A Simulated Annealing Algorithm for Noisy Multiobjective Optimization

This paper presents a new simulated annealing (SA) algorithm for noisy multiobjective optimization with continuous decision variables. A novel feature of the algorithm in the context of SA is that the performance of a candidate solution is determined by estimating the probabilities that the candidate is dominated by the current non-dominated solutions. The sum of these probabilities provides a scalar performance measure that is used to determine the acceptance of the candidate as the current solution and whether the candidate is inserted into the non-dominated set. The second novel feature of the algorithm is the technique utilized for generating candidate solutions. Empirical probability distributions for sampling the new values of the decision variables are constructed on the basis of the values of the variables in the current non-dominated set. Thus, the information contained by the non-dominated set is utilized to improve the quality of the generated candidates, whereas this information is ignored in the existing multiobjective SA algorithms. The proposed algorithm is compared with a reference state-of-the-art evolutionary algorithm as well as two other SA algorithms in numerical experiments involving 16 problems from commonly applied test suites. The proposed algorithm performs as good or better compared with the reference algorithms in majority of the experiments and therefore represents a promising solution method for noisy multiobjective optimization problems. Copyright (C) 2012 John Wiley & Sons, Ltd.