Lexicographic Goal Programming and Assessment Tools for a Combinatorial Production Problem

Abstract

NP-complete combinatorial problems often necessitate the use of near-optimal solution techniques including heuristics and metaheuristics. The addition of multiple optimization criteria can further complicate comparison of these solution techniques due to the decision-maker’s weighting schema potentially masking search limitations. In addition, many contemporary problems lack quantitative assessment tools, including benchmark data sets. This chapter proposes the use of lexicographic goal programming for use in comparing combinatorial search techniques. These techniques are implemented here using a recently formulated problem from the area of production analysis. The development of a benchmark data set and other assessment tools is demonstrated, and these are then used to compare the performance of a genetic algorithm and an H-K general-purpose heuristic as applied to the production-related application.