Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem

José Figueira (), Luís Paquete (), Marco Simões () and Daniel Vanderpooten ()

Computational Optimization and Applications, 2013, vol. 56, issue 1, 97-111

Abstract: This paper presents several methodological and algorithmic improvements over a state-of-the-art dynamic programming algorithm for solving the bi-objective {0,1} knapsack problem. The variants proposed make use of new definitions of lower and upper bounds, which allow a large number of states to be discarded. The computation of these bounds are based on the application of dichotomic search, definition of new bound sets, and bi-objective simplex algorithms to solve the relaxed problem. Although these new techniques are not of a common application for dynamic programming, we show that the best variants tested in this work can lead to an average improvement of 10 to 30 % in CPU-time and significant less memory usage than the original approach in a wide benchmark set of instances, even for the most difficult ones in the literature. Copyright Springer Science+Business Media New York 2013

Keywords: Bi-objective 0-1 knapsack problems; Multi-objective combinatorial optimization; Bounds sets; Dichotomic search; Bi-objective simplex algorithm (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10589-013-9551-x

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