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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), r/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

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)

MOMHLib++

Multiple-Objective MetaHeuristics Library in C++

EMOO

Evolutionary Multi-objective Optimization (incl links to software)

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.

PROTASS

Linear multiobjective problems. Based on lp_solve. only Win-binaries.

FGM/RGM

Linear and nonlinear problems; feasible/resonable goals method. Windows binaries.