Duplicates in Pareto frontier using gamultiobj

I am using gamultiobj in the Global Optimization Toolbox to solve a knapsack problem. I use the following code:

[xbest, fbest, exitflag] = gamultiobj(@KnapsackWeightMulti, 22, [], [], [], [], ...
      lb, ub, @const_knap, opts)

When I examine the xbest variable generated, which to my understanding represents the Pareto frontier of solutions, many of the solutions are duplicates. Why is this?

Answer 1

[Alan Weiss]

The genetic algorithm does not remove duplicate points that it finds.

I do not know how you are implementing the constraints for the problem, but I believe that this is an integer-constrained problem. It is entirely possible that gamultiobj does not have a large enough population to give you a diverse Pareto front with the constraints satisfied, or there might not be that many points on the Pareto front even with a large initial population that is well-dispersed. In other words, it is possible that the solution is, by its nature, just a few points, so gamultiobj has to have a lot of duplicates in its solution.

Alan Weiss

MATLAB mathematical toolbox documentation