| The use of evolutionary algorithms (EAs) to solve problems of this nature has been motivated mainly because of the population-based nature chosen and genetic. Its main character is the search strategy and the exchange between individuals. What's more, it is particularly appropriate for dealing with the problems that traditional search methods are difficult to tackle and nonlinear problems and can be widely used in the areas of combinatorial optimization, machine learning, adaptive control, planning and design and Artificial Life. With the multi-objective evolutionary algorithm in solving practical problems efficiently, more and more researchers get into multi-objective evolutionary research field. How to construct the non-dominated set can mostly affect the efficiency and performance of the GA algorithms. In this paper, we introduce a new non-dominated sorting algorithm based on Pareto optimal solutions which alleviates the problem of high computational complexity in NSGA-II. We use the Arena Principle in NSGA-II to retain the non-dominated solutions found during the evolutionary process. The main goal of this work is to keep the fast convergence exhibited by Arena Principle in global optimization when extending this heuristic to multi-objective optimization. The algorithm's computational complexity is O (rmN)Firstly, we introduce the GA's origins, its basic conceptions, general research circumstances and some foundation theories of GA. We address all of these issues and discuss the adequacy of these problems as real test problems, and we propose two methods of constructing the Pareto non-dominated set:Arena Principle evolutionary algorithm and the algorithm based on Arena Principle andε-Pareto parameter. Based on these test solutions, we find that Arena Principle is able to get much better spread of solutions than NSGA-Ⅱ. The results of this paper are important for various reasons and should encourage readers to find more applications using Arena Principle. |
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