Research On The Improvements Of Multi-objective Evolutionary Algorithms

In the real world,there are a wide variety of recognised multi-objective optimization problems.For instance,many real-world scientific and engineering problems involve multiple conflicting performance measures or objectives,which must be optimized simultaneously to achieve a tradeoff among these different objectives.Evolutionary algorithms are very suitable for multiobjective optimization due to their ability to find many solutions at once.As a matter of fact,there has been considerable interest in the study of multi-objective evolutionary algorithms(MOEAs).In particular,the research of many-objective evolutionary algorithms becomes a hotspot but also a difficulty in the area of evolutionary algorithms in the recent years.Classical MOEAs adopt Pareto dominance and carry on some type of vector ranking scheme,such as non-dominated sorting.In this thesis,we pay attention to the key technologies in MOEAs,and focus on how to improve the performance of MOEAs.The main contribution of this thesis is introduced as follows.(1)Propose a novel non-dominated sorting method.After analyzing the properties of Pareto dominance,we propose the dominance degree matrix for a set of vectors and design a fast method to construct this new data structure.Based on the dominance degree matrix,we develop a new method for non-dominated sorting called DDA-NS,which is efficient and easy to implement.Empirical results demonstrate that DDA-NS clearly outperforms six other representative approaches for non-dominated sorting in most cases,and DDA-NS performs well when dealing with large-size and many-objective populations.(2)Improve the performance of NSGA-III which is a many-objective evolutionary algorithm.Considering the issue that the Pareto dominance relied on by NSGA-III lacks enough selection pressure when the number of objectives is high,we construct the dominance indicator by taking advantage of the proposed dominance degree matrix.The dominance indicator can contribute to enhancing the selection pressure to pull the population towards Pareto Front.Empirical results indicate that the improved NSGA-III can obtain the improved convergence on some benchmark problems,and the improved NSGA-III performs better than NSGA-III on the whole.(3)Propose a constrained optimization evolutionary algorithm for specific problem.Focusing on the 4-th tensor power problem of matrix multiplication,we convert this practical problem,and design a constrained optimization evolutionary algorithm based on multiobjective optimization techniques.Empirical results show that this algorithm can effectively solve the 4-th tensor power problem.What is more,the feasible solution obtained by this algorithm is better than the current known solution of the problem.