Research On Evolutionary Many-Objective Optimization Algorithms

Most real-world problems in the field of science, engineering, and business management are multiobjective optimization problems (MOPs), and multiple objectives usually conflict with each other. It is recognized that evolutionary algorithms (EAs) are possibly well-suited to MOPs. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single simulation run. Secondly, EAs have the ability to handle complex problems, involving features such as discontinuities, multimodality, disjoint feasible spaces and noisy function evaluations, therefore, over the past decade, EAs have been extensively and successfully applied to resolve MOPs.So far, many multi-objective evolutionary algorithms (MOEAs) are widely established and well developed for problems with two or three objectives, and they can obtain encouraging results. Howerver, some multi-objective evolutionary algorithms, such as the nondominated sorting genetic algorithm II (NSGA-II) or strength Pareto evolutionary algorithm 2 (SPEA2), have been shown to not suited to solving optimization problems with more than three objectives involving poor performance and difficulties to get satisfied solutions, which have been termed many-objective optimization problems by Farina and Amato.Many optimization problems in real-world consist of a large number of objectives and there also have complex correlations among these objectives. It is urgent to extend evolutionary algorithms to many-objective optimization to resolve various engineering design optimization problems.In this dissertation, we focus on the study of evolutionary algorithms for solving many-objective optimization problems, and explore their application approaches, ways and means to effectively address many-objective optimization problems. The main contents and innovations of the dissertation are summarized as follows:1. In this dissertation, the behavior of many-objective evolution is examined throught computational experiments on multiobjective 0/1 knapsack problems and DTLZ test functions using NSGA-Ⅱ, and the reasons which result in the difficulties of evolutionary multi-objective optimization are revealed. The behavior of a minor change of NSGA-Ⅱfor many-objective problems is also examined, it is the assignment of a zero distance (instead of an infinity distance) to extreme solutions with maximum or minimum objective values as the crowding distance. In addition, a change using the weighted average ranking (RWAR) to repalce Pareto-dominance to improve NSGA-Ⅱis made, and thus, the algorithm RWAR-NSGA-II is constructed. The new algorithm is examined throught experiments on multiobjective 0/1 knapsack problems and DTLZ test functions. The experimental results show that the convergence of RWAR-NSGA-II is improved for many-objective problems, yet, this improvement is realized at the cost of diversity.2. Furthermore, the evolution of comparison relations in many-objective optimization spaces is investigated in the dissertation. It analyzes the properties of favour relation, and also compares its behavior with dominate through simulation experiments. The experimental results show that the former is able to enhance search abilities than the latter in many-objective optimization problems, and thus, favour relation can improve the convergence of EAs. The dissertation also examinesε-preferred relation, and comparesε-preferred with favour through some experiments. The experimental results show that the former is more robust than the latter in high dimensional spaces. The strategy of adjusting the individuals’ dominating regions is also examined through some experiments. The experimental results show that this strategy is effective in high-dimensional objective spaces. This dissertation also explores the winning scores mechanism and average ranking method which are very different in form, and the equivalence between the former and the latter has been proven.3. This dissertation examines two solutions can be close to the situation where one solution Pareto-dominates the other, and it measures this kind of closeness and use such measurements instead of the crowding distance for the secondary ranking in the NSGA-Ⅱalgorithm. The degree, by which a solution is nearly-dominated by the other, is measured with subvector dominance,δ-dominance and subobjective dominance count in the dissertation, respectively. These three measurement mechanisms are respective to replace the crowding distance in NSGA-Ⅱand thus three modified NSGA-Ⅱs are constructed. The modified NSGA-Ⅱs and the original NSGA-Ⅱare examined together on DTLZ test functions, and the experimental results show that both convergence and diversity of the modified NSGA-Ⅱs are improved comparing to the original NSGA-Ⅱ. And the dissertation also indicates two promising strategies for the application of NSGA-Ⅱto many-objective optimization problems.4. The dissertation defines a new comparison relation:Σ-dominance, which is based on ranks reevaluation functions. In this dissertation,Σ-dominance relation is used to substitute Pareto-dominance in MOEAs to construct the hybrid many-objective evolutionary algorithm:HMOEA. One characteristic of the new algorithm is adaptive, which is reflected in the fact that the next population composition varies with the current generation. Some properties ofΣ-dominance relation are investigated in the dissertation, and HMOEA,COGA and NSGA-II are examined together through DTLZ test functions to observe their behavior in many-objective optimization problems. Experimental results indicate that with respect to theΣ-dominance relation in hybrid many-objective evolutionary algorithm, a satisfied balance between convergence and diversity has been achieved. The idea is simply to increase diversity maintenance gradually during generations. The results also show that theΣ-dominance relation appears to be a promising alternative to the Pareto-dominance relation in many-objective optimization. The dissertation also analyzes the convergence of HMOEA, and the process of analysis illustrates that the probability of the convergence of the HMOEA equals to 1.