Originally posted by: SaumyaB

Hi,

I am working on a model (variant of RCPSP) where I use a goal programming approach to solve a bi-objective problem. The two objectives are conflicting with each other. So, after solving for the first objective, I take the solution obtained as the starting point for objective 2 (with the additional constraint that the first objective should not degrade). This involves setting a branching limit to obtain the solution for first objective, since I do not want a complete optimization of the first objective as this results in degradation of objective 2. Is there a way to obtain a pareto-optimal solution using CP optimizer, since setting up a branching limit for one problem instance may not work for all instances.

Appreciate any help on this.

Hi,

could

https://www.ibm.com/developerworks/community/forums/html/topic?id=193ecefc-757c-4c66-9905-7ac0dd81dc8f&ps=25

give you some ideas ?

regards

https://www.linkedin.com/pulse/%E0%A4%91%E0%A4%AA%E0%A4%9F%E0%A4%AE%E0%A4%87%E0%A4%9C%E0%A4%B6%E0%A4%A8-%E0%A4%95%E0%A4%AF-%E0%A4%B9-%E0%A4%94%E0%A4%B0-%E0%A4%AF%E0%A4%B9-%E0%A4%95%E0%A4%B8%E0%A4%86%E0%A4%AA%E0%A4%95-%E0%A4%95%E0%A4%AE-%E0%A4%B8-%E0%A4%85%E0%A4%A7%E0%A4%95-%E0%A4%95%E0%A4%B0%E0%A4%A8-%E0%A4%AE-%E0%A4%AE%E0%A4%A6%E0%A4%A6-%E0%A4%95%E0%A4%B0-%E0%A4%B8%E0%A4%95%E0%A4%A4-chauhan/?trackingId=7WoeaoGWcjf5IyiLYE8dwg%3D%3D

Originally posted by: SaumyaB

Hi Alex,

Thanks for the suggested approaches. For the weighted objective approach that I tried, my concern is setting up a weight value that would work for all/most problem instances. Since, my two objective terms are fairly different in terms of the range of values they take, so, I suspect a weight value that works for certain problem instances may or may not work for all.

For the lexicographic objective within CPO approach, my first minimization objective has the possibility to get optimized to 0, which in my case, is undesirable since it results in a high value of second objective (as the two objectives are conflicting). So in this case, is there a way to obtain a pareto optimal set?

Any insights into this would be really helpful. 

Originally posted by: rdumeur

Dear SaumyaB,

There is no built-in mechanism in CPO allowing to obtain a pareto optimal set of solutions.

You'd need to write some external algorithm to build it. You could consider approaches like: http://www-verimag.imag.fr/~maler/Papers/pareto.pdf which relies on an external solver.

I hope this helps. 

Cheers,