Simulation Assisted Evolutionary Algorithms for Stochastic Optimization

Stochastic optimization is a well-known challenging research topic. As of the literature, simulation-assisted optimization is a popular approach for solving stochastic optimization problems, in which the simulation and optimization approaches are applied independently with very little interaction between them. For it, the main challenge is to obtain high quality stochastic solutions, by minimizing computational cost to a reasonable level. Furthermore, reliability of the solutions of such problems is a vital requirement, especially for studies under worst-case scenarios. The objective of this thesis, is to propose a number of new simulation budget control strategies that improve the effectiveness of Simulation-assisted Evolutionary Algorithms, and to also provide a reliable framework in the presence of stochastic constraints. The algorithm is known as Simulation Optimization (Sim-Opt) Algorithm. This thesis considers Stochastic Constrained Optimization Problems (SCOPs), while Monte-Carlo Simulation (MCS) is considered as the simulation approach and Differential Evolution (DE) as the optimization approach. Chance Constrained Programming (CCP) is also considered as an alternative approach for handling constraints’ uncertainty for SCOPs. However, the main emphasis is to reduce the simulation budget in the Sim-Opt approach and to provide reliable and high fidelity solutions. Firstly, a novel Computational Budget Control (CBC) scheme is designed to reduce the computational cost in the proposed Simulation-assisted Differential Evolution (Sim-DE) algorithm, by maintaining an appropriate level of solution fidelity. Secondly, an Adaptive Segment Based Scheme (ASBS) is proposed for effective allocation of the simulation budget in the Sim-DE algorithm. Thirdly, a new two-stage Sim-DE with Reliable CCP (RCCP) algorithm (two-stage DE-CCP/RCCP) is proposed to deal with stochastic parameters in constraints. The performance of the proposed algorithms is compared with other state-of-the-art simulation budget allocation techniques, by solving a modified set of IEEE-CEC’2006 test problems and a wind-thermal power system application. The experimental results reveal that the first two algorithms are able to substantially reduce the simulation budget, with an insignificant effect on solution fidelity. While the third algorithm’s experimental results showed, that it is able to provide solutions with minimum possible infeasibility risk levels and high reliability levels