CODEWITHSUNDEEP
cplexopl
John
John

Reputation: 37

How to create a multi-objective model with objective priority

I'm trying to solve a multi-objective problem in which I have to minimize two different objectives but with one taking priority over the other one.

To solve the problem, and hence the question, I tried to use weighted sum of both objective functions. The problem here is that that approach finds the minimum value between the two problems which I don't want. I want to solve one objective and then, maintaning that specific value, I want to solve the other problem.

Upvotes: 1

Views: 435

Answers (2)

Alex Fleischer
Alex Fleischer

Reputation: 10059

You could use staticLex.

int nbKids=200;
float costBus40=500;
float costBus30=400;
float costBus50=625;

dvar int+ nbBus40;
dvar int+ nbBus30;
dvar int+ nbBus50;

dvar float cost;
dvar float co2emission;

minimize
  staticLex(cost,co2emission);

subject to
{
 cost==costBus40*nbBus40  +nbBus30*costBus30+nbBus50*costBus50;
 co2emission==nbBus50+nbBus40*1.1+nbBus30*1.2;

  40*nbBus40+nbBus30*30+nbBus50*50>=nbKids;
}

execute DISPLAY_After_SOLVE
{
  writeln("The minimum cost is ",cost);
  writeln("CO2 emission is ",co2emission);
  writeln("We will use ",nbBus40," 40 seats buses ",nbBus30,
  " 30 seats buses and ", nbBus50," buses 50 seats");
}

which gives

The minimum cost is 2500
CO2 emission is 4
We will use 0 40 seats buses 0 30 seats buses and 4 buses 50 seats

I posted this answer 5 days ago but that was deleted by a moderator.

See tiny example at https://www.ibm.com/developerworks/community/forums/html/topic?id=abac189a-0b99-4a08-bedf-78bbf919e14d

Upvotes: 1

Xavier Nodet
Xavier Nodet

Reputation: 5085

Version 12.9 of CPLEX has the ability to do exactly that: solve one objective, fix its value, and move to the next objective. Here's an example LP:

Maximize multi-objectives
first: abstol=2
   x1
second: priority=-1
   x2
Subject to
   x1 + x2 = 10
General
   x1 x2
End

This feature is described in the release notes, as well as in these slides.

Upvotes: 1

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