% 760 4933 2604 19 28145.0000000 31659.3953080 11.10% 765 4951 2608 19 28145.0000000 31641.0837646 11.05% 770 4977 2613 19 28145.0000000 31628.1407365 11.01% 775 4991 2613 19 28145.0000000 31617.4274150 10.98% 780 5003 2611 19 28145.0000000 31602.6621687 10.94% 785 5021 2608 19 28145.0000000 31585.7758024 10.89% 790 5039 2609 19 28145.0000000 31577.8457600 10.87% 795 5061 2619 19 28145.0000000 31566.7827296 10.84% 800 5081 2620 19 28145.0000000 31550.6579946 10.79% 805 5101 2627 19 28145.0000000 31535.7586141 10.75% 810 5131 2642 19 28145.0000000 31527.9858519 10.73% 815 5151 2646 19 28145.0000000 31521.2423383 10.71% 820 5169 2654 19 28145.0000000 31513.4690038 10.69% 825 5185 2654 19 28145.0000000 31507.8979001 10.67% 830 5215 2662 19 28145.0000000 31494.1198427 10.63% 835 5243 2671 19 28145.0000000 31478.5310731 10.59% 840 5269 2671 19 28145.0000000 31466.7105538 10.56% 845 5293 2672 19 28145.0000000 31452.8378365 10.52% 850 5315 2679 19 28145.0000000 31448.2860594 10.50% 856 5337 2686 19 28145.0000000 31434.3877225 10.46% 860 5357 2692 19 28145.0000000 31427.8724723 10.45% 865 5371 2693 19 28145.0000000 31419.5685490 10.42% 870 5399 2712 19 28145.0000000 31414.2272274 10.41% 875 5419 2717 19 28145.0000000 31409.3234172 10.39% 880 5439 2721 19 28145.0000000 31401.0348559 10.37% 885 5467 2712 19 28145.0000000 31376.9431268 10.30% 890 5493 2720 19 28145.0000000 31369.8282021 10.28% 895 5521 2729 19 28145.0000000 31366.3042864 10.27% 900 5545 2735 19 28145.0000000 31360.8535707 10.25% 905 5567 2733 19 28145.0000000 31345.2435070 10.21% 910 5585 2738 19 28145.0000000 31339.6080647 10.19% 915 5601 2738 19 28145.0000000 31333.8557987 10.18% 920 5617 2733 19 28145.0000000 31314.9885609 10.12% 925 5645 2746 19 28145.0000000 31295.8665007 10.07% 930 5667 2751 19 28145.0000000 31282.3228192 10.03% 935 5687 2749 19 28145.0000000 31270.9452029 10.00% 940 5731 2761 19 28145.0000000 31259.8266908 9.96% 945 5747 2765 19 28145.0000000 31253.9843707 9.95% 950 5773 2780 19 28145.0000000 31248.3476758 9.93% 955 5797 2780 19 28145.0000000 31229.4811517 9.88% 960 5821 2784 19 28145.0000000 31214.5203233 9.83% 965 5841 2785 19 28145.0000000 31212.7482320 9.83% 970 5875 2786 19 28145.0000000 31201.4393349 9.80% 975 5891 2788 19 28145.0000000 31192.3891289 9.77% 980 5911 2794 19 28145.0000000 31183.9955597 9.75% 985 5935 2791 19 28145.0000000 31172.6819452 9.71% 990 NOTE: The Decomposition algorithm is used. NOTE: The Decomposition algorithm time is 6.12 seconds. 5953 2796 19 28145.0000000 31170.3316371 9.71% 998 5958 2794 19 28145.0000000 31166.5521082 9.69% 1000 5977 2801 19 28145.0000000 31164.6478209 9.69% 1005 5997 2802 19 28145.0000000 31141.8412000 9.62% 1010 6011 2798 19 28145.0000000 31124.8481648 9.57% 1015 6037 2807 19 28145.0000000 31112.8074947 9.54% 1020 6059 2802 19 28145.0000000 31096.6127767 9.49% 1025 6085 2805 19 28145.0000000 31080.4842099 9.44% 1030 6111 2813 19 28145.0000000 31066.0601894 9.40% 1035 6137 2811 19 28145.0000000 31058.7464523 9.38% 1040 6165 2811 19 28145.0000000 31039.4046010 9.32% 1045 6191 2820 19 28145.0000000 31030.5413157 9.30% 1050 6213 2820 19 28145.0000000 31021.2509000 9.27% 1055 6245 2820 19 28145.0000000 31012.2740504 9.25% 1060 6266 2810 19 28145.0000000 31000.8594295 9.21% 1065 6290 2813 19 28145.0000000 30994.7728396 9.19% 1070 6308 2813 19 28145.0000000 30984.8892906 9.17% 1075 6336 2815 19 28145.0000000 30972.2501307 9.13% 1080 6364 2816 19 28145.0000000 30963.8722442 9.10% 1085 6389 2814 19 28145.0000000 30944.8459094 9.05% 1090 6411 2812 19 28145.0000000 30932.8344722 9.01% 1095 6441 2811 19 28145.0000000 30926.6559000 8.99% 1100 6458 2808 19 28145.0000000 30922.9934999 8.98% 1105 6480 2818 19 28145.0000000 30919.7516612 8.97% 1110 6504 2818 19 28145.0000000 30903.1248843 8.93% 1115 6528 2828 19 28145.0000000 30895.1233758 8.90% 1120 6548 2819 19 28145.0000000 30877.3744724 8.85% 1125 6574 2815 19 28145.0000000 30866.2296492 8.82% 1130 6603 2824 19 28145.0000000 30861.5464463 8.80% 1135 6627 2822 19 28145.0000000 30850.2852980 8.77% 1140 6643 2826 19 28145.0000000 30840.5007980 8.74% 1145 6663 2824 19 28145.0000000 30833.1029509 8.72% 1150 6681 2822 19 28145.0000000 30828.1494559 8.70% 1155 6697 2822 19 28145.0000000 30818.1857308 8.67% 1160 6719 2820 19 28145.0000000 30813.0598031 8.66% 1165 6745 2825 19 28145.0000000 30803.9174413 8.63% 1170 6773 2827 19 28145.0000000 30793.3588747 8.60% 1175 6793 2832 19 28145.0000000 30784.4708480 8.57% 1180 6826 2832 19 28145.0000000 30774.1311543 8.54% 1185 6844 2830 19 28145.0000000 30767.8337438 8.52% 1190 6862 2826 19 28145.0000000 30757.8096518 8.49% 1195 6892 2832 19 28145.0000000 30749.6852959 8.47% 1200 6914 2834 19 28145.0000000 30743.0137074 8.45% 1205 6934 2838 19 28145.0000000 30737.2977784 8.43% 1210 6958 2840 19 28145.0000000 30726.0418917 8.40% 1215 6980 2841 19 28145.0000000 30718.0924440 8.38% 1220 7012 2840 19 28145.0000000 30702.9764014 8.33% 1225 7030 2849 19 28145.0000000 30698.8592256 8.32% 1230 7052 2848 19 28145.0000000 30689.0788373 8.29% 1235 7084 2846 19 28145.0000000 30676.6284907 8.25% 1240 7108 2848 19 28145.0000000 30666.9338475 8.22% 1245 7126 2851 19 28145.0000000 30661.3489667 8.21% 1250 7154 2850 19 28145.0000000 30644.3265284 8.16% 1255 7174 2848 19 28145.0000000 30642.2477406 8.15% 1260 7198 2845 19 28145.0000000 30633.7700090 8.12% 1265 7234 2863 19 28145.0000000 30629.2858955 8.11% 1270 7254 2871 19 28145.0000000 30628.8963563 8.11% 1275 7278 2881 19 28145.0000000 30622.3366267 8.09% 1280 7320 2882 19 28145.0000000 30613.9028541 8.06% 1285 7373 2919 19 28145.0000000 30610.6178408 8.05% 1290 7390 2926 19 28145.0000000 30610.6178408 8.05% 1295 7408 2921 19 28145.0000000 30592.9903558 8.00% 1300 7427 2924 19 28145.0000000 30586.9428382 7.98% 1305 7447 2933 19 28145.0000000 30577.6573871 7.96% 1310 7471 2927 19 28145.0000000 30544.3898634 7.86% 1315 7494 2927 19 28145.0000000 30529.9787359 7.81% 1320 7518 2933 19 28145.0000000 30515.9473231 7.77% 1325 7538 2936 19 28145.0000000 30498.5796667 7.72% 1330 7583 2941 19 28145.0000000 30490.4009674 7.69% 1335 7615 2951 19 28145.0000000 30488.1019600 7.69% 1340 7653 2970 19 28145.0000000 30472.9928319 7.64% 1345 7669 2973 19 28145.0000000 30469.7965994 7.63% 1350 7693 2972 19 28145.0000000 30455.9228844 7.59% 1355 7721 2979 19 28145.0000000 30442.4549949 7.55% 1360 7749 2980 19 28145.0000000 30437.6443100 7.53% 1365 7771 2993 19 28145.0000000 30435.0773975 7.52% 1370 7795 2998 19 28145.0000000 30421.0076316 7.48% 1375 7825 3008 19 28145.0000000 30414.8618932 7.46% 1380 7853 3009 19 28145.0000000 30396.9389585 7.41% 1385 7877 3008 19 28145.0000000 30391.2805630 7.39% 1390 7895 3014 19 28145.0000000 30383.4729311 7.37% 1395 7917 3008 19 28145.0000000 30368.5003877 7.32% 1400 7937 3008 19 28145.0000000 30358.5342152 7.29% 1405 7954 2962 21 28377.0000000 30354.0070556 6.51% 1406 7991 2987 21 28377.0000000 30354.0048894 6.51% 1410 8013 2991 21 28377.0000000 30351.7927868 6.51% 1415 8039 2999 21 28377.0000000 30342.1725099 6.48% 1420 8077 3002 21 28377.0000000 30330.4487051 6.44% 1425 8105 3013 21 28377.0000000 30325.6722299 6.43% 1430 8123 3016 21 28377.0000000 30320.2449097 6.41% 1435 8147 3020 21 28377.0000000 30312.3317362 6.38% 1440 8171 3029 21 28377.0000000 30305.5201294 6.36% 1445 8193 3027 21 28377.0000000 30296.4700729 6.34% 1450 8223 3028 21 28377.0000000 30291.5585268 6.32% 1455 8253 3037 21 28377.0000000 30286.1465708 6.30% 1460 8283 3039 21 28377.0000000 30280.0215661 6.28% 1465 8315 3045 21 28377.0000000 30271.4497257 6.26% 1470 8343 3046 21 28377.0000000 30264.5152269 6.24% 1475 8367 3050 21 28377.0000000 30257.0498289 6.21% 1480 8397 3059 21 28377.0000000 30252.0000000 6.20% 1485 8419 3058 21 28377.0000000 30245.7570556 6.18% 1490 8469 3086 21 28377.0000000 30241.5436886 6.17% 1495 8507 3063 22 28377.0000000 30237.0630746 6.15% 1498 8537 3069 22 28377.0000000 30235.6697504 6.15% 1500 8557 3070 22 28377.0000000 30226.8200666 6.12% 1505 8573 3068 22 28377.0000000 30222.8339858 6.11% 1510 8593 3066 22 28377.0000000 30219.2588475 6.10% 1515 8621 3068 22 28377.0000000 30212.9012674 6.08% 1520 8645 3072 22 28377.0000000 30206.1541457 6.06% 1525 8667 3077 22 28377.0000000 30194.8968702 6.02% 1530 8705 3084 22 28377.0000000 30190.4535675 6.01% 1535 8737 3086 22 28377.0000000 30181.7429467 5.98% 1540 8761 3088 22 28377.0000000 30171.8923568 5.95% 1545 8793 3093 22 28377.0000000 30163.9782447 5.92% 1550 8813 3098 22 28377.0000000 30160.8494613 5.91% 1555 8841 3102 22 28377.0000000 30155.7801709 5.90% 1560 8867 3105 22 28377.0000000 30150.6676462 5.88% 1565 8938 3102 22 28377.0000000 30140.9458552 5.85% 1570 8956 3098 22 28377.0000000 30128.6396839 5.81% 1575 8980 3104 22 28377.0000000 30118.2164179 5.78% 1580 9006 3104 22 28377.0000000 30106.8965556 5.75% 1585 9036 3094 22 28377.0000000 30087.2973898 5.68% 1590 9054 3097 22 28377.0000000 30079.8133177 5.66% 1595 9090 3110 22 28377.0000000 30069.2563903 5.63% 1600 9120 3124 22 28377.0000000 30066.2830850 5.62% 1605 9146 3132 22 28377.0000000 30064.0152266 5.61% 1610 9172 3128 22 28377.0000000 30050.9527505 5.57% 1615 9202 3123 22 28377.0000000 30042.9244245 5.55% 1620 9232 3125 22 28377.0000000 30034.4884381 5.52% 1625 9252 3129 22 28377.0000000 30033.0655236 5.51% 1630 9274 3120 22 28377.0000000 30020.8964914 5.48% 1635 9296 3121 22 28377.0000000 30013.5925953 5.45% 1640 9332 3121 22 28377.0000000 30005.2451889 5.43% 1645 9370 3116 22 28377.0000000 29999.1820676 5.41% 1650 9402 3113 22 28377.0000000 29990.4178324 5.38% 1655 9422 3106 22 28377.0000000 29984.1962100 5.36% 1660 9478 3114 22 28377.0000000 29975.4572087 5.33% 1665 9524 3133 22 28377.0000000 29972.3040264 5.32% 1670 9558 3132 22 28377.0000000 29961.7311017 5.29% 1675 9614 3144 22 28377.0000000 29957.3776101 5.28% 1680 9644 3148 22 28377.0000000 29950.9345510 5.26% 1685 9674 3151 22 28377.0000000 29946.0509856 5.24% 1690 9706 3150 22 28377.0000000 29931.7755385 5.19% 1695 9748 3151 22 28377.0000000 29925.0403993 5.17% 1700 9772 3161 22 28377.0000000 29923.6526635 5.17% 1705 9802 3152 22 28377.0000000 29916.8352793 5.15% 1710 9826 3141 22 28377.0000000 29911.7581999 5.13% 1715 9852 3153 22 28377.0000000 29906.0788805 5.11% 1720 9880 3159 22 28377.0000000 29897.1360596 5.08% 1725 9942 3165 22 28377.0000000 29890.6666667 5.06% 1730 9970 3166 22 28377.0000000 29888.3346767 5.06% 1735 10010 3169 22 28377.0000000 29877.0786772 5.02% 1740 10034 3168 22 28377.0000000 29872.4218797 5.01% 1745 10102 3190 22 28377.0000000 29864.2968824 4.98% 1750 10158 3195 22 28377.0000000 29858.2085053 4.96% 1755 10202 3206 22 28377.0000000 29847.4413500 4.93% 1760 10272 3222 22 28377.0000000 29841.8555273 4.91% 1765 10316 3230 22 28377.0000000 29835.9014957 4.89% 1770 10356 3227 22 28377.0000000 29826.6479638 4.86% 1775 10400 3236 22 28377.0000000 29825.1219495 4.86% 1780 10524 3291 22 28377.0000000 29821.2997955 4.84% 1785 10574 3299 22 28377.0000000 29819.0007001 4.84% 1790 10630 3317 22 28377.0000000 29812.3438103 4.81% 1795 10650 3316 22 28377.0000000 29808.8163340 4.80% 1800 10678 3083 23 28728.0000000 29804.1681777 3.61% 1802 10716 3092 23 28728.0000000 29802.4759818 3.61% 1805 10758 3091 23 28728.0000000 29791.3621770 3.57% 1810 10792 3097 23 28728.0000000 29787.2476143 3.56% 1815 11060 2815 24 28728.0000000 29782.5918807 3.54% 1818 11241 2841 24 28728.0000000 29782.5918807 3.54% 1820 11284 2842 24 28728.0000000 29772.3232094 3.51% 1825 11350 2845 24 28728.0000000 29759.7305700 3.47% 1830 11376 2825 24 28728.0000000 29748.9004354 3.43% 1835 11418 2815 24 28728.0000000 29735.9171870 3.39% 1840 11466 2793 24 28728.0000000 29720.1231793 3.34% 1845 11526 2772 24 28728.0000000 29708.6215872 3.30% 1850 11562 2765 24 28728.0000000 29698.5250530 3.27% 1855 11622 2762 24 28728.0000000 29695.8530980 3.26% 1860 11684 2748 24 28728.0000000 29683.0807308 3.22% 1865 11744 2720 24 28728.0000000 29667.5425233 3.17% 1870 11790 2705 24 28728.0000000 29657.1525424 3.13% 1875 11846 2683 24 28728.0000000 29647.0845950 3.10% 1880 11896 2677 24 28728.0000000 29641.0000000 3.08% 1885 11954 2676 24 28728.0000000 29636.9848583 3.07% 1890 12012 2688 24 28728.0000000 29627.0618021 3.03% 1895 12068 2664 24 28728.0000000 29619.0999480 3.01% 1900 12102 2652 24 28728.0000000 29613.7731180 2.99% 1905 12164 2638 24 28728.0000000 29607.9448883 2.97% 1910 12218 2622 24 28728.0000000 29600.5000000 2.95% 1915 12286 2600 24 28728.0000000 29582.6748812 2.89% 1920 12332 2579 24 28728.0000000 29574.5611908 2.86% 1925 12380 2573 24 28728.0000000 29572.0470733 2.85% 1930 12446 2569 24 28728.0000000 29564.4011081 2.83% 1935 12522 2527 24 28728.0000000 29546.8138214 2.77% 1940 12562 2521 24 28728.0000000 29543.5071197 2.76% 1945 12614 2521 24 28728.0000000 29535.6896410 2.73% 1950 12684 2489 24 28728.0000000 29524.3076373 2.70% 1955 12740 2469 24 28728.0000000 29513.6161313 2.66% 1960 12788 2450 24 28728.0000000 29505.7223740 2.64% 1965 12842 2424 24 28728.0000000 29496.9771391 2.61% 1970 13024 2391 24 28728.0000000 29486.0426655 2.57% 1975 13088 2365 24 28728.0000000 29468.4576828 2.51% 1980 13151 2336 24 28728.0000000 29450.9021422 2.45% 1985 13193 2337 24 28728.0000000 29444.7923228 2.43% 1990 13255 2309 24 28728.0000000 29429.7050835 2.38% 1995 13309 2281 24 28728.0000000 29421.9782962 2.36% 2000 13357 2260 24 28728.0000000 29417.4588644 2.34% 2005 13437 2227 24 28728.0000000 29405.6666667 2.30% 2010 13525 2192 24 28728.0000000 29394.0339554 2.27% 2015 13587 2164 24 28728.0000000 29384.5008160 2.23% 2020 13655 2125 24 28728.0000000 29366.9237864 2.18% 2025 13723 2094 24 28728.0000000 29359.5000000 2.15% 2030 13823 2079 24 28728.0000000 29349.3640544 2.12% 2035 13887 2040 24 28728.0000000 29338.9432000 2.08% 2040 13953 2008 24 28728.0000000 29330.7875741 2.06% 2045 14027 1979 24 28728.0000000 29324.7076088 2.03% 2050 14123 1943 24 28728.0000000 29310.1735849 1.99% 2055 14189 1909 24 28728.0000000 29302.7318949 1.96% 2060 14255 1885 24 28728.0000000 29295.8783018 1.94% 2065 14319 1846 24 28728.0000000 29288.1592745 1.91% 2070 14391 1812 24 28728.0000000 29280.7650301 1.89% 2075 14467 1777 24 28728.0000000 29270.5145139 1.85% 2080 14543 1743 24 28728.0000000 29258.6263086 1.81% 2085 14683 1741 24 28728.0000000 29249.3342602 1.78% 2090 14759 1727 24 28728.0000000 29239.5422417 1.75% 2095 14845 1683 24 28728.0000000 29221.6677585 1.69% 2100 14927 1650 24 28728.0000000 29208.2091632 1.64% 2105 15009 1615 24 28728.0000000 29202.5593769 1.63% 2110 15138 1546 24 28728.0000000 29188.1966017 1.58% 2115 15228 1519 24 28728.0000000 29165.9825052 1.50% 2120 15308 1472 24 28728.0000000 29142.0147221 1.42% 2125 15386 1433 24 28728.0000000 29127.4904247 1.37% 2130 15474 1385 24 28728.0000000 29115.0188169 1.33% 2135 15564 1338 24 28728.0000000 29100.9765660 1.28% 2140 15678 1267 24 28728.0000000 29084.5000000 1.23% 2145 15816 1191 24 28728.0000000 29064.0778424 1.16% 2150 15934 1123 24 28728.0000000 29050.7382513 1.11% 2155 16046 1055 24 28728.0000000 29033.5009201 1.05% 2160 16194 1011 24 28728.0000000 29011.1774004 0.98% 2165 16396 911 24 28728.0000000 28986.3993874 0.89% 2170 16586 784 24 28728.0000000 28955.4497516 0.79% 2175 17097 433 24 28728.0000000 28903.6666667 0.61% 2180 17478 160 24 28728.0000000 28780.5771932 0.18% 2185 17725 0 24 28728.0000000 28728.0000000 0.00% 2186 NOTE: Optimal. NOTE: Objective = 28728. 128 create data work.OptimalSolution from 129 [station a e]={c in stations, <a,e> in orientations: CHI[c,a,e]>0.5} CHI; NOTE: The data set WORK.OPTIMALSOLUTION has 8 observations and 4 variables. 130 quit; NOTE: PROCEDURE OPTMODEL used (Total process time): real time 37:09.96 user cpu time 1:11:59.03 system cpu time 8.45 seconds memory 2530550.54k OS Memory 2587700.00k Timestamp 12/13/2021 10:22:22 PM Step Count 78 Switch Count 5408 Page Faults 0 Page Reclaims 943191 Page Swaps 0 Voluntary Context Switches 1971953 Involuntary Context Switches 9604 Block Input Operations 0 Block Output Operations 896

genemroz · ‎12-13-2021

Thanks, Rob, for your prompt response. I implemented your suggestion (correctly, I hope) but a NOTE (at line131): indicates that "Constraint CHI_constraint[USL000] causes the problem to be infeasible. The MILP presolver found this problem to be infeasible." The logfile is below. Thanks for taking a look at this, Gene 72 Proc Optmodel; 73 options fullstimer; 74 /* Read CoverageMatrix data into index sets*/ 75 set <str> stations; 76 read data work.station_id into stations=[station]; NOTE: There were 8 observations read from the data set WORK.STATION_ID. 77 78 set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>}; 79 80 set <str> ORIENTATION_STRING=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /; 81 set ORIENTATIONS = setof {s in orientation_string} 82 <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>; 83 put orientations=; ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>} 84 85 86 87 set <str> Targets; 88 read data work.targets into TARGETS=[target]; NOTE: There were 195228 observations read from the data set WORK.TARGETS. 89 num Matrix {stations, ORIENTATION_string, TARGETS}; 90 read data work.RoO_Matrix into [station orientation_string target] 91 Matrix=k; NOTE: There were 12494592 observations read from the data set WORK.ROO_MATRIX. 92 93 /* Set Constants*/ 94 /* optimal number of cameras covering each target*/ 95 %Let k=3; 96 num k=&k; SYMBOLGEN: Macro variable K resolves to 3 97 98 /*Declare Variables*/ 99 var CHI {stations, ORIENTATIONS} binary; 100 101 var IsTriplyCovered {TARGETS} binary; 102 impvar XIT{target in TARGETS}=sum{station in stations, <a,e> in 103 orientations} matrix[station, a||'/'||e, target] *Chi[station,a,e]; 104 fix CHI['USL000',45,35]=1; 105 fix CHI['USL000',90,35]=1; 106 fix CHI['USL000',135,35]=1; 107 fix CHI['USL000',180,35]=1; 108 fix CHI['USL000',225,35]=1; 109 fix CHI['USL000',270,35]=1; 110 fix CHI['USL000',315,35]=1; 111 fix CHI['USL000',360,35]=1; 112 /* Declare Model*/ 113 max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t]; 114 115 /*Subject to Following Constraints*/ 116 con CHI_constraint {station in stations}: 117 sum{<a,e> in ORIENTATIONS}CHI[station,a,e] <=1; 118 119 con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t]; 120 121 set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a; 122 put AZIMUTHS=; AZIMUTHS={45,90,135,180,225,270,315,360} 123 set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45}; 124 put AZIMUTH_PAIRS=; AZIMUTH_PAIRS={<45,45>,<45,360>,<90,45>,<90,90>,<135,90>,<135,135>,<180,135>,<180,180>,<225,180>,<225,225>,<270,225>,<270,270>,<315, 270>,<315,315>,<360,315>,<360,360>} 125 126 con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}: 127 sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1; 128 /* expand; */ 129 130 /* Call Solver and Save Results:*/ 131 solve with milp/ heuristics=2 presolver=3 relobjgap=0.0; NOTE: Problem generation will use 2 threads. NOTE: The problem has 195292 variables (0 free, 8 fixed). NOTE: The problem uses 195228 implicit variables. NOTE: The problem has 195292 binary and 0 integer variables. NOTE: The problem has 195268 linear constraints (40 LE, 0 EQ, 195228 GE, 0 range). NOTE: The problem has 1142932 linear constraint coefficients. NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range). NOTE: The MILP presolver value AGGRESSIVE is applied. NOTE: Constraint CHI_constraint[USL000] causes the problem to be infeasible. NOTE: The MILP presolver found this problem to be infeasible. 132 create data work.OptimalSolution_&RoO from _ 22 WARNING: Apparent symbolic reference ROO not resolved. 132 create data work.OptimalSolution_&RoO from _ 200 ERROR 22-322: Syntax error, expecting one of the following: (, FROM. ERROR 200-322: The symbol is not recognized and will be ignored. 132 create data work.OptimalSolution_&RoO from ___ 525 ERROR 525-782: The symbol 'RoO' is unknown. 132 create data work.OptimalSolution_&RoO from ____ 525 ERROR 525-782: The symbol 'from' is unknown. 133 [station a e]={c in stations, <a,e> in orientations: CHI[c,a,e]>0.5} CHI; _ ___ 22 79 202 583 ERROR 22-322: Syntax error, expecting one of the following: !, !!, &, (, *, **, +, ',', -, .., /, <, <=, <>, =, >, ><, >=, AND, BY, CROSS, DIFF, ELSE, IN, INTER, NOT, OR, SYMDIFF, TO, UNION, WITHIN, [, ], ^, ^=, |, ||, ~, ~=. ERROR 79-322: Expecting a ]. ERROR 202-322: The option or parameter is not recognized and will be ignored. ERROR 583-782: The implied subscript count does not match array 'CHI', 0 NE 3. _______ _ 525 599 ERROR 525-782: The symbol 'station' is unknown. ERROR 599-782: The operand types for '=' are mismatched, found a number and a set. 133 ! [station a e]={c in stations, <a,e> in orientations: CHI[c,a,e]>0.5} CHI; _ 525 ERROR 525-782: The symbol 'e' is unknown. 134 quit; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE OPTMODEL used (Total process time): real time 42.47 seconds user cpu time 53.38 seconds system cpu time 2.45 seconds memory 2419788.07k OS Memory 2577124.00k Timestamp 12/13/2021 08:41:55 PM Step Count 73 Switch Count 56 Page Faults 0 Page Reclaims 743338 Page Swaps 0 Voluntary Context Switches 6196 Involuntary Context Switches 144 Block Input Operations 0 Block Output Operations 40 135 /*Print Results*/ 136 136 ! proc print data=work.optimalsolution_&RoO; WARNING: Apparent symbolic reference ROO not resolved. 136 proc print data=work.optimalsolution_&RoO; _ 22 ERROR 22-322: Syntax error, expecting one of the following: ;, (, BLANKLINE, CONTENTS, DATA, DOUBLE, GRANDTOTAL_LABEL, GRANDTOT_LABEL, GRAND_LABEL, GTOTAL_LABEL, GTOT_LABEL, HEADING, LABEL, N, NOOBS, NOSUMLABEL, OBS, ROUND, ROWS, SPLIT, STYLE, SUMLABEL, UNIFORM, WIDTH. 136 proc print data=work.optimalsolution_&RoO; _ 200 ERROR 200-322: The symbol is not recognized and will be ignored. WARNING: Apparent symbolic reference ROO not resolved. ERROR: File WORK.OPTIMALSOLUTION_.DATA does not exist. 137 Title "Optimal Solution RoO=&RoO x &RoO km"; WARNING: Apparent symbolic reference ROO not resolved. WARNING: Apparent symbolic reference ROO not resolved. 138 run; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE PRINT used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 225.06k OS Memory 77412.00k Timestamp 12/13/2021 08:41:55 PM Step Count 74 Switch Count 1 Page Faults 0 Page Reclaims 31 Page Swaps 0 Voluntary Context Switches 10 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 0 139 /* Create Macro Variables for Station and Optimal Solution*/ 140 140 ! data macrovariables; 141 set optimalsolution_&RoO; _ 22 200 WARNING: Apparent symbolic reference ROO not resolved. ERROR: File WORK.OPTIMALSOLUTION_.DATA does not exist. ERROR: File WORK.ROO.DATA does not exist. ERROR 22-322: Syntax error, expecting one of the following: a name, a quoted string, (, -, :, ;, CUROBS, END, INDSNAME, KEY, KEYRESET, KEYS, NOBS, OPEN, POINT, _DATA_, _LAST_, _NULL_. ERROR 200-322: The symbol is not recognized and will be ignored. 142 suffix=put(_n_,5.); 143 call symput (cats('Sta_Code',suffix),Station); 144 call symput (cats('Opt_Orientation',suffix),catx('/',a,e)); 145 run; NOTE: Numeric values have been converted to character values at the places given by: (Line):(Column). 143:43 NOTE: The SAS System stopped processing this step because of errors. WARNING: The data set WORK.MACROVARIABLES may be incomplete. When this step was stopped there were 0 observations and 4 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 649.50k OS Memory 77672.00k Timestamp 12/13/2021 08:41:55 PM Step Count 75 Switch Count 2 Page Faults 0 Page Reclaims 91 Page Swaps 0 Voluntary Context Switches 11 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 264 146 147 data plot; 148 set RoO_Matrix; 149 where k>=1; 150 x=input(scan(target,1,'/'),8.); 151 y=input(scan(target,2,'/'),8.); 152 z=input(scan(target,3,'/'),8.); 153 run; NOTE: There were 947544 observations read from the data set WORK.ROO_MATRIX. WHERE k>=1; NOTE: The data set WORK.PLOT has 947544 observations and 7 variables. NOTE: DATA statement used (Total process time): real time 0.74 seconds user cpu time 0.57 seconds system cpu time 0.17 seconds memory 3447.31k OS Memory 80492.00k Timestamp 12/13/2021 08:41:56 PM Step Count 76 Switch Count 5 Page Faults 0 Page Reclaims 543 Page Swaps 0 Voluntary Context Switches 20 Involuntary Context Switches 158 Block Input Operations 0 Block Output Operations 133640 154 proc sort data=plot; 155 by z descending station orientation_string; 156 run; NOTE: There were 947544 observations read from the data set WORK.PLOT. NOTE: The data set WORK.PLOT has 947544 observations and 7 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.38 seconds user cpu time 0.64 seconds system cpu time 0.18 seconds memory 132041.67k OS Memory 208648.00k Timestamp 12/13/2021 08:41:56 PM Step Count 77 Switch Count 8 Page Faults 0 Page Reclaims 32131 Page Swaps 0 Voluntary Context Switches 3296 Involuntary Context Switches 12 Block Input Operations 0 Block Output Operations 133640 157 ods graphics / reset width=6.4in height=6.4in; 158 proc sgplot data=plot aspect=1; 159 by z; 160 where ((station="&Sta_Code1" and orientation_string= "&Opt_Orientation1") or WARNING: Apparent symbolic reference STA_CODE1 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION1 not resolved. 161 (station="&Sta_Code2" and orientation_string="&Opt_Orientation2") or WARNING: Apparent symbolic reference STA_CODE2 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION2 not resolved. 162 (station="&Sta_Code3" and orientation_string="&Opt_Orientation3") or WARNING: Apparent symbolic reference STA_CODE3 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION3 not resolved. 163 (station="&Sta_Code4" and orientation_string="&Opt_Orientation4") or WARNING: Apparent symbolic reference STA_CODE4 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION4 not resolved. 164 (station="&Sta_Code5" and orientation_string="&Opt_Orientation5") or WARNING: Apparent symbolic reference STA_CODE5 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION5 not resolved. 165 (station="&Sta_Code6" and orientation_string="&Opt_Orientation6") or WARNING: Apparent symbolic reference STA_CODE6 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION6 not resolved. 166 (station="&Sta_Code7" and orientation_string="&Opt_Orientation7") or WARNING: Apparent symbolic reference STA_CODE7 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION7 not resolved. 167 (station="&Sta_Code8" and orientation_string="&Opt_Orientation8") or WARNING: Apparent symbolic reference STA_CODE8 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION8 not resolved. 168 (station="&Sta_Code9" and orientation_string="&Opt_Orientation9") or WARNING: Apparent symbolic reference STA_CODE9 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION9 not resolved. 169 (station="&Sta_Code10" and orientation_string="&Opt_Orientation10") or WARNING: Apparent symbolic reference STA_CODE10 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION10 not resolved. 170 (station="&Sta_Code11" and orientation_string="&Opt_Orientation11") or WARNING: Apparent symbolic reference STA_CODE11 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION11 not resolved. 171 (station="&Sta_Code12" and orientation_string="&Opt_Orientation12") or WARNING: Apparent symbolic reference STA_CODE12 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION12 not resolved. 172 (station="&Sta_Code13" and orientation_string="&Opt_Orientation13") or WARNING: Apparent symbolic reference STA_CODE13 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION13 not resolved. 173 (station="&Sta_Code14" and orientation_string="&Opt_Orientation14") or WARNING: Apparent symbolic reference STA_CODE14 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION14 not resolved. 174 (station="&Sta_Code15" and orientation_string="&Opt_Orientation15")); WARNING: Apparent symbolic reference STA_CODE15 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION15 not resolved. 175 176 Title "New Azimuth (N),New Elevation Angles by Level"; 177 scatter x=x y=y /group=station transparency=.85 markerattrs=(symbol=circlefilled); 178 xaxis grid min=-800 max=800; 179 yaxis grid min=-800 max=800; 180 run; NOTE: There were 0 observations read from the data set WORK.PLOT. WHERE 0 /* an obviously FALSE WHERE clause */ ; NOTE: PROCEDURE SGPLOT used (Total process time): real time 0.00 seconds user cpu time 0.01 seconds system cpu time 0.00 seconds memory 1947.00k OS Memory 79720.00k Timestamp 12/13/2021 08:41:56 PM Step Count 78 Switch Count 1 Page Faults 0 Page Reclaims 312 Page Swaps 0 Voluntary Context Switches 6 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 8 181 182 183 184 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK; SYMBOLGEN: Macro variable GRAPHTERM resolves to GOPTIONS NOACCESSIBLE; 194 User: u44673568

genemroz · ‎12-13-2021

Esteemed Advisers: I'm looking for advice on how to improve the performance of my Proc Optmodel code. The present code takes about 37 minutes to solve. I've attached the relevant portions of the log file below. The purpose of the code is to optimize the orientation of 8 cameras so as to maximize 3-camera coverage over the largest possible area. Each camera has 8 possible orientations. The spatial coverage of each orientation of each camera is represented by a binary coverage matrix on a 3-D Cartesian grid. Currently, there are 12.5 million observations in coverage matrix and perhaps that's contributing to the slow execution times. I could reduce this number significantly by reducing the spatial resolution of the Cartesian Grid but I am reluctant to take this step at this time. The orientation of one of the cameras is fixed and not subject to optimization but, not knowing how else to deal with this camera, I just assigned the identical binary coverage matrix to each orientation so, for this camera, all orientations have the same identical coverage. Perhaps there's a more efficient way to handle this circumstance. As always, any suggestions or advice is greatly appreciated. Regards, Gene 72 Proc Optmodel; 73 options fullstimer; 74 /* Read CoverageMatrix data into index sets*/ 75 set <str> stations; 76 read data work.station_id into stations=[station]; NOTE: There were 8 observations read from the data set WORK.STATION_ID. 77 78 set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>}; 79 80 set <str> ORIENTATION_STRING=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /; 81 set ORIENTATIONS = setof {s in orientation_string} 82 <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>; 83 put orientations=; ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>} 84 85 86 87 set <str> Targets; 88 read data work.targets into TARGETS=[target]; NOTE: There were 195228 observations read from the data set WORK.TARGETS. 89 num Matrix {stations, ORIENTATION_string, TARGETS}; 90 read data work.RoO_Matrix into [station orientation_string target] 91 Matrix=k; NOTE: There were 12494592 observations read from the data set WORK.ROO_MATRIX. 92 93 /* Set Constants*/ 94 /* optimal number of cameras covering each target*/ 95 %Let k=3; 96 num k=&k; SYMBOLGEN: Macro variable K resolves to 3 97 98 /*Declare Variables*/ 99 var CHI {stations, ORIENTATIONS} binary; 100 var IsTriplyCovered {TARGETS} binary; 101 impvar XIT{target in TARGETS}=sum{station in stations, <a,e> in 102 orientations} matrix[station, a||'/'||e, target] *Chi[station,a,e]; 103 104 /* Declare Model*/ 105 max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t]; 106 107 /*Subject to Following Constraints*/ 108 con CHI_constraint {station in stations}: 109 sum{<a,e> in ORIENTATIONS}CHI[station,a,e] <=1; 110 111 con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t]; 112 113 set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a; 114 put AZIMUTHS=; AZIMUTHS={45,90,135,180,225,270,315,360} 115 set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45}; 116 put AZIMUTH_PAIRS=; AZIMUTH_PAIRS={<45,45>,<45,360>,<90,45>,<90,90>,<135,90>,<135,135>,<180,135>,<180,180>,<225,180>,<225,225>,<270,225>,<270,270>,<315, 270>,<315,315>,<360,315>,<360,360>} 117 118 con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}: 119 sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1; 120 /* expand; */ 121 122 /* Call Solver and Save Results:*/ 123 solve with milp/ heuristics=2 presolver=3 relobjgap=0.0; NOTE: Problem generation will use 2 threads. NOTE: The problem has 195292 variables (0 free, 0 fixed). NOTE: The problem uses 195228 implicit variables. NOTE: The problem has 195292 binary and 0 integer variables. NOTE: The problem has 195268 linear constraints (40 LE, 0 EQ, 195228 GE, 0 range). NOTE: The problem has 1142932 linear constraint coefficients. NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range). NOTE: The MILP presolver value AGGRESSIVE is applied. NOTE: The MILP presolver removed 192680 variables and 192689 constraints. NOTE: The MILP presolver removed 1107728 constraint coefficients. NOTE: The MILP presolver modified 801 constraint coefficients. NOTE: The presolved problem has 2612 variables, 2579 constraints, and 35204 constraint coefficients. NOTE: The MILP solver is called. NOTE: The parallel Branch and Cut algorithm is used. NOTE: The Branch and Cut algorithm is using up to 2 threads. Node Active Sols BestInteger BestBound Gap Time 0 1 3 23990.0000000 61138.0000000 60.76% 9 0 1 3 23990.0000000 39312.0000000 38.98% 9 0 1 3 23990.0000000 38127.7801515 37.08% 11 0 1 3 23990.0000000 37130.9544114 35.39% 11 0 1 3 23990.0000000 36692.3216045 34.62% 12 0 1 3 23990.0000000 36504.1395405 34.28% 12 0 1 3 23990.0000000 36420.4284890 34.13% 12 0 1 3 23990.0000000 36356.7490045 34.02% 13 0 1 3 23990.0000000 36274.3886694 33.87% 13 0 1 3 23990.0000000 36204.5574512 33.74% 13 0 1 3 23990.0000000 36137.2290216 33.61% 14 0 1 3 23990.0000000 36123.2972914 33.59% 14 0 1 3 23990.0000000 36119.0474640 33.58% 14 0 1 3 23990.0000000 36106.1955179 33.56% 15 0 1 3 23990.0000000 36097.8491496 33.54% 15 0 1 3 23990.0000000 36092.0621002 33.53% 15 0 1 3 23990.0000000 36084.1711840 33.52% 16 0 1 3 23990.0000000 36080.1799044 33.51% 16 NOTE: The MILP solver added 785 cuts with 4461 cut coefficients at the root. 1 2 3 23990.0000000 36080.1799044 33.51% 16 92 84 3 23990.0000000 35678.8140111 32.76% 20 202 189 3 23990.0000000 35438.1099578 32.30% 25 307 287 4 24330.0000000 35317.9985736 31.11% 27 347 325 5 24436.0000000 35299.0728640 30.77% 28 376 353 5 24436.0000000 35270.9243489 30.72% 30 498 465 5 24436.0000000 35179.5881591 30.54% 35 622 582 5 24436.0000000 35156.6853080 30.49% 40 747 1 5 24436.0000000 35019.6880171 30.22% 47 819 69 6 24522.0000000 35019.6880171 29.98% 50 820 70 6 24522.0000000 35019.6880171 29.98% 50 925 170 9 27481.0000000 35019.6880171 21.53% 53 935 175 9 27481.0000000 35019.6880171 21.53% 55 1035 272 9 27481.0000000 35019.6880171 21.53% 60 NOTE: The Decomposition algorithm is used. NOTE: The Decomposition algorithm time is 0.62 seconds. 1164 396 9 27481.0000000 34670.4366167 20.74% 65 1225 450 9 27481.0000000 34530.2041077 20.41% 70 1239 462 10 27492.0000000 34530.2041077 20.38% 71 1273 491 11 27500.0000000 34523.2661646 20.34% 73 1313 528 11 27500.0000000 34462.2905258 20.20% 75 1413 617 11 27500.0000000 34426.7564570 20.12% 80 1477 672 11 27500.0000000 34278.6085959 19.78% 85 1567 750 11 27500.0000000 34212.6188681 19.62% 90 1617 792 11 27500.0000000 34175.6139980 19.53% 95 1689 858 11 27500.0000000 34154.3283232 19.48% 100 1721 887 12 27503.0000000 34126.7849157 19.41% 100 1724 888 13 27505.0000000 34087.9161005 19.31% 100 1805 951 13 27505.0000000 33933.0291500 18.94% 105 1865 998 13 27505.0000000 33881.4232385 18.82% 110 1925 1041 13 27505.0000000 33781.8296720 18.58% 115 1927 1041 14 27512.0000000 33778.3581663 18.55% 115 1971 1074 14 27512.0000000 33718.8824519 18.41% 120 2010 1102 14 27512.0000000 33653.9319331 18.25% 125 2021 1107 16 27545.0000000 33640.0080999 18.12% 126 2045 1123 16 27545.0000000 33606.3341194 18.04% 130 2065 1139 16 27545.0000000 33598.7736264 18.02% 135 2115 1179 16 27545.0000000 33566.4744542 17.94% 140 2147 1201 16 27545.0000000 33539.2577104 17.87% 145 2185 1234 16 27545.0000000 33527.8809774 17.84% 150 2213 1256 16 27545.0000000 33526.0634607 17.84% 155 2249 1282 16 27545.0000000 33457.3006099 17.67% 160 2285 1313 16 27545.0000000 33439.9249790 17.63% 165 2313 1332 16 27545.0000000 33401.0503735 17.53% 170 2319 1336 17 27600.0000000 33401.0503735 17.37% 171 2339 1351 17 27600.0000000 33380.2229475 17.32% 175 2367 1374 17 27600.0000000 33363.9691902 17.28% 180 2407 1405 17 27600.0000000 33324.8202323 17.18% 185 2429 1418 19 28145.0000000 33318.7316262 15.53% 185 2485 1449 19 28145.0000000 33243.4193147 15.34% 190 2516 1474 19 28145.0000000 33196.4363181 15.22% 195 2542 1490 19 28145.0000000 33173.9295788 15.16% 200 2572 1512 19 28145.0000000 33133.1622965 15.05% 205 2592 1520 19 28145.0000000 33087.2599557 14.94% 210 2618 1530 19 28145.0000000 33071.5510832 14.90% 215 2644 1545 19 28145.0000000 33060.5562038 14.87% 220 2670 1555 19 28145.0000000 33039.1870347 14.81% 225 2696 1575 19 28145.0000000 33032.2339526 14.80% 230 2722 1590 19 28145.0000000 33009.4990069 14.74% 235 2754 1610 19 28145.0000000 32999.2147639 14.71% 240 2772 1619 19 28145.0000000 32976.4766045 14.65% 245 2800 1639 19 28145.0000000 32959.4912991 14.61% 250 2818 1651 19 28145.0000000 32953.4373825 14.59% 255 2853 1674 19 28145.0000000 32947.3818875 14.58% 260 2875 1688 19 28145.0000000 32923.8618842 14.51% 265 2899 1696 19 28145.0000000 32899.3141391 14.45% 270 2919 1706 19 28145.0000000 32884.9747879 14.41% 275 2955 1731 19 28145.0000000 32862.5233079 14.36% 280 2984 1748 19 28145.0000000 32850.7181194 14.32% 285 3002 1761 19 28145.0000000 32836.8147487 14.29% 290 3020 1773 19 28145.0000000 32830.1314539 14.27% 295 3038 1778 19 28145.0000000 32815.9085915 14.23% 300 3060 1787 19 28145.0000000 32803.9852529 14.20% 305 3082 1799 19 28145.0000000 32785.5530456 14.15% 310 3108 1805 19 28145.0000000 32775.0551394 14.13% 315 3128 1816 19 28145.0000000 32765.6154429 14.10% 321 3140 1824 19 28145.0000000 32761.5960041 14.09% 325 3158 1830 19 28145.0000000 32738.4632111 14.03% 330 3180 1839 19 28145.0000000 32732.8342482 14.02% 335 3204 1851 19 28145.0000000 32705.7970474 13.94% 340 3232 1871 19 28145.0000000 32701.0509802 13.93% 345 3254 1882 19 28145.0000000 32690.0503606 13.90% 351 3267 1890 19 28145.0000000 32681.5042359 13.88% 355 3278 1895 19 28145.0000000 32667.8083419 13.84% 360 3303 1909 19 28145.0000000 32649.3681718 13.80% 365 3328 1923 19 28145.0000000 32614.9356086 13.71% 370 3352 1942 19 28145.0000000 32603.6748745 13.68% 375 3366 1953 19 28145.0000000 32601.6454232 13.67% 380 3386 1965 19 28145.0000000 32588.7128671 13.64% 385 3404 1974 19 28145.0000000 32575.6484314 13.60% 390 3426 1989 19 28145.0000000 32559.0282642 13.56% 395 3456 2005 19 28145.0000000 32536.7570941 13.50% 400 3472 2010 19 28145.0000000 32518.5190450 13.45% 405 3482 2013 19 28145.0000000 32512.0159007 13.43% 410 3500 2015 19 28145.0000000 32496.3336152 13.39% 415 3514 2017 19 28145.0000000 32480.4839933 13.35% 420 3532 2027 19 28145.0000000 32472.6505570 13.33% 425 3556 2044 19 28145.0000000 32465.7637762 13.31% 430 3572 2050 19 28145.0000000 32452.1383332 13.27% 435 3590 2056 19 28145.0000000 32438.8583534 13.24% 440 3612 2064 19 28145.0000000 32423.7320268 13.20% 445 3634 2077 19 28145.0000000 32412.7257155 13.17% 450 3648 2079 19 28145.0000000 32397.2139959 13.13% 455 3666 2090 19 28145.0000000 32394.1087595 13.12% 460 3692 2106 19 28145.0000000 32379.5514841 13.08% 465 3714 2123 19 28145.0000000 32368.3843400 13.05% 470 3732 2134 19 28145.0000000 32360.8961825 13.03% 475 3748 2137 19 28145.0000000 32340.7239412 12.97% 480 3764 2140 19 28145.0000000 32322.3870217 12.92% 485 3780 2147 19 28145.0000000 32306.3843408 12.88% 490 3800 2158 19 28145.0000000 32297.2113310 12.86% 495 3814 2162 19 28145.0000000 32281.3650356 12.81% 500 3838 2176 19 28145.0000000 32268.0789013 12.78% 505 3858 2181 19 28145.0000000 32259.8463500 12.76% 510 3880 2189 19 28145.0000000 32246.1066227 12.72% 515 3933 2219 19 28145.0000000 32227.8712174 12.67% 520 3957 2232 19 28145.0000000 32203.3375031 12.60% 525 3979 2238 19 28145.0000000 32181.7559460 12.54% 530 3998 2247 19 28145.0000000 32179.5539104 12.54% 535 4023 2258 19 28145.0000000 32149.9523511 12.46% 540 4042 2268 19 28145.0000000 32130.5662909 12.40% 545 4060 2269 19 28145.0000000 32124.7942211 12.39% 550 4072 2274 19 28145.0000000 32120.7030966 12.38% 555 4105 2293 19 28145.0000000 32112.2829868 12.35% 560 4125 2308 19 28145.0000000 32110.6155792 12.35% 565 4147 2311 19 28145.0000000 32088.1118559 12.29% 570 4177 2331 19 28145.0000000 32076.9986355 12.26% 575 4191 2334 19 28145.0000000 32063.4811472 12.22% 580 4211 2345 19 28145.0000000 32058.8866707 12.21% 585 4231 2348 19 28145.0000000 32051.9882892 12.19% 590 4251 2358 19 28145.0000000 32039.9803663 12.16% 595 4269 2369 19 28145.0000000 32034.9120998 12.14% 600 4295 2378 19 28145.0000000 32025.5849887 12.12% 605 4313 2383 19 28145.0000000 32007.8426337 12.07% 610 4329 2386 19 28145.0000000 32002.2382890 12.05% 615 4357 2404 19 28145.0000000 31998.7399175 12.04% 620 4381 2419 19 28145.0000000 31993.9017360 12.03% 625 4401 2428 19 28145.0000000 31982.0422003 12.00% 630 4417 2436 19 28145.0000000 31973.1543287 11.97% 635 4433 2435 19 28145.0000000 31947.9594590 11.90% 640 4459 2447 19 28145.0000000 31941.5292928 11.89% 645 4471 2446 19 28145.0000000 31924.0400141 11.84% 650 4487 2450 19 28145.0000000 31909.7785442 11.80% 655 4501 2452 19 28145.0000000 31901.4570743 11.78% 660 4519 2459 19 28145.0000000 31896.3190557 11.76% 665 4537 2473 19 28145.0000000 31889.2412703 11.74% 670 4557 2478 19 28145.0000000 31875.3841858 11.70% 675 4587 2491 19 28145.0000000 31867.5328649 11.68% 680 4609 2503 19 28145.0000000 31858.5873042 11.66% 686 4625 2507 19 28145.0000000 31846.5353177 11.62% 690 4641 2517 19 28145.0000000 31840.2175761 11.61% 695 4655 2523 19 28145.0000000 31833.0667937 11.59% 700 4671 2527 19 28145.0000000 31813.5334048 11.53% 705 4687 2529 19 28145.0000000 31800.9663253 11.50% 710 4707 2528 19 28145.0000000 31785.4222655 11.45% 715 4729 2534 19 28145.0000000 31777.2361368 11.43% 721 4741 2541 19 28145.0000000 31774.0803443 11.42% 725 4755 2544 19 28145.0000000 31764.7166133 11.40% 730 4818 2573 19 28145.0000000 31756.7200489 11.37% 735 4831 2579 19 28145.0000000 31744.7172772 11.34% 740 4845 2585 19 28145.0000000 31740.4014254 11.33% 745 4869 2594 19 28145.0000000 31710.5611454 11.24% 750 4887 2599 19 28145.0000000 31698.0618319 11.21% 755 4903 2600 19 28145.0000000 31687.0204269 11.18% 760 4925 2604 19 28145.0000000 31669.7820869 11.13% 765 4939 2606 19 28145.0000000 31648.9375050 11.07% 770 4963 2610 19 28145.0000000 31631.7046279 11.02% 775 4981 2613 19 28145.0000000 31626.4375050 11.01% 780 4995 2614 19 28145.0000000 31617.4274150 10.98% 785 5011 2610 19 28145.0000000 31595.3750000 10.92% 790 5027 2607 19 28145.0000000 31583.1386032 10.89% 795 5049 2615 19 28145.0000000 31572.9536734 10.86% 800 5071 2621 19 28145.0000000 31563.1484250 10.83% 805 5091 2628 19 28145.0000000 31550.6579946 10.79% 810 5119 2637 19 28145.0000000 31528.4255216 10.73% 815 5141 2644 19 28145.0000000 31524.8163774 10.72% 820 5157 2648 19 28145.0000000 31515.8808935 10.70% 825 5177 2653 19 28145.0000000 31510.0701357 10.68% 830 5205 2656 19 28145.0000000 31495.2335537 10.64% 835 5229 2666 19 28145.0000000 31482.1550632 10.60% 840 5259 2675 19 28145.0000000 31474.1611535 10.58% 845 5285 2674 19 28145.0000000 31459.9711935 10.54% 850 5307 2678 19 28145.0000000 31450.6973137 10.51% 855 5331 2684 19 28145.0000000 31439.3899540 10.48% 860 5355 2692 19 28145.0000000 31427.8724723 10.45% 866 5369 2692 19 28145.0000000 31420.2296025 10.42% 870 5397 2712 19 28145.0000000 31417.5723207 10.42% 875 5419 2717 19 28145.0000000 31409.3234172 10.39% 880 5439 2721 19 28145.0000000 31401.0348559 10.37% 885 5469 2713 19 28145.0000000 31374.1174316 10.29% 890 5493 2720 19 28145.0000000 31369.8282021 10.28% 895 5521 2729 19 28145.0000000 31366.3042864 10.27% 900 5543 2734 19 28145.0000000 31360.8535707 10.25% 905 5567 2733 19 28145.0000000 31345.2435070 10.21% 910 5585 2738 19 28145.0000000 31339.6080647 10.19% 915 5601 2738 19 28145.0000000 31333.8557987 10.18% 920 5615 2734 19 28145.0000000 31316.3540995 10.13% 925 5643 2745 19 28145.0000000 31296.4060410 10.07% 930 5663 2748 19 28145.0000000 31282.7523445 10.03% 935 5683 2748 19 28145.0000000 31271.1466449 10.00% 940 5727 2760 19 28145.0000000 31261.7283824 9.97% 945 5743 2765 19 28145.0000000 31254.2031728 9.95% 950 5769 2779 19 28145.0000000 31250.9519986 9.94% 955 5793 2780 19 28145.0000000 31232.5456679 9.89% 960 5815 2786 19 28145.0000000 31218.5723207 9.85% 965 5835 2784 19 28145.0000000 31212.7482320 9.83% 970 5867 2788 19 28145.0000000 31206.3806783 9.81% 975 5887 2791 19 28145.0000000 31194.4738148 9.78% 980 5905 2791 19 28145.0000000 31183.9955597 9.75% 985 5929 2792 19 28145.0000000 31173.7205192 9.72% 990 NOTE: The Decomposition algorithm is used. NOTE: The Decomposition algorithm time is 6.09 seconds. 5953 2796 19 28145.0000000 31170.3316371 9.71% 999 5954 2795 19 28145.0000000 31169.7528128 9.70% 1000 5973 2801 19 28145.0000000 31165.5756606 9.69% 1005 5993 2801 19 28145.0000000 31149.6939055 9.65% 1010 6009 2798 19 28145.0000000 31125.0996331 9.57% 1015 6031 2807 19 28145.0000000 31120.1368457 9.56% 1020 6053 2803 19 28145.0000000 31097.6382701 9.49% 1025 6075 2803 19 28145.0000000 31089.3954510 9.47% 1030 6103 2813 19 28145.0000000 31073.3288318 9.42% 1035 6129 2813 19 28145.0000000 31062.6350535 9.39% 1040 6153 2813 19 28145.0000000 31051.4001714 9.36% 1045 6187 2819 19 28145.0000000 31030.5413157 9.30% 1050 6209 2820 19 28145.0000000 31022.0072006 9.27% 1055 6241 2821 19 28145.0000000 31013.1995014 9.25% 1060 6257 2816 19 28145.0000000 31004.0686966 9.22% 1065 6291 2813 19 28145.0000000 30992.0996625 9.19% 1070 6310 2812 19 28145.0000000 30982.7909518 9.16% 1075 6341 2817 19 28145.0000000 30971.2494443 9.13% 1080 6365 2815 19 28145.0000000 30963.3444906 9.10% 1085 6383 2814 19 28145.0000000 30948.3672403 9.06% 1090 6407 2812 19 28145.0000000 30933.5900291 9.01% 1095 6435 2811 19 28145.0000000 30927.3063259 9.00% 1100 6457 2809 19 28145.0000000 30922.9934999 8.98% 1105 6488 2818 19 28145.0000000 30910.3972088 8.95% 1110 6510 2821 19 28145.0000000 30902.7438110 8.92% 1115 6527 2828 19 28145.0000000 30895.1233758 8.90% 1120 6547 2820 19 28145.0000000 30877.3744724 8.85% 1125 6573 2815 19 28145.0000000 30866.2296492 8.82% 1130 6593 2820 19 28145.0000000 30862.9113600 8.81% 1135 6621 2821 19 28145.0000000 30851.2137073 8.77% 1140 6637 2827 19 28145.0000000 30845.4350289 8.75% 1145 6659 2826 19 28145.0000000 30837.1310751 8.73% 1150 6673 2820 19 28145.0000000 30828.8800131 8.71% 1155 6691 2821 19 28145.0000000 30823.5307127 8.69% 1160 6711 2821 19 28145.0000000 30816.0734714 8.67% 1165 6733 2823 19 28145.0000000 30810.9673803 8.65% 1170 6759 2824 19 28145.0000000 30795.1803082 8.61% 1175 6783 2827 19 28145.0000000 30789.4754835 8.59% 1180 6815 2831 19 28145.0000000 30782.2124135 8.57% 1185 6837 2831 19 28145.0000000 30769.2381512 8.53% 1190 6861 2825 19 28145.0000000 30757.8096518 8.49% 1195 6889 2833 19 28145.0000000 30751.0472308 8.47% 1200 6919 2836 19 28145.0000000 30743.0137074 8.45% 1205 6939 2840 19 28145.0000000 30736.4381031 8.43% 1210 6965 2840 19 28145.0000000 30724.4140683 8.40% 1215 6983 2841 19 28145.0000000 30713.8457391 8.36% 1220 6997 2841 19 28145.0000000 30706.5867576 8.34% 1225 7023 2845 19 28145.0000000 30700.9131748 8.33% 1230 7049 2848 19 28145.0000000 30690.0879063 8.29% 1235 7075 2845 19 28145.0000000 30678.6715129 8.26% 1240 7101 2848 19 28145.0000000 30671.4591833 8.24% 1245 7131 2852 19 28145.0000000 30658.0418917 8.20% 1250 7153 2851 19 28145.0000000 30644.3265284 8.16% 1255 7179 2846 19 28145.0000000 30641.6251800 8.15% 1260 7197 2844 19 28145.0000000 30633.7700090 8.12% 1265 7221 2852 19 28145.0000000 30629.3380952 8.11% 1270 7265 2876 19 28145.0000000 30623.9881300 8.09% 1275 7285 2875 19 28145.0000000 30619.6653154 8.08% 1280 7307 2880 19 28145.0000000 30616.2939849 8.07% 1285 7325 2887 19 28145.0000000 30613.9028541 8.06% 1290 7391 2925 19 28145.0000000 30610.4819598 8.05% 1295 7411 2921 19 28145.0000000 30592.9903558 8.00% 1300 7429 2926 19 28145.0000000 30586.9428382 7.98% 1305 7449 2933 19 28145.0000000 30574.0227956 7.94% 1310 7471 2927 19 28145.0000000 30544.3898634 7.86% 1315 7494 2927 19 28145.0000000 30529.9787359 7.81% 1320 7518 2933 19 28145.0000000 30515.9473231 7.77% 1325 7548 2938 19 28145.0000000 30498.5796667 7.72% 1330 7583 2941 19 28145.0000000 30490.4009674 7.69% 1335 7609 2951 19 28145.0000000 30490.4009674 7.69% 1340 7649 2968 19 28145.0000000 30474.0243917 7.64% 1345 7667 2975 19 28145.0000000 30471.5436773 7.64% 1350 7689 2971 19 28145.0000000 30456.5423792 7.59% 1355 7717 2979 19 28145.0000000 30444.7566734 7.55% 1360 7747 2982 19 28145.0000000 30438.1062217 7.53% 1365 7763 2988 19 28145.0000000 30435.0773975 7.52% 1370 7787 2997 19 28145.0000000 30427.7082011 7.50% 1375 7817 3010 19 28145.0000000 30417.7673294 7.47% 1380 7843 3005 19 28145.0000000 30398.4820087 7.41% 1385 7867 3008 19 28145.0000000 30393.6528609 7.40% 1390 7885 3010 19 28145.0000000 30387.3341274 7.38% 1395 7909 3010 19 28145.0000000 30373.6975789 7.34% 1400 7929 3006 19 28145.0000000 30360.6256586 7.30% 1405 7954 2962 21 28377.0000000 30354.0070556 6.51% 1409 7979 2984 21 28377.0000000 30354.0048894 6.51% 1410 8005 2993 21 28377.0000000 30354.0048894 6.51% 1415 8031 2994 21 28377.0000000 30344.6311479 6.48% 1420 8069 3006 21 28377.0000000 30334.5430882 6.45% 1425 8089 3008 21 28377.0000000 30327.1260732 6.43% 1430 8115 3014 21 28377.0000000 30321.7074915 6.41% 1435 8135 3018 21 28377.0000000 30315.3680228 6.39% 1440 8161 3026 21 28377.0000000 30306.0815194 6.37% 1445 8185 3030 21 28377.0000000 30298.4067304 6.34% 1450 8215 3031 21 28377.0000000 30295.2604353 6.33% 1455 8241 3039 21 28377.0000000 30290.3159929 6.32% 1460 8269 3035 21 28377.0000000 30281.5839945 6.29% 1465 8301 3047 21 28377.0000000 30276.1252141 6.27% 1470 8335 3050 21 28377.0000000 30267.5917394 6.25% 1475 8353 3046 21 28377.0000000 30262.3587807 6.23% 1480 8375 3053 21 28377.0000000 30252.3875103 6.20% 1485 8411 3060 21 28377.0000000 30248.2755068 6.19% 1490 8465 3087 21 28377.0000000 30241.8392217 6.17% 1495 8507 3063 22 28377.0000000 30237.0630746 6.15% 1499 8533 3072 22 28377.0000000 30237.0630746 6.15% 1500 8555 3070 22 28377.0000000 30228.0285478 6.12% 1505 8573 3068 22 28377.0000000 30222.8339858 6.11% 1511 8593 3066 22 28377.0000000 30219.2588475 6.10% 1515 8619 3067 22 28377.0000000 30212.9012674 6.08% 1520 8643 3072 22 28377.0000000 30206.1541457 6.06% 1525 8661 3074 22 28377.0000000 30198.9176233 6.03% 1530 8701 3084 22 28377.0000000 30192.2384526 6.01% 1535 8727 3084 22 28377.0000000 30182.3342528 5.98% 1540 8755 3086 22 28377.0000000 30178.5561763 5.97% 1545 8787 3092 22 28377.0000000 30165.8875703 5.93% 1550 8809 3098 22 28377.0000000 30160.9893292 5.91% 1555 8825 3094 22 28377.0000000 30157.0704569 5.90% 1560 8861 3103 22 28377.0000000 30150.9040886 5.88% 1565 8927 3105 22 28377.0000000 30146.6909783 5.87% 1570 8948 3100 22 28377.0000000 30134.1816519 5.83% 1575 8972 3102 22 28377.0000000 30118.2164179 5.78% 1580 9000 3101 22 28377.0000000 30106.8965556 5.75% 1585 9028 3097 22 28377.0000000 30089.0535130 5.69% 1590 9050 3098 22 28377.0000000 30082.6140395 5.67% 1595 9076 3100 22 28377.0000000 30070.8339712 5.63% 1600 9110 3118 22 28377.0000000 30068.4625286 5.63% 1605 9136 3128 22 28377.0000000 30064.0152266 5.61% 1610 9166 3130 22 28377.0000000 30057.3074080 5.59% 1615 9190 3125 22 28377.0000000 30046.7148288 5.56% 1620 9220 3127 22 28377.0000000 30038.5209226 5.53% 1625 9244 3124 22 28377.0000000 30033.4427230 5.52% 1630 9264 3123 22 28377.0000000 30026.0430501 5.49% 1635 9286 3122 22 28377.0000000 30015.2208645 5.46% 1640 9310 3118 22 28377.0000000 30008.9018831 5.44% 1645 9356 3113 22 28377.0000000 30000.1439529 5.41% 1650 9386 3115 22 28377.0000000 29997.6628639 5.40% 1655 9412 3107 22 28377.0000000 29987.0964768 5.37% 1660 9466 3111 22 28377.0000000 29979.5803133 5.35% 1665 9502 3123 22 28377.0000000 29972.5427242 5.32% 1670 9544 3133 22 28377.0000000 29966.6017454 5.30% 1675 9572 3130 22 28377.0000000 29961.0120966 5.29% 1680 9626 3148 22 28377.0000000 29955.5175493 5.27% 1685 9656 3147 22 28377.0000000 29947.9108073 5.25% 1690 9684 3152 22 28377.0000000 29941.9013568 5.23% 1695 9720 3153 22 28377.0000000 29929.9327485 5.19% 1700 9754 3155 22 28377.0000000 29924.9978685 5.17% 1705 9780 3156 22 28377.0000000 29921.6843875 5.16% 1710 9808 3148 22 28377.0000000 29916.0586815 5.14% 1715 9830 3143 22 28377.0000000 29911.3219311 5.13% 1720 9860 3156 22 28377.0000000 29903.9830746 5.11% 1725 9884 3161 22 28377.0000000 29895.8908007 5.08% 1730 9944 3165 22 28377.0000000 29889.9725082 5.06% 1735 9972 3166 22 28377.0000000 29887.6555877 5.05% 1740 10012 3168 22 28377.0000000 29876.4164270 5.02% 1745 10036 3169 22 28377.0000000 29872.4218797 5.01% 1750 10102 3190 22 28377.0000000 29864.2968824 4.98% 1755 10160 3193 22 28377.0000000 29855.3481535 4.95% 1760 10202 3206 22 28377.0000000 29847.4413500 4.93% 1765 10270 3223 22 28377.0000000 29841.8555273 4.91% 1770 10322 3228 22 28377.0000000 29835.2716594 4.89% 1775 10358 3227 22 28377.0000000 29826.6479638 4.86% 1780 10408 3237 22 28377.0000000 29824.2035052 4.85% 1785 10534 3292 22 28377.0000000 29821.2997955 4.84% 1790 10594 3307 22 28377.0000000 29816.7022484 4.83% 1795 10632 3316 22 28377.0000000 29812.2366374 4.81% 1800 10660 3314 22 28377.0000000 29808.3335252 4.80% 1805 10678 3083 23 28728.0000000 29804.1681777 3.61% 1806 10728 3088 23 28728.0000000 29801.8040584 3.60% 1810 10760 3093 23 28728.0000000 29791.3621770 3.57% 1815 10810 3100 23 28728.0000000 29783.8158023 3.54% 1820 11060 2815 24 28728.0000000 29782.5918807 3.54% 1821 11253 2836 24 28728.0000000 29780.2506612 3.53% 1825 11322 2860 24 28728.0000000 29770.0602937 3.50% 1830 11356 2840 24 28728.0000000 29755.9749698 3.45% 1835 11378 2823 24 28728.0000000 29745.7540372 3.42% 1840 11424 2814 24 28728.0000000 29734.4411717 3.38% 1845 11468 2793 24 28728.0000000 29720.1231793 3.34% 1850 11526 2772 24 28728.0000000 29708.6215872 3.30% 1855 11562 2765 24 28728.0000000 29698.5250530 3.27% 1860 11618 2762 24 28728.0000000 29695.8530980 3.26% 1865 11680 2749 24 28728.0000000 29683.3684252 3.22% 1870 11740 2722 24 28728.0000000 29667.5425233 3.17% 1875 11780 2710 24 28728.0000000 29660.1468980 3.14% 1880 11836 2687 24 28728.0000000 29650.1926995 3.11% 1885 11884 2674 24 28728.0000000 29641.0000000 3.08% 1890 11932 2676 24 28728.0000000 29638.8348444 3.07% 1895 11986 2679 24 28728.0000000 29628.6606867 3.04% 1900 12050 2672 24 28728.0000000 29621.0000000 3.01% 1905 12088 2653 24 28728.0000000 29614.8340334 2.99% 1910 12136 2645 24 28728.0000000 29609.6975673 2.98% 1915 12200 2629 24 28728.0000000 29603.6667680 2.96% 1920 12258 2612 24 28728.0000000 29588.2417380 2.91% 1925 12298 2592 24 28728.0000000 29579.6011871 2.88% 1930 12350 2576 24 28728.0000000 29573.1199063 2.86% 1935 12408 2562 24 28728.0000000 29564.9908825 2.83% 1940 12500 2539 24 28728.0000000 29551.3895132 2.79% 1945 12544 2520 24 28728.0000000 29544.6055162 2.76% 1950 12600 2520 24 28728.0000000 29535.9013071 2.74% 1955 12664 2497 24 28728.0000000 29525.5990874 2.70% 1960 12724 2477 24 28728.0000000 29515.8503938 2.67% 1965 12774 2457 24 28728.0000000 29508.5738790 2.65% 1970 12824 2434 24 28728.0000000 29498.9581843 2.61% 1975 12997 2389 24 28728.0000000 29491.3229849 2.59% 1980 13064 2378 24 28728.0000000 29476.5402670 2.54% 1985 13135 2340 24 28728.0000000 29453.9988265 2.46% 1990 13177 2334 24 28728.0000000 29444.9581843 2.43% 1995 13237 2319 24 28728.0000000 29433.0000000 2.40% 2000 13285 2292 24 28728.0000000 29425.8976274 2.37% 2005 13341 2265 24 28728.0000000 29418.6191033 2.35% 2010 13391 2239 24 28728.0000000 29411.1673530 2.32% 2015 13507 2202 24 28728.0000000 29396.0754166 2.27% 2020 13567 2169 24 28728.0000000 29387.4877863 2.24% 2025 13631 2140 24 28728.0000000 29372.7131396 2.19% 2030 13709 2098 24 28728.0000000 29360.6669667 2.15% 2035 13807 2090 24 28728.0000000 29354.8755350 2.14% 2040 13869 2054 24 28728.0000000 29341.9604089 2.09% 2045 13937 2018 24 28728.0000000 29332.7765611 2.06% 2050 14013 1982 24 28728.0000000 29326.9321555 2.04% 2055 14103 1952 24 28728.0000000 29313.9473661 2.00% 2060 14165 1918 24 28728.0000000 29304.1666667 1.97% 2065 14245 1890 24 28728.0000000 29297.8756550 1.95% 2070 14305 1856 24 28728.0000000 29291.6165807 1.92% 2075 14377 1813 24 28728.0000000 29281.8447016 1.89% 2080 14441 1788 24 28728.0000000 29274.0210311 1.87% 2085 14521 1753 24 28728.0000000 29261.5465573 1.82% 2090 14655 1748 24 28728.0000000 29252.4308612 1.79% 2095 14737 1728 24 28728.0000000 29244.2792751 1.77% 2100 14807 1695 24 28728.0000000 29227.0326098 1.71% 2105 14889 1661 24 28728.0000000 29217.6737864 1.68% 2110 14967 1636 24 28728.0000000 29205.9933558 1.64% 2115 15041 1596 24 28728.0000000 29198.8633827 1.61% 2120 15174 1539 24 28728.0000000 29178.4475547 1.54% 2125 15256 1503 24 28728.0000000 29154.9924003 1.46% 2130 15338 1459 24 28728.0000000 29138.1806198 1.41% 2135 15422 1415 24 28728.0000000 29123.1117547 1.36% 2140 15514 1368 24 28728.0000000 29110.3114186 1.31% 2145 15606 1310 24 28728.0000000 29095.1257734 1.26% 2150 15720 1241 24 28728.0000000 29080.2155601 1.21% 2155 15854 1164 24 28728.0000000 29060.5870472 1.14% 2160 15972 1101 24 28728.0000000 29046.0726458 1.10% 2165 16090 1029 24 28728.0000000 29028.2805098 1.03% 2170 16256 981 24 28728.0000000 29004.6670039 0.95% 2175 16456 872 24 28728.0000000 28977.3254756 0.86% 2180 16622 757 24 28728.0000000 28949.2922417 0.76% 2185 17151 393 24 28728.0000000 28883.4169817 0.54% 2190 17558 107 24 28728.0000000 28763.4150965 0.12% 2195 17725 0 24 28728.0000000 28728.0000000 0.00% 2196 NOTE: Optimal. NOTE: Objective = 28728. 124 create data work.OptimalSolution_&RoO from SYMBOLGEN: Macro variable ROO resolves to 2000 125 [station a e]={c in stations, <a,e> in orientations: CHI[c,a,e]>0.5} CHI; NOTE: The data set WORK.OPTIMALSOLUTION_2000 has 8 observations and 4 variables. 126 quit; NOTE: PROCEDURE OPTMODEL used (Total process time): real time 37:19.12 user cpu time 1:12:08.86 system cpu time 7.98 seconds memory 2530752.29k OS Memory 2587444.00k Timestamp 12/13/2021 03:58:51 PM Step Count 150 Switch Count 5417 Page Faults 9 Page Reclaims 927759 Page Swaps 0 Voluntary Context Switches 2067173 Involuntary Context Switches 17601 Block Input Operations 20304 Block Output Operations 912

genemroz · ‎12-03-2021

Thanks so much! Exactly what I needed. Regards, Gene

genemroz · ‎12-02-2021

Thanks for the tips and suggestions. I implemented them in the code below but the result is unchanged--or nearly so, as some of the exdtraneous lines have disappeared but most remain. Thanks again, Gene data usmx_map_in; length map_id $6.; set mapsgfk.us_states (where=((statecode in('CA' 'AZ' 'NV' 'UT' 'NM' 'CO' 'TX')and density<=3))) mapsgfk.mexico (where=((id1 in('MX-02' 'MX-03' 'MX-08' 'MX-26' 'MX-05') and density <=3))); map_id=coalescec(statecode,id1); run; proc gproject data=usmx_map_in out=usmx_map_out latlong eastlong degrees dupok; id map_id; run; proc gmap map=usmx_map_out data=usmx_map_out; id map_id; pattern1 value=empty; choro segment / levels=1 nolegend coutline=gray88; run; quit;

genemroz · ‎12-02-2021

I'm preparing a map that includes the states in the southwestern US and the northern states of Mexico. The output map of the Mexican states are rendered with many extraneous lines. How can this be fixed? My source code and resultant output image is below: data usmx_map; set mapsgfk.us_states (where=((statecode='CA' or statecode='AZ' or statecode='NV' or statecode='UT' or statecode='NM' or statecode='CO' or statecode='TX')and density<=3)) mapsgfk.mexico (where=((id1='MX-02' or id1='MX-03' or id1='MX-08' or id1='MX-26' or id1='MX-05') and density <=3)); run; proc gproject data=usmx_map out=usmx_map latlong eastlong degrees dupok; id statecode; run; proc gmap map=usmx_map data=usmx_map; id statecode; pattern1 value=empty; choro segment / levels=1 nolegend coutline=gray88; run; quit; Thanks for any advice, Gene

genemroz · ‎11-23-2021

Rob: Thanks for walking me through this solution. I'll mark your last response as SOLVED as that response took care of the last problem in the code. Thanks so much for your patient assistance. This was a big help to my project. Regards, Gene

genemroz · ‎11-23-2021

Rob, I made your recommended changes but Proc Optmodel is still unhappy with how the implicit variable XIT is being defined. The log file output is below: Thanks for helping me with this.... Gene My Libraries 1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK; SYMBOLGEN: Macro variable _SASWSTEMP_ resolves to /home/u44673568/.sasstudio/.images/50c783a8-040f-4709-854f-70155036260a SYMBOLGEN: Some characters in the above value which were subject to macro quoting have been unquoted for printing. SYMBOLGEN: Macro variable GRAPHINIT resolves to GOPTIONS RESET=ALL GSFNAME=_GSFNAME; NOTE: ODS statements in the SAS Studio environment may disable some output features. 69 70 Proc Optmodel; 71 /* Read CoverageMatrix data into index sets*/ 72 set <str> stations; 73 read data work.station_id into stations=[station]; NOTE: There were 15 observations read from the data set WORK.STATION_ID. 74 75 set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>}; 76 77 set <str> ORIENTATION_STRING=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /; 78 set ORIENTATIONS = setof {s in orientation_string} 79 <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>; 80 put orientations=; ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>} 81 82 83 84 set <str> Targets; 85 read data work.targets into TARGETS=[target]; NOTE: There were 136206 observations read from the data set WORK.TARGETS. 86 num Matrix {stations, ORIENTATION_string, TARGETS}; 87 read data work.RoO_Matrix into [station orientation_string target] 88 Matrix=k; NOTE: There were 16344720 observations read from the data set WORK.ROO_MATRIX. 89 90 /* Set Constants*/ 91 /* optimal number of cameras covering each target*/ 92 %Let k=3; 93 num k=&k; SYMBOLGEN: Macro variable K resolves to 3 94 95 /*Declare Variables*/ 96 var CHI {stations, ORIENTATIONS} binary; 97 var IsTriplyCovered {TARGETS} binary; 98 impvar XIT{target in TARGETS}=sum{station in stations, <a,e> in 99 orientations} matrix[station, orientation_string, target] *Chi[station,a,e]; _ 620 ERROR 620-782: Subscript 2 may not be a set. 100 101 /* Declare Model*/ 102 max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t]; 103 104 /*Subject to Following Constraints*/ 105 con CHI_constraint {station in stations}: 106 sum{<a,e> in ORIENTATIONS}CHI[station,a,e] <=1; 107 108 con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t]; 109 110 set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a; 111 put AZIMUTHS=; AZIMUTHS={45,90,135,180,225,270,315,360} 112 set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45}; 113 put AZIMUTH_PAIRS=; AZIMUTH_PAIRS={<45,45>,<45,360>,<90,45>,<90,90>,<135,90>,<135,135>,<180,135>,<180,180>,<225,180>,<225,225>,<270,225>,<270,270>,<315, 270>,<315,315>,<360,315>,<360,360>} 114 115 con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}: 116 sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1; 117 expand; NOTE: Problem generation will use 2 threads. NOTE: Previous errors might cause the problem to be resolved incorrectly. ERROR: The implicit variable 'XIT' has an incomplete declaration. NOTE: The problem has 136326 variables (0 free, 0 fixed). NOTE: The problem uses 136206 implicit variables. NOTE: The problem has 136326 binary and 0 integer variables. NOTE: The problem has 47 linear constraints (47 LE, 0 EQ, 0 GE, 0 range). NOTE: The problem has 216 linear constraint coefficients. NOTE: The problem has 136206 nonlinear constraints (0 LE, 0 EQ, 136206 GE, 0 range). NOTE: Unable to create problem instance due to previous errors. 118 119 /* Call Solver and Save Results:*/ 120 solve with milp/ relobjgap=0; NOTE: Unable to create problem instance due to previous errors. 121 create data work.OptimalSolution_&RoO from SYMBOLGEN: Macro variable ROO resolves to 2000 122 [station a e]={c in stations, <a,e> in orientations: CHI[c,a,e]>0.5} CHI; NOTE: The data set WORK.OPTIMALSOLUTION_2000 has 0 observations and 4 variables. 123 quit; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE OPTMODEL used (Total process time): real time 36.32 seconds user cpu time 34.40 seconds system cpu time 2.30 seconds memory 2651482.51k OS Memory 2733480.00k Timestamp 11/23/2021 07:23:07 PM Step Count 283 Switch Count 52 Page Faults 0 Page Reclaims 738951 Page Swaps 0 Voluntary Context Switches 2892 Involuntary Context Switches 67 Block Input Operations 0 Block Output Operations 296

genemroz · ‎11-23-2021

Rob, Thanks for this suggestion. When I tried to implement it, I got errors starting with the declaration of the implicit variable XIT. I'm not clear on what's wrong here nor how to fix it The log output is shown below. I would be very grateful if you can take a look at this and help me get it sorted out. Thanks again for taking the time to help me with this, Gene 1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK; SYMBOLGEN: Macro variable _SASWSTEMP_ resolves to /home/u44673568/.sasstudio/.images/33c33bd7-7cdb-43d5-80e2-09efc7a773a1 SYMBOLGEN: Some characters in the above value which were subject to macro quoting have been unquoted for printing. SYMBOLGEN: Macro variable GRAPHINIT resolves to GOPTIONS RESET=ALL GSFNAME=_GSFNAME; NOTE: ODS statements in the SAS Studio environment may disable some output features. 69 70 Proc Optmodel; 71 /* Read CoverageMatrix data into index sets*/ 72 set <str> stations; 73 read data work.station_id into stations=[station]; NOTE: There were 15 observations read from the data set WORK.STATION_ID. 74 75 set <str> ORIENTATION_STRING=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /; 76 set ORIENTATIONS = setof {s in orientation_string} 77 <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>; 78 put orientations=; ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>} 79 80 81 set <str> Targets; 82 read data work.targets into TARGETS=[target]; NOTE: There were 136206 observations read from the data set WORK.TARGETS. 83 num Matrix {stations, ORIENTATION_string, TARGETS}; 84 read data work.RoO_Matrix into [station orientation_string target] 85 Matrix=k; NOTE: There were 16344720 observations read from the data set WORK.ROO_MATRIX. 86 87 /* Set Constants*/ 88 /* optimal number of cameras covering each target*/ 89 %Let k=3; 90 num k=&k; SYMBOLGEN: Macro variable K resolves to 3 91 /*Declare Variables*/ 92 var CHI {stations, ORIENTATIONS} binary; 93 var IsTriplyCovered {TARGETS} binary; 94 impvar XIT{target in TARGETS}=sum{station in stations, orientation in 95 orientations} matrix[station, orientation_string, target] *Chi[station, _ _ 516 620 96 orientation]; _ 619 ERROR 516-782: The indexing does not match the set element length, 1 NE 2. ERROR 620-782: Subscript 2 may not be a set. ERROR 619-782: The subscript count does not match array 'CHI', 2 NE 3. 97 98 /* Declare Model*/ 99 max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t]; 100 101 /*Subject to Following Constraints*/ 102 con CHI_constraint {station in stations}: 103 sum{orientation in ORIENTATIONS}CHI[station, orientation] <=1; _ _ 516 619 ERROR 516-782: The indexing does not match the set element length, 1 NE 2. ERROR 619-782: The subscript count does not match array 'CHI', 2 NE 3. 104 con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t]; 105 106 /*Rob Pratt's Code for "Conlfict Constraint"*/ 107 set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>}; 108 /* con NotSameOrientation {<s1,s2> in Station_Pairs, o in ORIENTATIONS}: */ 109 /* CHI[s1,o] + CHI[s2,o]<=1; */ 110 111 set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a; 112 put AZIMUTHS=; AZIMUTHS={45,90,135,180,225,270,315,360} 113 set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45}; 114 put AZIMUTH_PAIRS=; AZIMUTH_PAIRS={<45,45>,<45,360>,<90,45>,<90,90>,<135,90>,<135,135>,<180,135>,<180,180>,<225,180>,<225,225>,<270,225>,<270,270>,<315, 270>,<315,315>,<360,315>,<360,360>} 115 con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}: 116 sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1; 117 expand; NOTE: Problem generation will use 2 threads. NOTE: Previous errors might cause the problem to be resolved incorrectly. ERROR: The constraint 'CHI_constraint' has an incomplete declaration. ERROR: The implicit variable 'XIT' has an incomplete declaration. NOTE: The problem has 136326 variables (0 free, 0 fixed). NOTE: The problem uses 136206 implicit variables. NOTE: The problem has 136326 binary and 0 integer variables. NOTE: The problem has 32 linear constraints (32 LE, 0 EQ, 0 GE, 0 range). NOTE: The problem has 96 linear constraint coefficients. NOTE: The problem has 136206 nonlinear constraints (0 LE, 0 EQ, 136206 GE, 0 range). NOTE: Unable to create problem instance due to previous errors. 118 119 /* Call Solver and Save Results:*/ 120 solve with milp/ relobjgap=0; NOTE: Unable to create problem instance due to previous errors. 121 create data work.OptimalSolution_&RoO from SYMBOLGEN: Macro variable ROO resolves to 2000 122 [station orientation]={c in stations, o in orientations: CHI[c, o]>0.5} CHI; _ _ ___ 516 619 681 583 ERROR 516-782: The indexing does not match the set element length, 1 NE 2. ERROR 619-782: The subscript count does not match array 'CHI', 2 NE 3. ERROR 681-782: The implied subscript count does not match the index set, 2 NE 3. ERROR 583-782: The implied subscript count does not match array 'CHI', 2 NE 3. 123 quit; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE OPTMODEL used (Total process time): real time 38.42 seconds user cpu time 36.63 seconds system cpu time 2.21 seconds memory 2651460.17k OS Memory 2733476.00k Timestamp 11/23/2021 05:57:18 PM Step Count 79 Switch Count 52 Page Faults 0 Page Reclaims 752659 Page Swaps 0 Voluntary Context Switches 4231 Involuntary Context Switches 114 Block Input Operations 0 Block Output Operations 40 124 /*Print Results*/ 125 125 ! proc print data=work.optimalsolution_&RoO; SYMBOLGEN: Macro variable ROO resolves to 2000 ERROR: File WORK.OPTIMALSOLUTION_2000.DATA does not exist. 126 SYMBOLGEN: Macro variable ROO resolves to 2000 SYMBOLGEN: Macro variable ROO resolves to 2000 126 ! Title "Optimal Solution RoO=&RoO x &RoO km"; 127 run; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE PRINT used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 218.12k OS Memory 28832.00k Timestamp 11/23/2021 05:57:18 PM Step Count 80 Switch Count 1 Page Faults 0 Page Reclaims 17 Page Swaps 0 Voluntary Context Switches 10 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 0 128 /* Create Macro Variables for Station and Optimal Solution*/ 129 129 ! data macrovariables; 130 SYMBOLGEN: Macro variable ROO resolves to 2000 130 ! set optimalsolution_&RoO; ERROR: File WORK.OPTIMALSOLUTION_2000.DATA does not exist. 131 suffix=put(_n_,5.); 132 call symput (cats('Sta_Code',suffix),Station); 133 call symput (cats('Opt_Orientation',suffix),Orientation); 134 run; NOTE: Numeric values have been converted to character values at the places given by: (Line):(Column). 132:43 133:50 NOTE: The SAS System stopped processing this step because of errors. WARNING: The data set WORK.MACROVARIABLES may be incomplete. When this step was stopped there were 0 observations and 3 variables. WARNING: Data set WORK.MACROVARIABLES was not replaced because this step was stopped. NOTE: DATA statement used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 680.68k OS Memory 29092.00k Timestamp 11/23/2021 05:57:18 PM Step Count 81 Switch Count 0 Page Faults 0 Page Reclaims 58 Page Swaps 0 Voluntary Context Switches 0 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 16 135 136 data plot; 137 set RoO_Matrix; 138 where k=1; 139 x=input(scan(target,1,'/'),8.); 140 y=input(scan(target,2,'/'),8.); 141 z=input(scan(target,3,'/'),8.); 142 run; NOTE: There were 933866 observations read from the data set WORK.ROO_MATRIX. WHERE k=1; NOTE: The data set WORK.PLOT has 933866 observations and 7 variables. NOTE: DATA statement used (Total process time): real time 0.82 seconds user cpu time 0.61 seconds system cpu time 0.21 seconds memory 3446.46k OS Memory 31912.00k Timestamp 11/23/2021 05:57:19 PM Step Count 82 Switch Count 5 Page Faults 0 Page Reclaims 536 Page Swaps 0 Voluntary Context Switches 20 Involuntary Context Switches 3 Block Input Operations 0 Block Output Operations 131848 143 proc sort data=plot; 144 by z descending station orientation; ERROR: Variable ORIENTATION not found. 145 run; NOTE: The SAS System stopped processing this step because of errors. NOTE: PROCEDURE SORT used (Total process time): real time 0.00 seconds user cpu time 0.01 seconds system cpu time 0.00 seconds memory 1834.31k OS Memory 29860.00k Timestamp 11/23/2021 05:57:19 PM Step Count 83 Switch Count 0 Page Faults 0 Page Reclaims 241 Page Swaps 0 Voluntary Context Switches 0 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 0 146 ods graphics / reset width=6.4in height=6.4in; 147 proc sgplot data=plot aspect=1; 148 by z; 149 where ((station="&Sta_Code1" and orientation= "&Opt_Orientation1") or WARNING: Apparent symbolic reference STA_CODE1 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION1 not resolved. 150 (station="&Sta_Code2" and orientation="&Opt_Orientation2") or WARNING: Apparent symbolic reference STA_CODE2 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION2 not resolved. 151 (station="&Sta_Code3" and orientation="&Opt_Orientation3") or WARNING: Apparent symbolic reference STA_CODE3 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION3 not resolved. 152 (station="&Sta_Code4" and orientation="&Opt_Orientation4") or WARNING: Apparent symbolic reference STA_CODE4 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION4 not resolved. 153 (station="&Sta_Code5" and orientation="&Opt_Orientation5") or WARNING: Apparent symbolic reference STA_CODE5 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION5 not resolved. 154 (station="&Sta_Code6" and orientation="&Opt_Orientation6") or WARNING: Apparent symbolic reference STA_CODE6 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION6 not resolved. 155 (station="&Sta_Code7" and orientation="&Opt_Orientation7") or WARNING: Apparent symbolic reference STA_CODE7 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION7 not resolved. 156 (station="&Sta_Code8" and orientation="&Opt_Orientation8") or WARNING: Apparent symbolic reference STA_CODE8 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION8 not resolved. 157 (station="&Sta_Code9" and orientation="&Opt_Orientation9") or WARNING: Apparent symbolic reference STA_CODE9 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION9 not resolved. 158 (station="&Sta_Code10" and orientation="&Opt_Orientation10") or WARNING: Apparent symbolic reference STA_CODE10 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION10 not resolved. 159 (station="&Sta_Code11" and orientation="&Opt_Orientation11") or WARNING: Apparent symbolic reference STA_CODE11 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION11 not resolved. 160 (station="&Sta_Code12" and orientation="&Opt_Orientation12") or WARNING: Apparent symbolic reference STA_CODE12 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION12 not resolved. 161 (station="&Sta_Code13" and orientation="&Opt_Orientation13") or WARNING: Apparent symbolic reference STA_CODE13 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION13 not resolved. 162 (station="&Sta_Code14" and orientation="&Opt_Orientation14") or WARNING: Apparent symbolic reference STA_CODE14 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION14 not resolved. 163 (station="&Sta_Code15" and orientation="&Opt_Orientation15")); WARNING: Apparent symbolic reference STA_CODE15 not resolved. WARNING: Apparent symbolic reference OPT_ORIENTATION15 not resolved. ERROR: Variable orientation is not on file WORK.PLOT. 164 165 Title "New Azimuth (N),New Elevation Angles by Level"; 166 scatter x=x y=y /group=station transparency=.85 markerattrs=(symbol=circlefilled); 167 xaxis grid min=-800 max=800; 168 yaxis grid min=-800 max=800; 169 run; NOTE: PROCEDURE SGPLOT used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 1945.46k OS Memory 29860.00k Timestamp 11/23/2021 05:57:19 PM Step Count 84 Switch Count 1 Page Faults 0 Page Reclaims 243 Page Swaps 0 Voluntary Context Switches 7 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 8 170 171 172 173 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK; SYMBOLGEN: Macro variable GRAPHTERM resolves to GOPTIONS NOACCESSIBLE; 183 User: u44673568

genemroz · ‎11-23-2021

Hi Rob, Thanks so much for this suggestion. I think I understand your approach. However, in order to implement it, I think I need to somehow modify the dataset work.RoO_Matrix so that the ORIENTATION variable (which is a string variable) conforms to your proposed index set ORIENTATIONS (which is a pair of numbers). I don't know how to accomplish that. Can you suggest an approach? Thanks. Gene

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