Research On Many-objective Optimization Algorithm Based On Tchebycheff Method Decomposition

The previous multi-objective optimization algorithm can solve the optimization problem of two or three objects well,and it is difficult to obtain a better Pareto front when the number of targets increases.To this end,the many-objective optimization algorithm with the target number greater than 3 is studied.The key point of the many-objective optimization problem is how to ensure the diversity and convergence of the Pareto front.The many-objective optimization algorithm based on decomposition strategy has a good effect in solving the many-objective optimization problem.The commonly used methods are the penalty-based boundary cross decomposition method PBI and the Tchebycheff decomposition method TCH.In the original MOEA/D algorithm,the effect of penaltybased boundary cross decomposition method is better than that of TCH.Most researchers have studied the boundary crossing method of punishment,and the Tchebycheff method is rarely studied in depth.Therefore,this paper studies the many-objective optimization algorithm based on Tchebycheff method decomposition,the main content is the following two aspects:1.Further improvement of Tchebycheff decomposition method and modified Tchebycheff decomposition method,extending Tchebycheff decomposition method to generalized form Lp decomposition method,the smaller the p value,the better the convergence,the larger the p value,the more diverse Well,a p-value selection method is proposed,and a suitable better p-value is selected for each sub-question weight vector to better balance the convergence and diversity of the algorithm.However,the effect of pvalue on diversity is greater than the convergence,that is,the smaller the p-value is,the better the performance is.Therefore,the p-value self-selection method is to select a small p-value as much as possible.Therefore,in order to improve the diversity of the algorithm in the many-objective,a vertical distance-based update strategy is introduced to increase the diversity of the Pareto frontier.A many-objective optimization algorithm MOEA/DPD based on p-value selection method and vertical distance update strategy is proposed.2.The weight vector is extended to the p-norm form,and the geometric properties of the Tchebycheff decomposition method of the weight vector of the 2-norm are studied.Then,an update strategy based on the maximum fitness value enhancement is proposed.Compared with the update strategy with minimum fitness update strategy and random fitness improvement,the update strategy based on maximum fitness improvement has obvious advantages.a many-objective optimization algorithm MOEA/D-2TCHMI based on 2-TCH decomposition method and maximum fitness improvement is proposed.Finally,the two algorithms proposed in this paper compare the IDG,HV or NHV performance evaluation indicators of DTLZ and WFG benchmark problems with other algorithms,among which MOEA/D-PD and MOEA/D-2TCHMI are significantly better than others.Decomposed many-objective optimization algorithm,and compared with NSGA-III,GrEA and other algorithms also have outstanding performance.