Applying Memetic algorithm with Improved L-SHADE and Local Search Pool for the 100-digit challenge on Single Objective Numerical Optimization

In this paper, we have proposed a new optimization algorithm, Memetic improved L-SHADE with a local search pool, MiLSHADE-LSP, a memetic algorithm that combines an improved L-SHADE with a local search pool. Improved L-SHADE modifies several important parameters during the run to encourage exploration in initial stages and to focus later the search around the most promising solutions. The local search pool is responsible to continuously improve the best solutions. MiLSHADE-LSP uses a pool of two different local search, LS, methods, the Broyden-Fletcher-Goldfarb-Shanno method with limited memory, L-BFGS-B, and the Solis-Wets algorithms, with an adaptive mechanism to choose which one of them is applied in each iteration selecting which had obtained a greater improvement last time it was applied. In order to avoid waste LS applications, the proposed algorithm stores a list of individuals that were not previously improved by each LS method. It also includes a restart mechanism to explore new areas when the search is stuck, restarting the population but maintaining the best found solution, and resetting the LS Pool parameters. In the experimental section we have tested and analyzed MiLSHADE-LSP using the proposed benchmark for the competition 100-digit challenge on Single Objective Numerical Optimization, obtaining that the LS Pool improves the algorithm, both achieving more optima and with a better performance. Results obtained show that MiLSHADE-LSP is a very competitive algorithm.