A Smoothing Evolutionary Algorithm with Circle Search for Global Optimization

There are many global optimization problems arisen in various fields of applications. It is very important to design effective algorithms for these problems. However, one of the key drawbacks of the existing global optimization methods is that they are not easy to escape from the local optimal solutions and can not find the global optimal solution quickly. In order to escape from the local optimal solutions and find the global optimal solution fast, first, a smoothing function, which can flatten the landscape of the original function and eliminate all local optimal solutions which are no better than the best one found so far, is proposed. This can make the search of the global optimal solution much easier. Second, to cooperate the smoothing function, a tailor-made search scheme called circle search is presented, which can quickly jump out the flattened landscape and fall in a lower landscape quickly. Third, a better solution than the best one found so far can be found by local search. Fourth, a crossover operator is designed based on uniform design. Based on these, a smoothing evolutionary algorithm for global optimization is proposed. At last, the numerical simulations for eight high dimensional and very challenging standard benchmark problems are made. The performance of the proposed algorithm is compared with that of nine evolutionary algorithms published recently. The results indicate that the proposed algorithm is statistically sound and has better performance for these test functions.