Software Tools for Multi-Criteria Programming

Abstract

In the last few decades researchers’ efforts have concentrated particularly on the theory and methodology of Multiple Objective Programming. A considerable amount of theoretical properties and extensions of traditional mathematical programming to the case of multiple objective optimization, methodological approaches, methods, algorithms and procedures have been developed (Benayoun et al., 1971; Fishburn et al., 1990; Korhonen and Laakso, 1986; Lewandowski and Wierzbicki, 1989; Nakayama and Sawaragi, 1984; Sawaragi et al., 1985; Shin and Ravindran, 1991; Steuer, 1986; Wierzbicki, 1982; Zionts, 1988). Quite a lot real-life Multiple Objective Linear Programming (MOLP) problems have been solved by specific implementations of the developed methodology. Generally, many multiple objective interdisciplinary problems relevant in practice have multiple nonlinear objectives and nonlinear constraints. Within the past two decades research interest grows to involve Multiple Objective Nonlinear Programming (MONP). The progress has been mainly theoretically and methodologically oriented. Only few real-life applications were reported in literature (Nakayama and Furukawa, 1985; Nakayama and Sawaragi, 1984; Roy and Wallenius, 1992). Still, effective computer codes for MONP models are insufficiently available. Even if the MONP problem is well-structured as to settle itself to algorithmic procedures, there are inherent restraints to the practical achievement of optimal solutions. MONP problems need algorithms that are known to require exponentially much computer time — such problems are said to be NP-hard.