Research On ε-dominance Multi-Objective Evolutionary Algorithms In The Application Of Optimization Problems

Many real-world optimization problems consist of several conflicting objectives, the solutions of which are called the Pareto-optimal set. During the last decade, most evolutionary algorithms have been utilized to find an approximation of the Pareto-optimal set. However, the approximation set must possess solutions with higher convergence towards the Pareto-optimal set and better diversity.Many studies have used different ways of evolutionary algorithms to approach the Pareto-optimal front with a wide diversity among the solutions. However, most multi-objective evolutionary algorithms (MOEAs) are either good for achieving a well-distributed solutions at the expense of a large computationally effort or computationally fast at the expense of achiving a not-so-good distribution of solutions.The subject of this thesis is to propose a fast and steady MOEA (I-MOEA), and improve the existing MOEAs (NAGA-II).The I-MOEA algorithm is based on ε -dominance concept which proposed by Deb.The algorithm uses elitist strategy and archive update strategy, and hyper-grids division measure and G vector dominance strategy to obtain Pareto approximative optimal solutions .The elitist strategy is regarded as an effective method to maintain the diversity of the optimal solutions.The archive update strategy includes on-line archive and off-line archive. The on-line archive is used in the algorithm.The hyper grid division and G vector dominance which are proposed in the thesis are adopted to solve the diversity of solutions.The search space is divided into a number of grids and the diversity is maintained by ensuring that a grid can be occupied by only one solution. The motive ensures that no two obtained solutions are within the same ε value from each other in the objective.The G vector dominance is introduced in the selection of non-dominance solutions.It can pick out the most representative elitist individuals.Any MOEAs need not preserve all non-dominated solutions compeletely. So the algorithm uses Pareto-dominnace and ε -dominance to control the selection of non-dominated solutions. The size of the archive is notfixed on a number. A and e determine the size of archive. So the algorithm can not only reduce computational time, but also obtain perfect Pareto non-dominated solutions. Finding a good distribution of solutions near the Pareto-optimal front in a small computational time is an important goal for muti-objective EA researchers and practitioners.The I-MOEA algorithm can slove the problem commendably.The simulative experimental results demonstrate that the algorithm has better universal performance and computational efficiency.In I-NSGA-II algorithm, we analyze the litimitation of the NSGA-II algorithm firstly. Then the clustering method which used in SPEA2 replaces the crowding method straightly. The performance of the two algorithms represents good results on convergence and divisity by two performance metrics.The optimization solutions of I-NSGA-II algorithm distribute more slick than that of NSGA-II algorithm, and the I-MOEA algorithm has optimization solutions distributing perfectly, which optimizes two objectives without constraints or with constraintsand three objectives.The experimental results demonstrate the two algorithms have beter effect.