A three-ratio SACRO-based particle swarm optimization with local search scheme for the multidimensional knapsack problem

This study proposes a novel particle swarm optimization (PSO) to solve the multidimensional knapsack problem (MKP). This novel PSO is composed of a new three-ratio self-adaptive check and repair operator (SACRO) idea and a hill-climbing local search scheme. The SACRO idea was first proposed in 2015 and originally utilized only two dynamic ratios (namely, profit/weight utility and profit density) in repairing infeasible solutions. The third unique pseudo-utility ratio (that is, the surrogate relaxation ratio) was further introduced into SACRO, and three ratios (namely, surrogate relaxation ratio, profit/weight utility, and profit density) were used instead of two ratios. A local search idea (that is, the hill-climbing scheme) was also employed to avoid being trapped in the local optimal solutions. The proposed algorithm was tested using the benchmark problems from the OR-library to validate and demonstrate the efficiency of the proposed idea. Results were compared with those of two-ratio SACRO-based algorithms. The simulation and evaluation results showed that the three-ratio SACRO-based PSO with local search scheme is more competitive and robust than the two-ratio SACRO-based algorithm. Moreover, the SACRO idea could be combined with other population-based optimization algorithms to solve MKPs.