Evolutionary Algorithms For Multi-and Many-Objective Optimization Problems With Irregular Pareto Fronts

Multi objective optimization problems(MOPs)are widely seen in engineering practice and scientific research.An MOP contains several objective functions which need to be optimized at the same time,and objectives are often conflicting with each other.That is,improving the performance of one objective will often lead to the degradation of the performance of other objectives.As a result,a set of compromise solutions,instead of a single optimal solution,will be obtained.As a class of metaheuristic optimization algorithms,evolutionary algorithms(EAs)have shown clear advantages in solving MOPs.At present,EAs have become the most effective method to solve multi-objective optimization problems.However,they are still inefficient in solving some complex MOPs such as many-objective optimization and problems with irregular Pareto fronts.In addition,it remains challenging to design an effective evolutionary algorithm for a practical engineering optimization problem whose characteristics are not fully understood.This dissertation aims to address the above challenges by designing new strategies for mating pool selection,reference point setting,Pareto front estimation,reference vector adaptation for environmental selection,to improve the convergence and diversity of evolutionary multi-objective optimization algorithms in solving multi-or manyobjective optimization problems with irregular Pareto fronts.The main new contributions of this dissertation can be summarized as follows:(1)A clustering based adaptive evolutionary algorithm for multi-objective problems with irregular Pareto fronts is proposed.On top of the non-dominated sorting method to ensure convergence,a hierarchical clustering method is applied to adaptively generate a group of evenly distributed cluster center reference points in the individuals to be screened.A distance and crowding degree based fitness evaluation method tailored for irregular Pareto front is designed to improve the diversity of the population.We examine the performance of the algorithm on 18 widely used benchmark problems.Our results demonstrate the competitiveness of the proposed algorithm for multiobjective optimization,especially for problems with irregular Pareto fronts.In addition,the algorithm is shown to perform well on the optimization of the stretching parameters in the carbon fiber formation process.(2)A multiple reference vectors guided evolutionary algorithm is designed for a specific class of many-objective optimization problems with degenerate Pareto,which is difficult for most existing evolutionary algorithms to obtain well converged solutions.In this algorithm,a vector based Pareto front location method is proposed.In the located Pareto front area,the mapping and clustering methods are used to generate reference vectors at the cluster centers.The cluster centre reference vectors work together with the location vectors,the axis vectors and the randomly generated vectors in the located Pareto front area,to guide the population to converge to the Pareto front more efficiently.In addition,in order to further enhance the convergence,an enhanced mating pool selection method based on adjacent vectors is used to improve the ability of the algorithm to deal with degenerate Pareo fronts that are difficult to obtain well converged solutions.The effectiveness of the proposed algorithm is examined on two typical test problems with degenerate Pareto fronts and the results show that the proposed algorithm has a clear advantage in dealing with this class of many-objective optimization problems over the state-of-the-art methods.In addition,the proposed algorithm has also been successfully applied to optimization of process parameters of polyester fiber filament melt-transportation.(3)A more generic evolutionary algorithm based on normal vectors on the hyperplane is developed that is able to solve a wide range of multi-and many-objective optimization problems with irregular Pareto fronts.The normal vectors on the hyperplane is used to decompose the population and perform the environmental selection.A pruning selection mechanism is adopted to improve the diversity of the solution,in which the selected population is again compared with the parent population.Experimental results on multiple sets of benchmark problems and the optimization of polyster and the optimization of polyester fiber esterification process show that the proposed algorithm performs consistently well on various types of multi-/manyobjective problems having regular or irregular Pareto fronts.