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

Authors:
José Rui Figueira;Luís Paquete;Marco Simões;Daniel Vanderpooten
Affiliations:
CEG-IST, Center for Management Studies, Instituto Superior Técnico, Technical University of Lisbon, Porto Salvo, Portugal 2780-990;CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal 3030-290;CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal 3030-290;University Paris-Dauphine, Paris Cedex 16, France 75775
Venue:
Computational Optimization and Applications
Year:
2013

Citing 8
Cited 0

Knapsack problems: algorithms and computer implementations

Knapsack problems: algorithms and computer implementations
Introduction to algorithms

Introduction to algorithms
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
Approximating Multiobjective Knapsack Problems

Management Science
Bound sets for biobjective combinatorial optimization problems

Computers and Operations Research
Core problems in bi-criteria {0,1}-knapsack problems

Computers and Operations Research
Solving efficiently the 0-1 multi-objective knapsack problem

Computers and Operations Research

Quantified Score

Hi-index	0.00

Visualization

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.