An Exact Algorithm for the Biobjective 0-1 Linear Knapsack Problem with a Single Continuous Variable

Abstract

In this paper, we study one variant of the multiobjective knapsack problem, i.e., the biobjective 0-1 linear knapsack problem with a single continuous variable (BKPC). An exact algorithm, the biobjective branch and bound method (BOBB), is presented to find all nondominated points of the BKPC. We analyze the nondominated frontier of the BKPC and design a new branching strategy to improve the algorithm. Finally an illustrative example shows how the algorithm solves a practical problem.