An iterative surrogate-based optimization approach for multi-server queuing system design

Queuing systems play an important role in numerous domains, including banks, supermarkets, traffic control, call centers, and production processes. Traditional methods for designing multi-server queuing systems often rely on trial-and-error or extensive simulations, making them time-consuming and computationally expensive. This paper addresses these challenges using MEVO (Metamodel-based Evolutionary Optimizer), a surrogate-based optimization algorithm. MEVO employs a machine-learning model as a surrogate model, reducing reliance on computationally intensive simulations. The algorithm also integrates evolutionary operators for efficient solution space exploration, a long-term memory strategy to avoid redundant simulations, and a dynamic search space reduction mechanism to enhance optimization efficiency. A case study of a supermarket checkout system, modeled in FlexSim, demonstrates the algorithm's efficacy in optimizing queuing configurations under stochastic variables such as customer arrival rates, basket sizes, and transaction values. MEVO achieves solution-quality performance comparable to the FlexSim optimizer while significantly reducing computation times. MEVO also delivers comparable computational performance to Bayesian optimization while exhibiting lower variance in objective-function results than FlexSim, highlighting its consistency and robustness. © 2025 Elsevier B.V.