Autonomous Differential Evolution Algorithm:Design And Application

A large number of optimization problems exist in scientific research and engineering application areas. These problems have many complexities. For example, the objective functions have many decision variables and local optimum, and they are usually discontinuous, non-derivable and highly nonlinear. When tackling these problems, traditional optimization methods face great challenges and can not provide satisfactory results. The intelligence optimization methods, inspired by the phenomenon and mechanisms in nature, provide a new tool for solving complex optimization problems, due to the features of nonsensitive to the type of objective function, easy to use, good optimization performance and high efficiency. Among various intelligence optimization approaches, differential evolution (DE), with unique variation operation, few control parameters, easy to implement and low complexity, is a good candidate for function optimization and engineering optimization problems in continuous space. DE has been a hotspot in intelligence optimization or even natural science area. Although possessing many merits, DE still has some shortcomings. It is difficult to set proper parameter values and choose appropriate mutation operator, and its performance is unsatisfactory when solving more complex problems. As a result, researchers have made deep studies. In spite of plentiful works exist in literature; there is still much room to improve DE performance and it is worth further study.DE is a stochastic search optimizer in which the configuration determines the search behavior during the search process. For a specific problem, selecting a proper configuration is quite difficult; meanwhile, the search environment varies along with the search process. Therefore, fixed configuration could not produce satisfactory results especially for a complex problem. To handle this deficiency, this paper proposes a new design method called autonomous DE to enhance DE performance. This method introduces a bypass chain composed of evaluation unit and decision unit into DE. By using the evaluation unit to quantify certain information and then feeding back the information to the decision unit, the configuration of an algorithm can be autonomously and dynamical adjusted; hence, a maximized performance can be obtained under a certain computational resource. This adjustment procedure has an evident closed-loop feature and it does not need any interventions from the users, which makes an algorithm more adaptable to a complex problem. This ideal is not only helpful to improve DE performance, but also provides an important reference for other intelligence optimizers. By instantiating the type of feedback information, the evaluation unit and the decision unit, good DE variants can be designed.Based on the framework of autonomous DE, this paper defines four types of feedback information, including individual information, operator information, parameter information and search status information, and designs evaluation and decision units from the perspectives of distributed population structure, static and dynamic operator management and membrane algorithms. On this basis, six autonomous DE variants are proposed for single objective and multi-objective optimization problems, i.e., distributed DE with multicultural migration, DE based on Tissue P systems, multicriteria adaptive DE, population P systems based DE, grid-based adaptive multi-objective DE, and indicator-based adaptive DE. A large number of benchmark problems are employed to test algorithm performance. Experimental results show that the proposed algorithms are superior to many recently published algorithms in terms of several criteria.To further verify the practical application performance of the proposed autonomous DE algorithms, this paper applies two proposed algorithms to solve two engineering problems, including proton exchange membrane fuel cell modeling, and environmental/economic dispatch problems in power systems. The former one transforms the proton exchange membrane fuel cell modeling problem as a parameter identification problem and applies multicriteria adaptive DE to solve this problem. The later one models the environmental/economic dispatch problem as a two-objective parameter optimization problem and applies indicator-based adaptive DE to solve this problem. The simulating results on several cases show that the two autonomous DE algorithms produce satisfactory results.