Research On Multi-objective Optimization Algorithm Based On Swarm Cooperative Intelligence

Swarm intelligence optimization algorithm(SI)is a kind of random search algorithm that simulates the behavior of biological and abiotic groups in nature.It has been widely used because it is suitable for highly complex nonlinear problems.The advantages of SI in solving complex single objective system optimization problems have been fully reflected.However,the optimization problem in the real world is often multi-attribute,which is usually carried out for multiple objectives at the same time.In most cases,multiple objectives optimized at the same time affect and conflict with each other.In order to achieve the optimization of the overall goal,it is often necessary to consider the conflicting sub goals in a comprehensive way,that is,compromise among the sub goals.Therefore,in order to optimize multi-objective,evolutionary multi-objective algorithm appears.Most of the existing multi-objective optimization algorithms try to evenly distribute all solutions in the objective space.But for the irregular Pareto front(PF),it is difficult to find the real PF.Aiming at the multi-objective optimization problem with complex PF,a multi-objective evolutionary algorithm for adaptive fitting dominant hyperplane is developed.Before each iteration,non-dominated sorting is applied on all candidate solutions.Solutions in the first front are used to fit a hyperplane in the objective space,which is called the current dominant hyperplane(DH).DH reflects the evolution trend of the current generation of non-dominanted solutions and guides the rapid convergence of dominanted solutions.A new partial ordering relation determined by front number and crowding distance on DH is set.Dominant solutions participate in screening non dominant solutions,so that the population is evenly distributed on the irregular Pareto front.The main contributions of this paper are as follows:(1)The dominant hyperplane is proposed.Before each iteration,the solution of the first layer of non dominated sorting is fitted into a hyperplane in the target space,which is called Pareto dominant surface.The Pareto dominance surface can well reflect the non dominated solution evolution state of the current generation population.With the continuous evolution of the population,the Pareto dominance surface gradually approaches the shape of the real Pareto frontier.(2)The crowding distance between the points projected to the dominant hyperplane is proposed as a new index to screen the last front.Since the solution before the last front is also projected onto the dominant surface,all projected points are covered when calculating the congestion distance,and the truly evenly distributed last front can be selected into the next generation.(3)This paper constructs a new partial order relation.Firstly the front numbers of individua are judged,the one with the smallest front number is the best solution.When the front numbers are the same,the crowding distance of the projected points on the dominant surface is considered.The one with largest crowding distance is the best solution.The order relation speeds up the convergence speed of the algorithm under the condition of ensuring the diversity of the population.(4)A multi-objective evolutionary algorithm is proposed to adaptively fit the dominant surface.The crowding distance based on the projection point of the dominant surface is used as the partial order relationship for environment selection.In the critical layer,the individuals with large crowding distance enter the next generation.This method effectively improves the diversity of the population.(5)A multi-objective particle swarm optimization algorithm for adaptive fitting the dominant surface is proposed.The density of the projection point of the dominant surface is taken as the particle fitness.When selecting the particles in the critical layer to enter the archive set,the individuals with the best fitness ranking will enter the archive set.When the particle learns from the optimal individual,the optimal particle()is selected by roulette with the probability of projection point density,so that the multi-objective particle swarm optimization algorithm can converge quickly.