Adaptive differential evolution with a Lagrange interpolation argument algorithm

Abstract Differential evolution (DE) is a simple yet powerful evolutionary algorithm that has been used to solve various complex optimization problems in numerous engineering fields. However, DE has some problems, such as premature convergence and sensitivity to parameter settings. To improve the performance of DE and extend its application, an adaptive differential evolution with the Lagrange interpolation argument algorithm (ADELI) is proposed in this paper. To accelerate the convergence speed of DE, a local search with Lagrange interpolation (LSLI) is introduced into DE. LSLI performs a local search in the neighborhood of the best individual in the current generation to enhance the exploitation capability of DE. Meanwhile, an adaptive argument strategy is presented to adaptively determine whether to use LSLI in terms of its performance in the previous generation, which can balance the global exploration capability and the local exploitation capability of ADELI. To verify the feasibility and effectiveness of ADELI, 30 test functions in the CEC 2014 benchmark sets with different dimensions were simulated. Moreover, a path synthesis problem was also optimized. The results demonstrated that ADELI considerably outperforms other EAs in most functions and obtains the most accurate solution among the compared algorithms in the application of path generation.