vecmin f(x) subject to h(x)=0, g(x)>=0,
n=dim(x), m=dim(g), p=dim(h).
Many problems in real life are multiple criteria decision problems. These are usually solved by proper scalarization and parametrization. The vecmin means usually a Pareto optimum. An optimum in the sense of the natural halforder of R^n need not exist.
Solvers which explicitly provide for multiple objectives are
MOSQP | SQP method for differentiable constrained NLPs, AMPL interface (Matlab) |
PolySciP | solver for multi-criteria integer programming and multi-criteria linear programming with an arbitrary number of objectives |
NSGA-II | evolutionary method (Matlab) |
LIONsolver | reactive search, free for research |
PaGMO/PyGMO | Parallel Global Multiobjective Optimizer (C++/Python) |
FSQP (f77, C) | FFSQP(f77), CFSQP(C), specifically strong for large number of inequalities. generate feasible iterates, ADIFOR interface for automatic differentiation. |
AMPL interface to CFSQP | |
MCDM | Overview of commercial and other MCDM software |
MOEA | Multiobjective optimization framework in Java |
NDA_PMIN | An SQP variable metric method for minimax optimization, linear constraints. |
NLPJOB | Interactively changeable scalarization and solution by NLPQL |
CONMAX (f77) | uses ODEs to generate search direction followed by Newton to correct back to feasible region, authors claim it is very robust but somewhat slow. |
NIMBUS | to be used interactively through a web-interface ,allows nonsmooth problems, uses bundle method |
NBI | Normal Boundary Intersection (Matlab) |
jMetal | extensive Multiple-Objective MetaHeuristics library in Java |
EMOO | Evolutionary Multi-objective Optimization (Python, MPI) |
SPEA | Strength Pareto Evolutionary Algorithm (C++) |
SPEA-TSP | SPEA implementation for the TSP (C++) |
HIPRE 3+ | Decision analytic tool for Windows 95/98/NT |
MCMA | From IIASA. Linear multiobjective problems. Needs HOPDM and others. only binaries for Solaris 2.5 and Windows 95. |
FGM/RGM | Linear and nonlinear problems; feasible/resonable goals method. Windows binaries. |