Research On Correlation Guided Many-Objective Evolutionary Optimization

There are many multi-objective optimization problems in the real world. In these problems, at least one conflict exists between the objectives. Therefore, the result of multi-objective optimization is not a unique optimum but a solution set containing many non-dominated solutions which cannot be distinguished according to quality. As a swarm intelligent search method, evolutionary algorithms can find multiple approximate optima, and thus fit to deal with multi-objective problems.However, many multi-objective problems, namely, many-objective problems, contain more than three objectives. In these problems, the proportion of non-dominated solutions increases rapidly with the increase in the number of objectives according to Pareto dominance. The conventional multi-objective evolutionary algorithms cannot distinguish numerous non-dominated solutions, and thus cannot approximate the optimal solution set fast and accurately. Therefore, it is necessary to research on evolutionary algorithms for many-objective problems.In many-objective problems, the relationships among the objectives are more intricate because not only more conflicts could exist in the objectives but also no conflicts could exist in some objectives and even some objectives can stimulate each other. In addition, as key ingredients in multi-objective evolutionary algorithms, selection strategies and variation operators have significant impacts on performance of the algorithms. Thus, we commence from the correlations between the objectives to reduce the number of objectives by combining the conflict-free objectives into one, and distinguish some non-dominated solutions. Then, research on evolutionary algorithms for many-objective optimization problems, from the perspectives of selection strategies and variation operators.The main research work and innovation are shown as follows:1) The dissertation reviews the research status of evolutionary multi-objective optimization, introduce the basic concepts on multi-objective optimization. Meanwhile, it introduces the research focus and points out the shortages in the current many-objective optimization.2) The dissertation expounds the roles played by three key ingredients in multi-objective evolutionary algorithms and proposes a new performance indicator to evaluate the distribution of non-dominated solution over the objective space. The indicator is inspired from the representation of non-dominated solutions on parallel coordinate, and evaluates how evenly and broadly the solutions are scattered along the discovered front simultaneously. 3) An objective reduction technique is proposed aiming at many-objective optimization problems. There are a few methods for solving many-objective optimization problems. Among them, objective reduction methods have been turned out to be an effective technique. However, some of them have a high time-complexity and are not apt to be implemented. Thus, there are only a few researches focusing on online objective reduction. To tackle with this problem, we use correlation coefficient to analysis the relations among the objectives and reduce the number of objectives by combining the conflict-free objectives into one, and finally distinguish some non-dominated solutions. The method has a lower time-complexity than some other approaches, and thus fit for online objective reduction. The dissertation does not only prove its feasibility in theory, but also validate its effectiveness by experiments.4) A framework of many-objective evolutionary optimization is proposed based on objective reduction. To investigate the effectiveness of the framework, NSGA-II (non-dominated sorting genetic algorithm â…¡) and IBEA (indicator-based evolutionary algorithm) are embedded into the framework and examined on several many-objective test instances. The experimental results show that objective reduction method can improve the convergence significantly. Thus, the proposed algorithm framework is an effective approach to solve many-objective optimization problems.5) Multi-selection strategy is proposed and integrated with the proposed algorithm framework to solve many-objective optimization problems. Selection strategy is a key ingredient in multi-objective evolutionary algorithms. Different selection strategies have their own advantages and disadvantages. Moreover, the ability of single selection strategy to adjust selection pressure is limited. Therefore, we proposed multi-selection strategy. In multi-selection strategy, non-dominated sorting incorporating with crowding distance selection and indicate-based selection are selected exclusively for one generation in a preset probability. In addition, the calculation of crowding distance and the procedure of indicate-based selection are modified to fit many-objective optimization from the view of reducing dominance resistant solutions. The experimental results show that the methods can utilize the advantages and disadvantages of the two selection strategies, and reach a better balance between the convergence and distribution performance.6) A many-objective optimization algorithm is designed based on self-adaptive K-order differential evolution and objective reduction. Variation operators are also key ingredients in multi-objective evolutionary algorithms. The variation operator in differential evolution is an integration of crossover and mutation with a powerful search ability, and fit for multi-objective evolutionary optimization. The way to construct differential vector has a significant impact on the convergence of the algorithm as well as the values of crossover probability and scaling factor. Therefore, we commence the research from two aspects. First, inspired from K-order differential equation, K-order differential evolution is proposed. K-order differential expands the concept of differential mutation in differential evolution. Second, self-adaptive parameter strategy is embedded into K-order differential evolution, and a self-adaptive K-order differential evolution for multi-objective optimization is presented. Finally, the algorithm is integrated with the algorithm framework for many-objective evolutionary optimization. The experiment aiming at multi-objective K-order differential evolution shows that2-order differential evolution is better than1-order differential evolution. The experiment aiming at self-adaptive multi-objective K-order differential evolution shows that self-adaptation in parameters can not only avoid the frequent tuning, but also obtain the results close to or better than the results with best parameters. The experimental results on many-objective test instances show that self-adaptive many-objective K-order differential evolution performs better than the opponents according to convergence and distribution.