A novel optimal replication allocation strategy for particle swarm optimization algorithms applied to simulation optimization problem

Abstract

This study proposes a simulation optimization algorithm, called optimal replication allocation strategy (ORAS), for particle swarm optimization (PSO) algorithms in simulation models with high computing cost in large design spaces. In this study, the PSO is employed to explore and exploit near-optimal or optimal solution in the design space. Given the uncertainties in real-word applications, a simulation model is constructed to evaluate the performance of each design alternative. Optimal computing budget allocation (OCBA), a state-of-the-art resampling method, is combined with metaheuristic principles to improve the accuracy of estimating best solutions and enhancing efficiency by intelligently allocating the number of replications. However, the solution space is nonlinear or multimodal; that is, various local or global solutions exist. In OCBA, the probability of correct selection (P(CS)) in the currect best solution serves as an important measurement. P(CS) refers to the probability that the “best” of k populations is selected according to some specified criteria of best. OCBA can halt allocation when P(CS) reaches higher than the desired value, i.e., P(CS)*. The multimodal solution space features a high probability of reaching a low P(CS) as many solutions perform closely to the current best of each generation. This situation indicates that P(CS) cannot achieve P(CS)*; OCBA cannot stop allocation, and additional computational cost may be wasted. In this study, we redefine and modify P(CS). The new version is P(CSE), which considers calculation of global best, called the super individual, instead of current best solution within a confidence level. The proposed ORAS can provide an asymptotically optimal allocation rule for combining with population metaheuristics based on P(CSE). We apply ORAS using an original particle swarm optimization (PSO) and two variants of PSO to address stochastic buffer allocation problem and stochastic function optimization problem compared with several state-of-the-art technologies from literature. The resulting ORAS with three PSOs is an effective procedure as it intelligently utilizes limited computing resources. Numerical tests indicate that ORAS increases P(CSE) in each generation and subsequently enhances the efficiency of PSO algorithms.