Integrating partial optimization with scatter search for solving bi-criteria {0, 1}-knapsack problems

This paper deals with the problem of inaccuracy of the solutions generated by metaheuristic approaches for bi-criteria {0,1}-knapsack problems. A hybrid approach which combines systematic and heuristic search is proposed to reduce that inaccuracy in the context of a scatter search method. The components of the method are used to determine regions in the decision space to be systematically searched. Comparisons with small and medium size instances exactly solved are presented. Large size instances are also considered and the quality of the approximation is made by taking into account the proximity to the upper frontier, devised by the linear relaxation, and the diversity of the solutions. The results show the e¤ectiveness of this approach both in small, medium and large size instances. Key-words: Metaheuristics, exact methods, scatter search, bi-criteria knapsack problems, combinatorial optimization, intensi...cation strategies ¤Corresponding author yVisiting Researcher (March, 2004) at Department of Engineering Science, The University of Auckland, Auckland, NZ