Surrogate assisted Simulated Annealing (SASA) for constrained multi-objective optimization

Real life optimization problems often involve a tradeoff between multiple objectives. They also comprise constraints, which may be due to various factors such as the strength of materials, stability and safety of design, limits on operational time, financial viability and many others. In recent years, Evolutionary Algorithms (EAs) have been a popular choice for solving such multi-objective, constrained problems for various reasons. Point to point search methods, such as Simulated Annealing (SA) have been largely unexplored for such problems. However, some recent studies have suggested that with certain enhancements, SA can also be an effective tool to deal with such problems. The ability of SA to accept uphill moves (unlike EAs) during the search makes it a less prone to getting trapped in a local minimum, and is therefore attractive for solving optimization problems. For many engineering design problems, evaluating a candidate solution can be computationally intensive. This can often put a restriction on the number of function evaluations to find a near optimum solution. To mitigate this problem, often suitable approximations (surrogates) are used in optimization instead of real function evaluations. Surrogate assisted approaches have so far been used in the paradigm of Evolutionary Algorithms (EA). In this paper, we extend the use of surrogates to another well known heuristic, Simulated Annealing (SA), for constrained, multi-objective problems. A comparison with currently prevalent EAs on a difficult set of constrained problems has been included in order to highlight the efficacy of the proposed approach.