Computational performance of basic state reduction based dynamic programming algorithms for bi-objective 0-1 knapsack problems

Authors:
Aiying Rong;José Rui Figueira
Affiliations:
Cemapre (Center of Applied Mathematics and Economics), ISEG -Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal;CEG-IST, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 11
Cited 0

Fundamentals of Computer Alori

Fundamentals of Computer Alori
Tabu Search Based Procedure for Solving the 0-1 MultiObjective Knapsack Problem: The Two Objectives Case

Journal of Heuristics
Two-phases Method and Branch and Bound Procedures to Solve the Bi–objective Knapsack Problem

Journal of Global Optimization
Solving bicriteria 0-1 knapsack problems using a labeling algorithm

Computers and Operations Research
An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization

Management Science
Multicriteria Optimization

Multicriteria Optimization
Solving efficiently the 0-1 multi-objective knapsack problem

Computers and Operations Research
Finding non-dominated solutions in bi-objective integer network flow problems

Computers and Operations Research
Labeling algorithms for multiple objective integer knapsack problems

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

Computers & Mathematics with Applications
Using bound sets in multiobjective optimization: application to the biobjective binary knapsack problem

SEA'10 Proceedings of the 9th international conference on Experimental Algorithms

Quantified Score

Hi-index	0.09

Visualization

Abstract

This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0-1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking.