Global optimization using the asymptotically independent Markov sampling method

Abstract

In this paper, we introduce a new efficient stochastic simulation method, AIMS-OPT, for approximating the set of globally optimal solutions when solving optimization problems such as optimal performance-based design problems. This method is based on Asymptotically Independent Markov Sampling (AIMS), a recently developed advanced simulation scheme originally proposed for Bayesian inference. This scheme combines importance sampling, Markov chain Monte Carlo simulation and annealing for efficient sampling from an arbitrary target distribution over a multi-dimensional space. Instead of a single approximation of the optimal solution, AIMS-OPT produces a set of nearly optimal solutions where the accuracy of the near-optimality is controlled by the user. Having a set of nearly optimal system designs, for example, can be advantageous in many practical cases such as when there exists a whole set of optimal designs or in multi-objective optimization where there is a Pareto optimal set. AIMS-OPT is also useful for efficient exploration of the global sensitivity of the objective function to the design parameters. The efficiency of AIMS-OPT is demonstrated with several examples which have different topologies of the optimal solution sets. Comparison is made with the results of applying Simulated Annealing, a well-known stochastic optimization algorithm, to the three two-dimensional problems.