Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems

• Published in: Journal of global optimization Vol. 57; no. 2; pp. 549 - 573
• Main Authors: Beheshti, Zahra, Shamsuddin, Siti Mariyam, Yuhaniz, Siti Sophiayati
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.10.2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Chromosomes; Combinatorial analysis; Computer Science; Exploitation; Genetic algorithms; Heuristic; Knapsack problem; Laws, regulations and rules; Mathematical models; Mathematical optimization; Mathematics; Mathematics and Statistics; Methods; Mutation; Newton's laws of motion; Operations Research/Decision Theory; Operators; Optimization; Optimization algorithms; Police; Population; Problem solving; Real Functions; Studies; Topology; Multidimensional Knapsack Problem; NP-hard problem; Meta-heuristic algorithm; Binary Accelerated Particle Swarm Algorithm; Binary Particle Swarm Optimization; Combinatorial Optimization Problem
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-012-0006-1

The majority of Combinatorial Optimization Problems (COPs) are defined in the discrete space. Hence, proposing an efficient algorithm to solve the problems has become an attractive subject in recent years. In this paper, a meta-heuristic algorithm based on Binary Particle Swarm Algorithm (BPSO) and the governing Newtonian motion laws, so-called Binary Accelerated Particle Swarm Algorithm (BAPSA) is offered for discrete search spaces. The method is presented in two global and local topologies and evaluated on the 0–1 Multidimensional Knapsack Problem (MKP) as a famous problem in the class of COPs and NP-hard problems. Besides, the results are compared with BPSO for both global and local topologies as well as Genetic Algorithm (GA). We applied three methods of Penalty Function (PF) technique, Check-and-Drop (CD) and Improved Check-and-Repair Operator (ICRO) algorithms to solve the problem of infeasible solutions in the 0–1 MKP. Experimental results show that the proposed methods have better performance than BPSO and GA especially when ICRO algorithm is applied to convert infeasible solutions to feasible ones.