Simulation-Based Robust and Adaptive Optimization Method for Heteroscedastic Transportation Problems

Simulation-based optimization is an effective solution to complex transportation problems relying on stochastic simulations. However, existing studies generally perform a fixed number of evaluations for each decision vector across the design space, overlooking simulation heteroscedasticity and its effects on solution efficiency and robustness. In this paper, we treat the number of evaluations as an adaptive variable depending upon the simulation heteroscedasticity and the potential optimality of each decision vector. A statistical method, which automatically determines the variable number of evaluations, is presented for a range of derivative-free optimization methods. By fusing Bayesian inference with the probability of correct selection, it permits adaptive allocation of budgeted computational resources to achieve improved solution efficiency and robustness. The method is integrated with the deterministic global optimizer DIviding RECTangles (DIRECT) to yield NoisyDIRECT as a continuous simulation-based robust optimization method (which is open sourced). The key properties of the method are proved and discussed. Numerical experiments on difficult test functions are first conducted to verify the improvement of NoisyDIRECT compared with DIRECT and Bayesian optimization. Given the same computational budget, NoisyDIRECT can better locate the global optimum than the other two alternatives. Applications to representative simulation-based transportation problems, including an M/M/1 queueing problem and a parking pricing problem, are then presented. The results demonstrate the ability of NoisyDIRECT to pinpoint the optimal solution via adaptive computational resources allocation, achieving the desired level of robustness.