A Socio-Cognitive Particle Swarm Optimization for Multi-Dimensional Knapsack Problem

Abstract

The multidimensional knapsack problem (MKP), which is a generalization of the 0-1 simple Knapsack problem, is one of the classical NP-hard problems in operations research having a number of engineering applications. Several exact as well as heuristic algorithms are available in literature for its solution. In this paper, we propose a new particle swarm optimization (PSO) algorithm namely socio-cognitive particle swarm optimization (SCPSO) for solving the MKP. Comparing with the basic binary particle swarm optimization (BPSO), this improved algorithm introduces the distance between gbest and pbest as a new velocity update equation which maintains the diversity in the swarm and makes it more effective and efficient in solving MKP. We present computational experiments with various data instances for fine tuning of parameters of SCPSO and to validate our ideas and demonstrate the efficiency of the proposed algorithm.