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Quartz | Level 8
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Posted 12-13-2021 12:13 PM
(1055 views)
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
10 REPLIES 10
SAS Super FREQ
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For the station with a fixed orientation, you are introducing symmetry, which is usually bad news for a MILP solver. I recommend using a FIX statement to fix the CHI[station,a,e] variable to 1 for that specific <station,a,e>. Please rerun and show the new log.
Quartz | Level 8
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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
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You should be fixing that station USL000 to only one orientation (one FIX statement). What you tried violates the CHI_constraint for that station.
Quartz | Level 8
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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
SAS Super FREQ
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OK, it looks like the MILP presolver was already doing something like the fixing of that variable. In both cases, you get:
NOTE: The presolved problem has 2612 variables, 2579 constraints, and 35204 constraint coefficients.The small changes in the BestBound value are typical of the branch-and-cut algorithm, which improves the linear programming bound by branching and adding cutting planes.
The MILP solver also has a decomposition algorithm that can sometimes yield dramatic performance improvements over branch-and-cut. The simplest invocation involves just adding the DECOMP keyword to the SOLVE WITH MILP statement options.
If you can provide the code and data, I'll see if I can recommend anything else.
Quartz | Level 8
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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
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For the RoO_Matrix data set, only the nonzero observations are needed.
Quartz | Level 8
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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
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I will have Technical Support contact you with instructions for sending the data sets.
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Hi, please check your private messages under your SAS Profile for details regarding opening a track with Technical Support so that you may upload your data. Thank you.
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12-13-2021 12:13 PM
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