A hybrid evolutionary algorithm with simplex local search

Presented in this paper is a hybrid algorithm simplex search enabled evolutionary algorithm (SSEA) which is fundamentally an evolutionary algorithm (EA) embedded with a local simplex search for unconstrained optimization problems. Evolutionary algorithms have been quite successful in solving a wide class of intractable problems and the Non-dominated Sorting Genetic Algorithm (NSGA-II) is a popular choice. However, like any other evolutionary algorithms, the rate of convergence of NSGA-II slows down with generations and often there is no improvement in the best candidate solution over a number of generations. The simplex search component comes into effect once the basic evolutionary algorithm encounters a slow rate of convergence. To allow exploitation around multiple promising regions, the simplex search is invoked from multiple promising regions of the variable space identified using hierarchical agglomerative clustering. In this paper, results are presented for a series of unconstrained optimization test problems that cover problems with a single minimum, a few minima and a large number of minima. Provided is a comparison of results with NSGA-II, Fast Evolutionary Strategy (FES), Fast Evolutionary Programming (FEP) and Improved Fast Evolutionary Programming (IFEP) where it's clear that SSEA outperforms all other algorithms for unimodal problems. On the suite of problems with large number of minima, SSEA performs better on some of them. For problems with fewer minima, SSEA performs better than FES, FEP and IFEP while demonstrating comparable performance to NSGA-H.