Subset simulation for unconstrained global optimization

摘要

Global optimization problem is known to be challenging, for which it is difficult to have an algorithm that performs uniformly efficient for all problems. Stochastic optimization algo rithms are suitable for these problems, which are inspired by natural phenomena, such as metal annealing, social behavior of animals, etc. In this paper, subset simulation, which is originally a reliability analysis method, is modified to solve unconstrained global optimiza tion problems by introducing artificial probabilistic assumptions on design variables. The basic idea is to deal with the global optimization problems in the context of reliability anal ysis. By randomizing the design variables, the objective function maps the multi-dimen sional design variable space into a one-dimensional random variable. Although the objective function itself may have many local optima, its cumulative distribution function has only one maximum at its tail, as it is a monotonic, non-decreasing, right-continuous function. It turns out that the searching process of optimal solution(s) of a global optimi zation problem is equivalent to exploring the process of the tail distribution in a reliability problem. The proposed algorithm is illustrated by two groups of benchmark test problems. The first group is carried out for parametric study and the second group focuses on the sta tistical performance.