A Multi-objective Evolutionary Algorithm Based On An Adaptive Evaluation Strategy Of Individuals

Nowadays multi-objective evolutionary algorithms (MOEAs) have become one class of powerful algorithms for multi-objective optimization problems (MOPs), whereas there are still some issues to be investigated for the theoretical analyses and algorithm design. The present theoretical results are mostly based on the notion ofε-Pareto set that can be improved to some extent. Thus, this dissertation presents a new definition of a uniformly distributed approximate Pareto front, the B-Pareto front, and designs an adaptive evaluation method of individuals that can identify the shape of the true Pareto front to improve the selection pressure of update strategies. Combined with an extra diversity strategy, it drives the population converging to reasonable approximations of the Pareto fronts. To verify the validity of this method, theoretical analyses and experimental comparisons are performed in this dissertation.First, we present the definition of B-Pareto front and a sufficient condition for an MOEA with an archive to converge with probability one to the B-Pareto fronts of regular multi-objective optimization problems (RMOPs). The MOEA utilizes an adaptive evaluation strategy identifying the true Pareto front, and a diversity strategy is introduced to keep the diversity of the population. Comparisons show that this theoretical framework of MOEAs outperforms some other methods of fixed population size and archive size such as SPEA2, NSGAII and hypervolume-based MOEAs.Then, the convergence rate of a (λ+1)MOEA based on the adaptive evaluation strategy is analyzed by estimating the expected iterations until it reaches a reasonable approximation of the true Pareto front. Theoretical results demonstrate that the (λ+ 1)MOEA achieves the uniform representations of both a polynomial Pareto front and an exponential Pareto front in polynomial expected time, and for any give precision the expected time to achieve the reasonable approximation of a continuous MOP is also polynomial. These show that the adaptive evaluation strategy can accelerate the convergence of MOEAs, and the effectiveness of the proposed diversity strategy is also confirmed.At last, an adaptive multi-objective evolutionary algorithm (AMOEA) for MOPs is designed. Because the true Pareto front is unknown when the MOEAs are utilized to solve a practical MOP, the T nearest non-dominated solutions to the present individual are taken as the approximation of the true Pareto front to evaluate the individuals in the population. By comparing the different performances of AMOEA for respective parameter settings, the influences of parameters are analyzed. These results can provide the instruction for solving other complex MOPs. Numerical results demonstrate that the proposed AMOEA is efficient for MOPs.