Many-Objective Evolutionary Optimization: Theory And Method

Multi-objective optimization problems(MOPs)are commonly seen in daily life,industry production,and scientific researches.MOPs with more than three objectives are refered to as many-objetive optimization problems(MaOPs).A great number of multi-objective evolutionray algororithms have been proposed for solving MOPs.However,they experience grand challenges in solving MaOPs.In addition,the objective functions often have multi-modal properties,which add more difficulties in achieving all Pareto optimal solutions.Therefore,five evolutionary algorithms were proposed from different perspectives for solving MaOPs in this study.The detailed contents are described as follows.First,a many-objective evolutionary optimization algorithm based on problem decomposition,termed as MOEA-PD,was proposed.In MOEA-PD,the many-objective optimization problem is decomposed into several sub-problems.Then,a multi-population parallel evolutionary algorithm is adopted to solve these sub-problems.The pressure on selecting non-dominated solutions for a sub-problem is improved by taking full advantage of information obtained from other sub-populations.The final solution set is achieved by archiving those sets of non-dominated solutions coming from the sub-populations.Second,to further strengthen the selection pressure towards to the Pareto front,a reference points-based evolutionary algorithm,termed as RPEA,was proposed.In RPEA,a series of reference points with good performances in convergence and distribution are continuously generated according to the current population to guide the evolution.Furthermore,superior individuals are selected based on the evaluation of each individual by calculating the distances between the reference points and the individual in the objective space.Next,by extending the distance betweem a solution and a reference point to be as a convergence indicator,a many-objective evolutionary algorithm using a one-by-one selection strategy,termed as 1by1 EA,was proposed.The main idea of 1by1 EA is that in the environmental selection,offspring individuals are selected one by one based on a computationally efficient convergence indicator to increase the selection pressure towards the Pareto optimal front.In the one-by-one selection,once an individual is selected,its neighbors are de-emphasized using a niche technique to guarantee the diversity of the population,in which the similarity between individuals is evaluated by means of a distribution indicator.Moreover,corner solutions are utilized to enhance the spread of the solutions.Then,based on the knowledge of convergence and diversity from the the above algorthim,a meta-objective approach,termed as MeO,was proposed for many-objective evolutionary optimization.MeO transforms a many-objective optimization problem into a new optimization problem,which is much easier to be solved by the Pareto-based algorithms.The new optimization problem has the same Pareto optimal solutions and the number of objectives with the original one.Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution,respectively.MeO can be readily incorporated within any multi-objective evolutionary algorithms.Particularly,it can boost the Pareto-based algorithms ability to solve many-objective optimization problems.Last but most important,aiming to address the issues caused by the multi-modal properties,a multi-modal many-objective evolutionary algorithm based on convergence and diversity analysis,termed as MMMOEA-C&D,was proposed.In MMMOEA-C&D,the properties of decision variables and the relationships among them are analyzed at first to guide the search of multiple Pareto optimal solutions.Then,a general framework using two archives,i.e.,the convergence and diversity archives,is adopted to cooperatively solve these problems.The convergence archive focuses on searching multiple Pareto solutions with good convergence;whilist the diversity archive simultaneously employs a reference-point-based clustering strategy to guarantee diversity in the objective space and a clearing strategy to promote that in the decision space.The above research results can not only enrich and deepen the existing many-objective evolutionray optimization theories but also fill in a blank of multi-modal multi(many)-objective evolutionary optimizatiom,thereby promote the application of these theories in real-world applications.