Research On Many-objective Evolutionary Algorithm Based On Reference Vector

In the field of optimization,simultaneous optimization of multiple objective is a problem often encountered in real life and needs to be solved.In order to solve this kind of problem,multi-objective evolutionary algorithm is proposed and becomes the indispensable mainstream algorithm.Multi-objective evolutionary algorithm is a heuristic search algorithm,which provides a good solution to the optimization problem by referring to the existing mechanism of natural selection and biological intelligence.At present,the mainstream multi-objective evolutionary algorithm has shown competitive in solving two-dimensional or three-dimensional optimization problems.However,when there are more than three objectives,the multi-objective evolutionary algorithm cannot solve such problems well.Decomposing-based multi-objective evolutionary algorithm(MOEA/D)greatly alleviates the selection pressure in high-dimensional optimization problems,and shows efficiency in many-objective optimization problems.MOEA/D solves the original problem by decomposing the problem into a certain number of sub-problems through a set of preset reference vectors.In the optimization process,each sub-problem is represented by a reference vector to find the Pareto optimal solution.Decomposition based multi-objective evolutionary algorithms have been successfully applied in many fields.However,these preset reference vectors are not good enough to solve some more complex multi-objective optimization problems.In this dissertation,the multi-objective evolutionary algorithm based on reference vector is further studied and explored.For some complicated problems,this dissertation proposes a new adaptive algorithm based on decomposed reference vectors to solve these complex problems instead of using preset reference vectors.On the one hand,this dissertation proposes two new reference vector adaptive strategiesfor many-objective optimization problems with irregular Pareto frontier characteristics.These two strategies can be combined in most algorithms based on reference vectors to achieve better diversity distribution of the population.On the one hand,a new boundary point finding strategy is proposed for the many-objective optimization problem with inverted Pareto characteristics,which can effectively find all boundary points of problems.Then,based on these boundary points,an adaptive strategy for generating reference vectors with internally uniform complements is proposed.The main contributions of this dissertation are as follows:1)In this dissertation,two new reference vector adaptive strategies,are proposed for many-objective optimization problems with irregular Pareto characteristics.In particular,to solve an optimization problem with concave or convex Pareto characteristics,a vector scaling strategy introduces a specific center vector,which is used to scale and adjust all the vectors around the center vector.In addition,for optimization problems with the characteristics of discontinuous and degenerate problems,the population with good diversity converts into a group of reference vectors with high diversity,so as to obtain a uniformly distributed population.In addition,the combination of these two strategies can effectively solve most optimization problems with irregular Pareto characteristics.2)A new boundary point finding strategy is proposed for the many-objective optimization problem with inverted Pareto frontier characteristics.This strategy is not only simple and easy to use,but also fast and efficient.Then,based on these boundary points,a reference vector generation method is proposed to generate uniform reference vectors within the population,so as to obtain a better diversity distribution.Specifically,a set of boundary point is generated at first,and a set of uniform sub-reference vectors are generated between the barycenter point and the two adjacent boundary point areas at each time.Finally,all the sub-reference vectors are connected and the finally uniformly distributed reference vectors are obtained.This kind of adaptive reference vector generation method is a good substitute for the problem with inverse Pareto characteristics.3)We remake the IDTLZ and IWFG problem set,which have the inverted Pareto characteristics.They have the same problem nature as the original DTLZ and WFG.This dissertation will test whether the multi-objective evolutionary algorithm has strong general robustness on IDTLZ and IWFG problems.It is verified that the new generated reference vector proposed in this dissertation has good adaptability in the problem with inverted Pareto characteristics.