Coarse-to-fine evolutionary search for large-scale multi-objective optimization: An application to ratio error estimation of voltage transformers

Multi-objective optimization problems (MOPs) are commonly confronted in various fields, such as condition monitoring for renewable energy systems, and ratio error estimation of voltage transformers. With the increase in decision variables of MOPs, their exponentially growing search spaces are challenging for existing evolutionary algorithms. To handle this challenge, this paper suggests a coarse-to-fine large-scale evolutionary multi-objective search, called CF-LEMO. In the coarse search phase, CF-LEMO performs evolutionary search on both the original and transformed large-scale MOPs alternately, accelerating the population to approach the Pareto-optimal fronts. In addition, to alleviate the issue of diversity loss, we design a diversity preservation mechanism to preserve a well-distributed archive to support subsequent fine search. In the fine search stage, CF-LEMO conducts local search on the current population to mine high-quality solutions, which are used to update the population and archive. Then, based on the archive, the multi-objective optimization based on decomposition is employed to evolve all decision variables, so as to obtain a population with good convergence and diversity near the Pareto-optimal fronts. To assess the effectiveness of the proposed CF-LEMO, we compare its performance against four representative baseline algorithms on a benchmarks suite LSMOP1-LSMOP9 with 2 and 3 objectives. The empirical results confirm its super performance by significanlty outperforming all the four competitors on 12 out of 18 benchmarks. Moreover, the experiments demonstrate the superior performance of CF-LEMO in sovling multi-objective ratio error estimation problems with up to 6,000 decision variables.