Solving bicriteria 0–1 knapsack problems using a labeling algorithm

Abstract

This paper examines the performances of a new labeling algorithm to find all the efficient paths (or non-dominated evaluation vectors) of the bicriteria 0–1 knapsack problem. To our knowledge this is the first time a bicriteria 0–1 knapsack is solved taking advantage of its previous conversion into a bicriteria shortest path problem over an acyclic network. Computational experiments and results are also presented regarding bicriteria instances of up to 900 items. The algorithm is very efficient for the hard bicriteria 0–1 knapsack instances considered in the paper. Scope and purpose The knapsack problem is a well-known combinatorial optimization problem. While most of the existing papers in the literature studied the single criterion model, this paper deals with the knapsack problem with two criteria. Literature on this topic is scarce. There is a growing need for new algorithms able to compute non-dominated solutions quickly. The motivation of this study was to explore the use of efficient labeling algorithms to obtain non-dominated solutions of combinatorial optimization problems that can be formulated as network models. The purpose of the article is to implement a new algorithm for the bicriteria 0–1 knapsack problem. After converting the knapsack model into a bicriteria path problem over an acyclic network, the methodology proposes the use of a very efficient labeling algorithm. The scope of applications of the algorithm includes capital budgeting problems, transportation investments, and so on. The major advantage of our approach is to compute non-dominated solutions for bicriteria 0–1 knapsack problems faster than other approaches as shown by the computational results.