Accelerated Driving-Training-Based Optimization for Solving Constrained Bi-Objective Stochastic Optimization Problems

Abstract

The constrained bi-objective stochastic optimization problem (CBSOP) considers the optimization problem with stochastic bi-objective functions subject to deterministic constraints. The CBSOP is part of a set of hard combinatorial optimization problems regarding time complexity. Ordinal optimization (OO) theory provides a commonly recognized structure to handle hard combinatorial optimization problems. Although OO theory may solve hard combinatorial optimization problems quickly, the deterministic constraints will critically influence computing performance. This work presents a metaheuristic approach that combines driving-training-based optimization (DTBO) with ordinal optimization (OO), abbreviated as DTOO, to solve the CBSOP with a large design space. The DTOO approach comprises three major components: the surrogate model, diversification, and intensification. In the surrogate model, the regularized minimal-energy tensor product with cubic Hermite splines is utilized as a fitness estimation of design. In diversification, an accelerated driving-training-based optimization is presented to determine N remarkable designs from the design space. In intensification, a reinforced optimal computing budget allocation is used to find an extraordinary design from the N remarkable designs. The DTOO approach is applied to a medical resource allocation problem in the emergency department. Simulation results obtained by the DTOO approach are compared with three heuristic approaches to examine the performance of the DTOO approach. Test results show that the DTOO approach obtains an extraordinary design with higher solution quality and computational efficiency than the three heuristic approaches.