Novel hybrid approach with elite group optimal computing budget allocation for the stochastic multimodal problem

Abstract

The stochastic multimodal problem commonly arises in the search for efficiency and solution quality in practice. In this study, a hybrid approach is developed for the stochastic multimodal problem. The proposed approach comprises particle swarm optimization (PSO), constriction factor PSO (CPSO), and elite group optimal computing budget allocation (EGOCBA). CPSO or PSO is applied to determine the correct direction in the design space, and EGOCBA is adopted to allocate the appropriate number of samples to each alternative and provide reliable evaluations and identifications to rank particles in the CPSO or PSO procedure. This work improves the searching efficiency of optimal computing budget allocation (OCBA) in the stochastic multimodal problem. Several alternatives referred to as the “elite group,” the performance of which is close to that of the current best solution in each swarm, absorb most of the computing budget of OCBA. However, distinguishing the best solution from the elite group is time consuming because of the various local and global optima in the stochastic multimodal problem. Therefore, this study proposes EGOCBA that avoids extra computing costs for the elite group by implementing a new selection procedure. This EGOCBA reserves all the solutions of the elite group and filters them to form an optimal set that contains all the best solutions having an equal mean performance without a significant difference. These tasks are achieved through a confidence interval test in the end of the algorithm. The optimal set can provide more than one best solution to support multiple decisions depending on different decision variables. Two experiments are conducted on stochastic multimodal optimization problem and stochastic resource allocation problem. Experimental results reveal the efficiency and effectiveness of the proposed approach in deriving multiple optimal solutions in a multimodal class and stochastic environment.