Multi-surrogate multi-tasking optimization of expensive problems

Abstract

Multiple surrogates can be trained in surrogate-assisted optimization of expensive problems to describe different characteristics of the real fitness landscape. It has been shown that optimization assisted by multiple surrogate models are beneficial compared to a single surrogate. Along this line of research, we propose to train two surrogate models, one global surrogate model trained using all available data, and the other one local surrogate model trained using only part of the data subsequently selected from the data sorted according to an ascending order of the objective value. Different from most existing multi-surrogate based approaches, however, we adopt the multi-tasking optimization framework to accelerate the convergence by regarding the two surrogates as two related tasks. This way, two optimal solutions found by the multi-tasking algorithm will be evaluated using the real expensive objective function, and consequently, both the global and local models will be updated. This process repeats until the allowed computational budget is exhausted. Experiments are conducted on twelve widely used benchmark problems of up to 200 dimensions to examine the performance of the proposed algorithm. Our results show that the proposed method is very competitive, has quick convergence and scales well with the increase in the number of decision variables for solving computationally expensive single-objective optimization problems.