Set-based particle swarm optimization applied to the multidimensional knapsack problem

Abstract

Particle swarm optimization algorithms have been successfully applied to discrete-valued optimization problems. However, in many cases the algorithms have been tailored specifically for the problem at hand. This paper proposes a generic set-based particle swarm optimization algorithm for use on discrete-valued optimization problems that can be formulated as set-based problems. A detailed sensitivity analysis of the parameters of the algorithm is conducted. The performance of the proposed algorithm is then compared against three other discrete particle swarm optimization algorithms from literature using the multidimensional knapsack problem, and is shown to statistically outperform the existing algorithms.

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

“…Some of these proposals have studied other neighborhood topologies (Kennedy, 2000;Clerc, 2006;Mohais et al, 2005) and (Parrott and Li, 2006) while others have tried to introduce different techniques to simulate particle flights by direct sampling using a random number generator with a certain probability distribution (Pampara et al, 2005;Langeveld and Engelbrecht, 2012;Kennedy, 2003; and . The Quantum PSO represents one of the most efficient versions due to its effective global search ability and out-performance on several optimization problems as demonstrated in Krohling and dos Santos Coelho (2006).…”

Particle Swarm Algorithm variants for the Quadratic Assignment Problems - A probabilistic learning approach

“…Another popular approach is to rely on the set-based operations to discretize PSO (Clerc, 2004;Correa et al, 2006;Neethling and Engelbrecht, 2006;Veenhuis, 2008;Chen et al 2010;Langeveld and Engelbrecht, 2011;Langeveld and Engelbrecht, 2012). In (Correa et al, 2006), a set-based approach is used for attribute selection in data mining applications; where the position is represented by attribute set and the velocity is a two dimensional array.…”

“…However, the proposed setbased operations lead to set bloating effect in both the position and the velocity and requires a complex mechanism to solve this problem. A set-based approach with redefined operators was proposed in (Clerc, 2004;Chen et al 2010;Langeveld and Engelbrecht, 2012). Clerc (Clerc, 2004) redefined the mathematical operators used in the velocity update equation in the discrete PSO applied to TSP.…”

“…Clerc (Clerc, 2004) redefined the mathematical operators used in the velocity update equation in the discrete PSO applied to TSP. In (Langeveld and Engelbrecht, 2011) and (Langeveld and Engelbrecht, 2012), similar redefined operators are used for the Multidimensional Knapsack Problem (MKP). These approaches are generic, but the proposed set-based operation leads to increased complexity of an otherwise fairly simple PSO algorithm.…”

“…The common limitation of these approaches (Clerc, 2004;Correa et al, 2006;Neethling and Engelbrecht, 2006;Veenhuis, 2008;Chen et al 2010;Langeveld and Engelbrecht, 2011;Langeveld and Engelbrecht, 2012;Pang et al, 2004;Liu et al, 2007a;Liu et al, 2007b) is that each one is specifically designed as a new algorithm to solve a specific problem. Hence, they lack the ability to harness the existing research efforts dedicated to improving PSO's performance in the continuous domain.…”