Free and Open Source software

Name License Brief info

ADMB BSD nonlinear optimization framework, using automatic differentiation

ALGENCAN GPL Fortran code for general nonlinear programming. Interfaces with AMPL, C/C++, CUTEr, Matlab, Python, Octave and R.

APMonitor BSD MATLAB Toolbox and Python APIs to Mixed Integer Nonlinear Programming Solvers

ASCEND GPL mathematical modelling system

BOBYQA An algorithm that seeks the least value of a nonlinear function subject to bound constraints, without using derivatives of the objective function. By Michael J. D. Powell. Source code is freely available online.

COBYLA An algorithm that seeks the least value of a nonlinear function subject to nonlinear inequality constraints, without using derivatives of the objective function or the constraints. By Michael J. D. Powell. Source code is freely available online.

CONDOR GPL Non-linear Continuous Objective Function for small dimension (n

Hi there. Have you tried optimization package in Matlab?

It does the job for you if your problem doesn't have several constraints and so on and at least you will get the Pareto frontier. If you do not like to use the toolbox, please use this command in Matlab mfile

---

options=gaoptimset('PopulationSize',120,'PlotFcn',@gaplotpareto);

[x,F]=gamultiobj(@name_of_mfile,number of decision variables,[],[],[],[],[lower bond],[upper bond],options);

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Thanks Mr. Pouria Ahmadi

I have not tried MATLAB as I do not have one. Hence asked for open source softwares.

Free and Open Source software

Name License Brief info

ADMB BSD nonlinear optimization framework, using automatic differentiation

ALGENCAN GPL Fortran code for general nonlinear programming. Interfaces with AMPL, C/C++, CUTEr, Matlab, Python, Octave and R.

APMonitor BSD MATLAB Toolbox and Python APIs to Mixed Integer Nonlinear Programming Solvers

ASCEND GPL mathematical modelling system

BOBYQA An algorithm that seeks the least value of a nonlinear function subject to bound constraints, without using derivatives of the objective function. By Michael J. D. Powell. Source code is freely available online.

COBYLA An algorithm that seeks the least value of a nonlinear function subject to nonlinear inequality constraints, without using derivatives of the objective function or the constraints. By Michael J. D. Powell. Source code is freely available online.

CONDOR GPL Non-linear Continuous Objective Function for small dimension (n

You can also use Standard Pso or Minimum Population Search both of their source are available from internet.

You cane benefit from Matlab Toolbox. It can do the job for you depending on your problem. 

You can use Octave (http://www.gnu.org/software/octave/), that is an open source and free alternative to Matlab and is able to execute programs (.m) written in Matlab.