Solving constrained optimization problems via Subset Simulation

This paper extends the application of Subset Simulation (SS), an advanced Monte Carlo algorithm for reliability analysis, to solve constrained optimization problems encountered in engineering. The proposed algorithm is based on the idea that an extreme event (optimization problem) can be considered as a rare event (reliability problem). The Subset Simulation algorithm for optimization is a population-based stochastic global optimization approach realized with Markov Chain Monte Carlo and a simple evolutionary strategy, and so it does not require initial guess or gradient information. The constraints are handled by a priority-based fitness function according to their degree of violation. Based on this constraint fitness function, a double-criterion sorting algorithm is used to guarantee that the feasible solutions are given higher priority over the infeasible ones. Four well studied constrained engineering design problems in the literature are studied to investigate the efficiency and robustness of the proposed method. Comparison is made with other well-known stochastic optimization algorithms, such as genetic algorithm, particle swarm optimization and evolutionary strategy.