Research On Visualized Test Problems And Neighbor Punishment Mechanism In Many-objective Evolutionary Optimization

In the area of many-objective optimization problems, a problem that long-term persecutes the researchers is that when the objective is more than three, the visualization of solution in objective space is difficult. The change of population in objective space can not be observed directly like that in 2 or 3 objective space, so the properties can not be seen intuitively. Especially in the case of questionable algorithms, we can only conjecture through experimental data, which brings big challenges to the design, development and test of multi-objective evolutionay algorithms. In order to effective improve the visualization difficulties in many-objective optimization. The Circle test problem is proposed in this paper.The Circle test problem has three features.a) the Pareto optimal solutions are located in the circle decision space of the 2 dimentional coordinate, So that we can directly observe the decision space solution set;b) the decision space has graph similarity to its corresponding objective space. And the shadow in 2 dimentional space of the graph in the arbitrary objevtive space has ratio relationship with the graph in 2 dimensional decision space;c) this test problem can accept any number of objevtive dimension.In this way, we can observe convergence and distribution of objective vectors in many-objective space through observing the distribution of solution in the circle space,So it is possible to provide a more direct tool for algorithm designers to design and modify algorithms.In many-objective optimization, the Pareto dominace relation loses effectiveness, many researchers denote themselves to improving the convergence of population for many-objevtive problems, and they modified the Pareto dominace relation and proposed flabby Pareto dominance relation, which can not achive a satisfied result. This paper proposed the e neighborhood punishment mechanism based e-NPM algorithm which is a weight-based approach. Firstly, the objective function values of all goals are summed. Secondly, it sorts through the sum values of all solutions to form total ordered relation. Thus, we can easily distinguish between good and bad individuals and improve the speed of convergence. After selecting the elites into the archive, it then uses the eneighborhood punishment mechanism to publish individuals, whose purpose is avoiding the simultaneous selection of the elites and individuals edominated by these elites. Thus, it can improve the distribution of the many-objective evolutionay algorithm. In this paper, the e-NPM compare with five classic high-dimension objective algorithm include NSGA-II, AR, Gr EA, MSOPS and e-MOEA,the final experiment result shows that e-NPM almost have best convergence and distribution of six algorithms.