A Multi-objective Optimization Algorithm Based On Pyramid Structure

Multi-objective optimization problem widely exists in practical life and is one of the main research contents of optimization problems.The sub-object cannot achieve the optimal simultaneously because each sub-goal usually constrains with each other.In view of above problems,scholars proposed the concept of Pareto optimal solution.Therefore,the core of solving multi-objective optimization problem is to find as many Pareto optimal solutions as possible to make the optimal solution set approximate the real Pareto optimal frontier.The multi-objective optimization algorithm is deeply studied in this paper.In view of the shortcomings of traditional optimization methods which can easily destroy the sub-objective constraints,scholars proposed multi-objective evolutionary algorithms,including NSGA-II and SPEA2.Although these swarm intelligence algorithms are simple to operate and have fast convergent speed,they cannot balance the individual's competition and cooperation ability,exploration and mining ability during the optimization process.To solve these problems,this paper begins with the pyramid structure,defines a group evolutionary framework based on individuals' promotion and functional assignment.Then it proposes a Multi-objective optimization algorithm based on Pyramid Structure(Mo-PS).The main content and innovation points are as follows:1.Based on the talent training method,a strategy of assigning functions is proposed according to the population adaptability.After stratifying the population according to the non-dominated hierarchy and fitness value,the strategy assigns different functions to each layer: the top layer is responsible for mining,the middle layers are responsible for cultivation and transmitting;and the bottom layer is responsible for exploration.This strategy balances the individual's ability of exploration and exploitation during the evolutionary process.2.In view of the imbalance of competition and cooperation ability of the population during the evolutionary process,an individual promotion strategy is proposed by the talent incentive mechanism.This strategy uses the single elite roulette method to transfer the excellent individuals in under layers to higher layers to achieve inner-layer competition and inter-layer cooperation.Since each layer has different functions,the Mo-PS algorithm designs the corresponding sub-fitness functions for each layer and updates the sub-fitness functions through the differential idea.So,the adaptive evaluation criteria are realized and the population can quickly approach the true Pareto optimal frontier.In Section 4.2,the experimental results of ten benchmark functions verify the convergence of the Mo-PS algorithm.3.In order to prevent the group falls into local optimum during the evolutionary process,this paper proposes a diversity strategy in the competitive operation of the exploratory level.By designing a strategy to randomly generate new solutions at the bottom of the pyramid,the diversity of the population is guaranteed.In the external storage process,Mo-PS algorithm uses the grid technology to randomly delete the crowded solutions,so that the non-dominated solutions are evenly distributed in the solution space.Compared the experimental results with similar algorithms,the Mo-PS algorithm has better distribution.