Multiobjective Optimization

The problem to be solved:

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

	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
	NDA_PMIN	An SQP variable metric method for minimax optimization, linear constraints.
	NLPJOB	Interactively changeable scalarization and solution by NLPQL
	NBI	Matlab source (4.0 up) downloadable. Theory in SIOPT 8 (1998), 631--657
	CONMAX (f77)	uses ODE's 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
	MOMHLib++	Multiple-Objective MetaHeuristics Library in C++
	SPEA	Strength Pareto Evolutionary Algorithm (C++)
	SPEA implementation for the TSP	SPEA implementation for the TSP (C++)
	HIPRE 3+	Decision analytic tool for Windows 95/98/NT
	MCDSS	Collection of Multiple Criteria Decision Support Software
	MCMA	From IIASA. Linear multiobjective problems. Needs HOPDM and others. no_s, only binaries for Solaris 2.5 and Windows 95.
	PROTASS	Linear multiobjective problems. Based on lp_solve. no_s, only Win-binaries.