Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem

Abstract

The multidimensional knapsack problem (MKP) is a difficult combinatorial optimization problem, which has been proven as NP-hard problems. Various population-based search algorithms are applied to solve these problems. The particle swarm optimization (PSO) technique is adapted in our study, which proposes two novel PSO algorithms, namely, the binary PSO with time-varying acceleration coefficients (BPSOTVAC) and the chaotic binary PSO with time-varying acceleration coefficients (CBPSOTVAC). The two proposed methods were tested using 116 benchmark problems from the OR-Library to validate and demonstrate the efficiency of these algorithms in solving multidimensional knapsack problems. The results were then compared with those in the other two existing PSO algorithms. The simulation and evaluation results showed that the proposed algorithms, BPSOTVAC and CBPSOTVAC, are superior over the other methods according to its success rate, mean absolute deviation, mean absolute percentage error, least error, and standard deviation.