A two state reduction based dynamic programming algorithm for the bi-objective 0-1 knapsack problem

Authors:
Aiying Rong;José Rui Figueira;Margarida Vaz Pato
Affiliations:
Cemapre (Center of Applied Mathematics and Economics), ISEG -Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal;INPL, Ecole des Mines de Nancy, Laboratoire LORIA, Parc de Saurupt- CS 14 234, 54 052 Nancy Cedex, France;Centro de Investigação Operacional, FC - University of Lisbon, ISEG - Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 9
Cited 2

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Abstract

In this paper, we present a dynamic programming (DP) algorithm for the multi-objective 0-1 knapsack problem (MKP) by combining two state reduction techniques. One generates a backward reduced-state DP space (BRDS) by discarding some states systematically and the other reduces further the number of states to be calculated in the BRDS using a property governing the objective relations between states. We derive the condition under which the BRDS is effective to the MKP based on the analysis of solution time and memory requirements. To the authors' knowledge, the BRDS is applied for the first time for developing a DP algorithm. The numerical results obtained with different types of bi-objective instances show that the algorithm can find the Pareto frontier faster than the benchmark algorithm for the large size instances, for three of the four types of instances conducted in the computational experiments. The larger the size of the problem, the larger improvement over the benchmark algorithm. Also, the algorithm is more efficient for the harder types of bi-objective instances as compared with the benchmark algorithm.