An Adaptive Sampling Algorithm for Simulation-Based Optimization With Descriptive Complexity Preference

Abstract

Many systems nowadays follow not only physical laws but also manmade rules. These systems are known as discrete-event dynamic systems (DEDSs), where simulation is the only faithful way for performance evaluation. Due to various advantages in practice, designs (or solution candidates) with low descriptive complexity (called simple designs) are usually preferred over complex ones when their performances are close. However, the descriptive complexity (DC) is usually nonlinear and takes discrete value, which makes traditional methods such as linear programming and gradient-based local search not applicable. Existing methods for simulation-based optimization (SBO) do not explore the preference on descriptive complexity and thus cannot solve the problem efficiently. The major contributions of this paper are to point out the importance of considering SBO problems with DC preference, and to develop an adaptive sampling algorithm (ASA) to find the simplest good design. It is shown that ASA terminates within finite iterations and with controllable probability of making mistake. The computational complexity of ASA and its dependence on various parameters are discussed. ASA is then applied to three parameter optimization problems and a node activation policy optimization problem in a wireless sensor network. Numerical results show that ASA is more efficient than blind picking and Levin search in most cases. We hope this work can shed some insight to how to find simple and good designs in general.