A simulated annealing algorithm for constrained Multi-Objective Optimization

Abstract

In this paper, we introduce a simulated annealing algorithm for constrained Multi-Objective Optimization (MOO). When searching in the feasible region, the algorithm behaves like recently proposed Archived Multi-Objective Simulated Annealing (AMOSA) algorithm [1], whereas when operating in the infeasible region, it tries to minimize constraint violation by moving along Approximate Descent Direction (ADD) [2]. An Archive of non-dominated solutions found during the search is maintained. The acceptance probability of a new point is determined by its feasibility status, and its domination status as compared to the current point and the points in the Archive. We report the performance of the proposed algorithm on a set of seven constrained bi-objective test problems (CTP2 to CTP8), which have been known to pose difficulties to existing multi-objective algorithms. A comparative study of current algorithm with the widely used multi-objective evolutionary algorithm NSGA-II has been included.