# Multi-Population Differential Evolution Algorithm with Uniform Local Search
###### Abstract  
Differential evolution (DE) is a very effective stochastic optimization algorithm based on population for solving various real-world problems. The quality of solutions to these problems is mainly determined by the combination of mutation strategies and their parameters in DE. However, in the process of solving these problems, the population diversity and local search ability will gradually deteriorate. Therefore, we propose a multi-population differential evolution (MUDE) algorithm with a uniform local search to balance exploitation and exploration. With MUDE, the population is divided into multiple subpopulations with different population sizes, which perform different mutation strategies according to the evolution ratio, i.e., DE/rand/1, DE/current-to-rand/1, and DE/current-to-pbest/1. To improve the diversity of the population, the information is migrated between subpopulations by the soft-island model. Furthermore, the local search ability is improved by way of the uniform local search. As a result, the proposed MUDE maintains exploitation and exploration capabilities throughout the process. MUDE is extensively evaluated on 25 functions of the CEC 2005 benchmark. The comparison results show that the MUDE algorithm is very competitive with other DE variants and optimization algorithms in generating efficient solutions.  
differential evolution; multiple strategies; multiple population; soft island model; uniform local search +
Footnote †: journal: Applied sciences  
is randomly assigned to different domains of space in the process of evolution. According to the domain characteristics, appropriate operations and parameters are allocated to the corresponding domain in order to facilitate search efficiency.  
Motivated by these investigations, a novel multi-population DE algorithm, the multi-population differential evolution algorithm with uniform local search (MUDE), was proposed. With MUDE, the whole population is separated into multiple subpopulations with the stochastic method. The best mutation operator is assigned to the subpopulation according to the evolution ratio of each subpopulation. Information migration between subpopulations is performed according to the soft island model to improve population diversity. After the subpopulation has evolved, the best solution for each subpopulation is performed with a uniform local search (UL) to improve solution precision. To analyze the efficiency of MUDE, 25 functions of CEC 2005 with 30 dimensions were extensively conducted. Extensive statistical results revealed that MUDE is an effective and competitive DE revision.  
The main objectives of the proposed MUDE include the following:  
1. A novel multi-population DE with multi-strategies is proposed to solve multi-modal problems.
2. The soft-island model is applied to exchange information between subpopulations for improving population diversity.
3. The uniform local search is used to improve the local search capability of the population.  
The remainder of this paper is organized as follows. Section 2 introduces DE. Section 3 reviews the related work. Our proposed DE algorithm, MUDE, is presented in detail in Section 4. Section 5 gives the experimental results. Section 6 is the conclusions and future work.