I'm using optimization tool box in Matlab to solve multi-objective optimization, I have linear and nonlinear constraint, after running the optimization, I got Pareto front (see the file attached in this message), increasing the population size give me the same result.
what do you think ?
in my opinion, your objective functions have only 1 optimized solution.
I think there's something funny with your result because it seems the two objectives have not a trade off. It may be the case but I would review the model and code for wrong signs or some mistake.
I assume that if you look at the output from the optimizer, you will see many solutions which are the same. This means that your objectives 1 and 2 are not in conflict with each other, i.e. at some point, optimizing one objective doesn't negatively affect the other objective. Therefore, using multi-objective optimization may not be suitable for your problem as it is main used when you have conflicting objectives (hence the reason for obtaining the Parto front). Instead you may want to combine the objectives (make one objectives) and use a single objective optimization which is faster. That should give you the same solution you have above (assuming it is optimal) but faster.
I hope this helps.
thank you for the responses,
what methods do you use in multi-objective optimization with nonlinear constraints. do you have examples that can help ?
thank you
best regards
- Hello Achour,
When I face multi-objective problems, I frequently use some evolutionary algorithm (MOEA, NSGA2, etc). To include constraints in them, you can make a penalty function, or force the solutions back to the feasible set with a reflection operator. Both methods work for inequality constraints, but reflection only should be a problem if the feasible set has zero or close to zero volume. There is plenty of fresh articles with ideas about it, so just do some search and you'll be fine.
Att
Felipe
I think the problem is with nonlinear constraint that you have defined. If you try to ignore the nonlinear constraints, you will get many trade-off solutions. You might have complex model which nonlinear constraints leads the error solution.
Did you solve the problem?
My graph also came the same way as that of Achour Hadjar . Do we have to add constraints in Genetic Algorithm (gamultiobj in MATLAB). Because if non-linear constraints are ignored then Parento front is being plotted in the correct way but on adding constraints its showing only 1 point. what might be the problem?
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