A Multi-Surrogate Assisted Multi-Tasking Optimization Algorithm for High-Dimensional Expensive Problems

Surrogate-assisted evolutionary algorithms (SAEAs) are widely used in the field of high-dimensional expensive optimization. However, real-world problems are usually complex and characterized by a variety of features. Therefore, it is very challenging to choose the most appropriate surrogate. It has been shown that multiple surrogates can characterize the fitness landscape more accurately than a single surrogate. In this work, a multi-surrogate-assisted multi-tasking optimization algorithm (MSAMT) is proposed that solves high-dimensional problems by simultaneously optimizing multiple surrogates as related tasks using the generalized multi-factorial evolutionary algorithm. In the MSAMT, all exactly evaluated samples are initially grouped to form a collection of clusters. Subsequently, the search space can be divided into several areas based on the clusters, and surrogates are constructed in each region that are capable of completely describing the entire fitness landscape as a way to improve the exploration capability of the algorithm. Near the current optimal solution, a novel ensemble surrogate is adopted to achieve local search in speeding up the convergence process. In the framework of a multi-tasking optimization algorithm, several surrogates are optimized simultaneously as related tasks. As a result, several optimal solutions spread throughout disjoint regions can be found for real function evaluation. Fourteen 10- to 100-dimensional test functions and a spatial truss design problem were used to compare the proposed approach with several recently proposed SAEAs. The results show that the proposed MSAMT performs better than the comparison algorithms in most test functions and real engineering problems.