If your problem is a multiobjective optimization problem with constraints, and both the objectives and constraints are nonlinear/ non convex in nature then an appropriate method of choice is evolutionary multiobjective optimization method. Click here for the list of reference and methods that can be used for your problem.

In terms of software,

• I'm familiar with Global optimization toolbox in Matlab has a multiobjective evolutionary solver than can handle linear constraints.
• $R$ has an excellent package called MCO that is multiobjective optimization solver that handles both linear and nonlinear constraints. I have had excellent results using this package.

Both the aforementioned software implements Deb's a very popular NSGAII algorithm.

Please tell us if you succeed in using these for your problem and if you have any questions.

If your problem is a multiobjective optimization problem with constraints, and both the objectives and/or constraints are nonlinear/ non convex in nature then an appropriate method of choice is evolutionary multiobjective optimization method. Click here for the list of reference and methods that can be used for your problem.

In terms of software,

• I'm familiar with Global optimization toolbox in Matlab has a multiobjective evolutionary solver than can handle linear constraints.
• $R$ has an excellent package called MCO that is multiobjective optimization solver that handles both linear and nonlinear constraints. I have had excellent results using this package.

Both the aforementioned software implements Deb's a very popular NSGAII algorithm.

Please tell us if you succeed in using these for your problem and if you have any questions.