Help Wanted: Coding a Costraint (Continued)

[genemroz]

A few days ago Rob Pratt provided a valuable solution to my post entitled "Help Wanted: Coding a Constraint". I now find that I need expand on that constraint a bit.

To restate the problem: the goal to find the optimal orientations for a set of cameras. For specific pairs of cameras, certain orientations are considered "forbidden". Mr. Pratt provided a solution for one such forbidden situation: when both members of the camera pair are oriented in the same direction resulting in a complete overlap or duplication of the field of view.

Another "forbidden" situation is when the members of the camera pair are aimed in partially overlapping orientations. There are 8 Orientations in the model. It is desired to avoid solutions where the two selected cameras are assigned to adjacent azimuths. For example, it is undesireable for one camera to be at azimuth=45 and the other camera to be at either of the adjacent azimuths of 90 or 360 as that would result in excessive overlap of the fields of view.

The current code for Proc Optmodel is provided below. Note that the index set ORIENTATION is a cheracter variable that expresses both the azimuth angle and elevation angle. So part of the question is how to extract the azimuth portion of ORIENTATION and use that in the formulation of the constraint.

Thanks in advance for your help with this,

Regards,

Gene

Proc Optmodel;
	/* Read CoverageMatrix data into index sets*/
						set <str> stations;
						read data work.station_id into stations=[station];

						set <str> ORIENTATIONS=/'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35' /;
						
						set <str> Targets;
						read data work.targets into TARGETS=[target];
						num Matrix {stations, ORIENTATIONS, TARGETS};
						read data work.RoO_Matrix into [station orientation target] 
							Matrix=k;

						/* Set Constants*/
						/* optimal number of cameras covering each target*/						
						%Let k=3;
						num k=&k;
						/*Declare Variables*/
						var CHI {stations, ORIENTATIONS} binary;
						var IsTriplyCovered {TARGETS} binary;
						impvar XIT{target in TARGETS}=sum{station in stations, orientation in 
							orientations} matrix[station, orientation, target] *Chi[station, 
							orientation];

						/* Declare Model*/
						max NumTriplyCovered=sum{t in TARGETS} IsTriplyCovered[t];

						/*Subject to Following Constraints*/
						con CHI_constraint {station in stations}: 
						sum{orientation in ORIENTATIONS}CHI[station, orientation] <=1;
						con TriplyCoveredCon {t in TARGETS}: XIT[t] >=k * IsTriplyCovered[t];
						
						/*Rob Pratt's Code for "Conlfict Constraint"*/					
						set Station_Pairs={<'US000S','US001R'>,<'US000V','US001Q'>};
						con NotSameOrientation {<s1,s2> in Station_Pairs, o in ORIENTATIONS}:
						CHI[s1,o] + CHI[s2,o]<=1;

						/* Call Solver and Save Results:*/
						solve with milp/ relobjgap=0;
						create data work.OptimalSolution_&RoO from 
						[station orientation]={c in stations, o in orientations: CHI[c, o]>0.5} CHI;
					quit;

[RobPratt]

Here's one approach, where I have replaced the strings with pairs of numbers:

proc optmodel;
   set STATIONS = /A B C D/;
/*	set ORIENTATIONS = /'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35'/;*/
   set ORIENTATIONS = {<45,35>, <90,35>, <135,35>, <180,35>, <225,35>, <270,35>, <315,35>, <360,35>};
   var CHI {STATIONS, ORIENTATIONS} binary;
   set STATION_PAIRS = {<'A','B'>, <'C','D'>};
   set AZIMUTHS = setof {<a,e> in ORIENTATIONS} a;
   put AZIMUTHS=;
   set AZIMUTH_PAIRS = {a1 in AZIMUTHS, a2 in AZIMUTHS: mod(a1-a2+360,360) <= 45};
   put AZIMUTH_PAIRS=;
   con NotAdjacentAzimuths {<s1,s2> in STATION_PAIRS, <a1,a2> in AZIMUTH_PAIRS}:
      sum {<a,e> in ORIENTATIONS: a in {a1,a2}} (CHI[s1,a,e] + CHI[s2,a,e]) <= 1;
   expand;
quit;

Note that this "clique" constraint subsumes the "conflict" constraint (from my answer to your previous question) that prevents identical azimuths from being assigned to both stations in a pair.

[genemroz]

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

[RobPratt]

You can use the INPUT and SCAN functions to do this, either in the DATA step or in PROC OPTMODEL.  Here's the latter approach:

	set MY_STRINGS = /'45/35' '90/35' '135/35' '180/35' '225/35' '270/35' '315/35' '360/35'/;
	set ORIENTATIONS = setof {s in MY_STRINGS} <input(scan(s,1,'/'),best.),input(scan(s,2,'/'),best.)>;
    put ORIENTATIONS=;

The PUT statement yields the following in the log:

ORIENTATIONS={<45,35>,<90,35>,<135,35>,<180,35>,<225,35>,<270,35>,<315,35>,<360,35>}

[genemroz]

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

[RobPratt]

ORIENTATIONS is now a set of pairs of numbers <a,e> rather than a set of strings.  You need to change orientation in ORIENTATIONS to <a,e> in ORIENTATIONS.  Also, CHI now has three subscripts instead of two, so change CHI[station,orientation] to CHI[station,a,e].

[genemroz]

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

[RobPratt · Accepted solution]

ORIENTATION_STRING is a set of strings, but you are trying to use it as the second subscript of matrix[], which expects a single string.  The following statement uses the string concatenation operator || to construct the desired string from the <a,e> pair:

impvar XIT{target in TARGETS} = sum{station in STATIONS, <a,e> in ORIENTATIONS} matrix[station, a||'/'||e, target] * Chi[station,a,e];

[genemroz]

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