Research On Differential Evolution Algorithm For Solving Global Optimization Problems

How to effectively solve the global optimization problem always is inevitable in scientific research and engineering practice. With the continuous development of economy, science and technology, the global optimization problems arising in scientific and engineering areas often can be characterized as non-convexity, discontinuity, non-differentiability and multi-modality, and they are becoming increasingly complex. Thus solving these optimization problems through traditional derivative-based methods is becoming a great challenge task. Inspired by nature selection and survival of the fittest, a lot of derivative-free population-based intelligent evolutionary algorithms(EAs) have been proposed, which have shown great potential to handle these complex optimization problems. At present, EAs have been very widely used in many fields.Differential evolutionary algorithm(DE for short) is a branch of EAs. Due to its outstanding characteristics, such as compact structure, ease to use and robustness, DE has captured much attention and has been applied to solve many practical optimization problems since its invention. Although DE has been proposed 20 years, there are still some problems to be studied and solved, such that it easily falls into local optimum and causes premature convergence or stagnation. To address these concerning issues and increase the universality, efficiency and robustness of DE, in this thesis, we propose two improved DE variants for solving global optimization are proposed. The main contributions are summarized as follows:1. Generally, the original DE and many DE variants only evolve one population by using certain kind of DE operators. However, as observed in nature, the working efficiency can be improved by using the concept of work specialization. It means that the entire group should be divided into several sub-groups, which are responsible for different tasks according to their capabilities. Inspired by this phenomenon, an adaptive differential evolution algorithm with novel mutation strategies in multiple sub-populations is designed, named MPADE, in which the parent population is split into three sub-populations based on the fitness values and then three novel DE strategies respectively perform in different sub-populations to take on the responsibility for either exploitation or exploration. Furthermore, a simple yet effective adaptive approach is designed for parameter adjustment in the three DE strategies and a replacement strategy is put forward to fully exploit the useful information from the trial vectors and target vectors. The results of simulation experiments conducted on 55 benchmark functions and 15 real world optimization problem demonstrate that MPADE is better than many state-of-the-art DE variants.2. JADE and CoDE are two well-known state-of-the-art DE algorithms for solving global optimization problems(GOPs). JADE is found to be suitable for solving unimodal and simple multimodal functions as an exploitation mutation strategy, i.e., “DE/current/to-pbest”, is employed. While CoDE is shown to fit for handling complicated multimodal functions due to its exploration mutation strategies, such as “DE/rand/1/bin”, “DE/currant-to-rand/1”, and “DE/rand/2/bin”. To further improve the comprehensive optimization performance of DE, in this dissertation, we firstly modify JADE and CoDE, yielding MJADE and MCoDE, which further enhance the exploitation ability of JADE and exploration ability of CoDE respectively. Moreover, to combine their merits of MJADE and MCoDE for tackling different types of GOPs, a novel hybrid framework is designed based on MJADE and MCoDE, and a novel hybrid differential evolution algorithm is proposed, named HMJCDE. The results of simulation experiment conducted on 30 benchmark functions demonstrate that MJADE and MCoDE is better than JADE and CoDE respectively, and HMJCDE is better than MJADE, MCoDE and many other state-of-the-art DE variants.