Help Wanted: Coding a Constraint

genemroz — Fri, 19 Nov 2021 15:36:08 GMT

Esteemed Advisers

I'm working to develop a general optimization approach for aiming a network of meteor cameras. The goal of this particular version of the model is to find the optimal orientation of 5 stations.

I would like to include a "constraint" in the model such that the optimal solution does not allow selected stations to be oriented in the same direction. To wit: given five stations (A,B,C,D and E), where Stations A and B are co-located as are Stations C and D (at a different location than A,B). How do I code a constraint that prohibits solutions where stations A,B have the same orientation and stations C,D have the same orientation?

The code below is the current Proc Optmodel statement that I am using.

Many thanks in advance for any guidance you can provide.

Regards,

Gene

Proc Optmodel;
	/* Read CoverageMatrix data into index sets*/
						set <str> stations;
						read data work.stationindex into stations=[station];
/* 						
/*						Modify Orientations below to reflect addition of elevation angles of 40 and 50 degrees */
						set <str> ORIENTATIONS=/'360/55' '360/50' '360/45' '360/40' '360/35' '45/55' '45/50' 
						'45/45' '45/40' '45/35' '90/55' '90/50' '90/45' '90/40' '90/35' '135/55' '135/50' 
						'135/45' '135/40' '135/35' '180/55' '180/50' '180/45' '180/40' '180/35' '225/55' 
						'225/50' '225/45' '225/40' '225/35' '270/55' '270/50' '270/45' '270/40' '270/35' 
						'315/55' '315/50' '315/45' '315/40' '315/35'/;
							
						set <str> Targets;
						read data work.targets into TARGETS=[target];
						num Matrix {stations, ORIENTATIONS, TARGETS};
						read data work.RoOMatrix 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];

						/* Call Solver and Save Results:*/
						solve with milp/ relobjgap=&relobjgap;
/* 						solve; */
						create data work.OptimalSolution_&RoO from 
						[station orientation]={c in stations, o in orientations: CHI[c, o]>0.5} CHI;
					quit;
						/*Print Results*/
						proc print data=work.optimalsolution_&RoO;
						Title "Optimal Solution RoO=&RoO x &RoO km";
					run;

Re: Help Wanted: Coding a Constraint

RobPratt — Fri, 19 Nov 2021 15:45:59 GMT

If I understand correctly, you want to include the following "conflict" constraints that prohibit both binary variables from taking the value 1 simultaneously:

   set STATION_PAIRS = {<'A','B'>, <'C','D'>};
   con NotSameOrientation {<s1,s2> in STATION_PAIRS, o in ORIENTATIONS}:
      CHI[s1,o] + CHI[s2,o] <= 1;

Re: Help Wanted: Coding a Constraint

genemroz — Fri, 19 Nov 2021 23:04:27 GMT

Thanks, Rob! I implemented your suggested code and it works perfectly. This was a big help. I'm marking your solution as accepted. Thanks again for your help with this.

Gratefully,

Gene

topic Help Wanted: Coding a Constraint in Mathematical Optimization, Discrete-Event Simulation, and OR

Help Wanted: Coding a Constraint

Re: Help Wanted: Coding a Constraint

Re: Help Wanted: Coding a Constraint