Gamultiobj only finding one point on pareto front

I am implementing gamultiobj to solve three cost functions. When the program runs it only finds one point on the pareto front when I am sure there should be multiple solutions.

Are there any solver settings I can modify to find multiple solutions on the pareto front?

[Ahmed Ellithy]

Hello Hannah,

I have the same question, and I would like to know if you have any updates?

My Pareto front has multiple points on top of each other, and I am sure this is not the global minima, so the algorithm is stuck on this local minima and cannot generate a Pareto front with the normal shape of distributed points.

[Hannah Dinovitzer]

Hi Ahmed, I believe my issue was that the cost functions were not very sensitive to changes in my decision variables. I had to change the definition of my cost functions to get better results.

Answer 1

[Alan Weiss]

I suggest that you find the single-objective minima as in Start from Single-Objective Solutions or Start from Single-Objective Solutions. These are two different examples that show the value of starting from the single-objective solutions to obtain a wider Pareto set.

You can also try the paretosearch solver, which sometimes finds a wider Pareto set on badly-scaled problems, as in this example.

If, by some chance, you still end up with a single point, then it is possible that there is only one feasible Pareto point.

Alan Weiss

MATLAB mathematical toolbox documentation

[Hannah Dinovitzer]

Thanks for the suggestions. I have tried using starting points that are generated from single objective solutions and I sill always find one point on the pareto front. The paretosearch solver is also not able to resolve my issue.

I am fairly certain that there should be multiple points on the pareto front, are there maybe some other solver options that would help with finding multiple points on the pareto front?

[Alan Weiss]

If the single-objective problems all have the same solution then that is your answer. There is nothing else. There is no tradeoff curve (Pareto front) because all the objectives are minimized at the same point.

The only other possibility that I can see is to try starting the single-objective solvers from different start points. Maybe there are multiple local minima.

Alan Weiss

MATLAB mathematical toolbox documentation