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][1] for the list of reference and methods that can be used for your problem.

In terms of software, 

 - I'm familiar with [Global optimization][2] toolbox in Matlab has a
   multiobjective evolutionary solver than can handle linear
   constraints.
 - $R$ has an excellent package called [MCO][3] 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][4] algorithm.

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


  [1]: http://www.lania.mx/~ccoello/EMOO/EMOObib.html
  [2]: http://www.mathworks.com/products/global-optimization/
  [3]: http://cran.r-project.org/web/packages/mco/mco.pdf
  [4]: http://www.iitk.ac.in/kangal/Deb_NSGA-II.pdf