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

• Published in: European journal of operational research Vol. 177; no. 3; pp. 1656 - 1677
• Main Authors: Gomes da Silva, Carlos, Figueira, José, Clímaco, João
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.03.2007; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Approximation; Bi-criteria knapsack; Combinatorial optimization; Comparative analysis; Exact methods; Heuristic; Knapsack problem; Metaheuristics; Optimization; Scatter search; Studies; Exact methods; Scatter search; Bi-criteria knapsack; Combinatorial optimization; Metaheuristics
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2005.10.013

This paper deals with the problem of inaccuracy of the solutions generated by metaheuristic approaches for combinatorial optimization bi-criteria {0, 1}-knapsack problems. A hybrid approach which combines systematic and heuristic searches is proposed to reduce that inaccuracy in the context of a scatter search method. The components of this method are used to determine regions in the decision space to be systematically searched. Comparisons with small and medium size instances solved by exact methods are presented. Large size instances are also considered and the quality of the approximation is evaluated by taking into account the proximity to the upper frontier, devised by the linear relaxation, and the diversity of the solutions. Comparisons with other two well-known metaheuristics are also performed. The results show the effectiveness of the proposed approach for both small/medium and large size instances.