Design And Application Of Self-Organizing Multi-objective Particle Swarm Optimization Algorithm

Multi-objective optimization problems(MOPs)consist of multiple conflicting and influencing optimization Problems,which are widely exist in the fields of engineering practice and scientific research,such as optimal control,optimal scheduling and data mining.In order to solve MOPs effectively,the population-based heuristic evolutionary algorithms have been proposed by many scholars at home and abroad.Among them,multi-objective particle swarm optimization(MOPSO)algorithm is more suitable for solving MOPs due to its characteristics of strong universality,simple process,rapid convergence and easy implementation.However,the existing MOPSO algorithms usually have a fixed population size during the evolutionary process,which affects the performance of MOPSO seriously and limites the application of MOPSO.Therefore,the current research hotspot of evolutaionary algorithms is that how to adjust the population size of MOPSO automatically during the evolutionary process and improve the performance of MOPSO,which has great theoretical significance and application value.In this study,a self-organizing multi-objective particle swarm optimization(SOMOPSO)algorithm is proposed to solve the problem that the population size of MOPSO is difficult to be adjusted automatically.First,an adjustment gist of swarm population is proposed innovatively by analyzing the relationship between the performance indicators and the population size,which can determine whether the population size of algorithm needs to be adjstand according to the evolutionary states.Second,a self-organizing mechanism of population size is developed to self-organizing the population size of MOPSO.Meanwhile,an adaptive parameter adjustment mechanism is invented to adjust the flight parameters of MOPSO,which enhances the performance of MOPSO.Finally,to solve the dynamic multi-objective optimization problems(DMOPs)with a changing number of objectives,a dynamic self-organizing MOPSO(DSOMOPSO)is designed to adjust the population size and the nondominzted solutions in the external archive self-organized,which match the algorithm with the number of objectives in DMOPs,and consequently improve the effectiveness of solutions.The proposed DSOMOPSO is applied to the urban waste water treatment process(WWTP),which realized the desinge of the DSOMOPSO-based optimal controller(DSOMOPSO-OC).The experimental results show that the optimal controller can realize the dynamic optimal control of the WWTP.The main research work and innovation points of this paper are as follows:1.The design of an adjustment gist of population size in MOPSO.In order to solve the problem that the population size of MOPSO can't be determined accurately,a judgement criterion of swarm population based on the informance of indicators is proposed.First,the performance indicators of MOPSO are analyzed deeply to describe the evolutionary states of the optimization process.Secondly,based on the relationship between the evolutionary states and the population size,an expression model about the performance indicators and population size of MOPSO is established.Finally,based on the expression model,the judgement criterion of population size is designed to judge the population size during the evolutionary process.2.The design of a self-organizing MOPSO.In order to solve the problem that the population size of MOPSO can't adjusted self-organized during the evolutionary states,a self-organizing MOPSO(SOMOPSO)is proposed.First,a self-organizing mechanism of the population size is designed based on the judgement criterion of the population size to add and prune the population size of MOPSO automatically.Secondly,an adaptive parameter adjustment mechanism is designed to adjust the ineritia weight and the acceleration coefficient of MOPSO during the evolutionary process adaptively,which can balance the exploration ability and exploitation ability of the algorithm.Finally,the proposed SOMOPSO is applied to the benchmark functions and the water supply network experiments.The experimental results show that the proposed SOMOPSO can adjust the population size and the inertia weight selforganized,which can obtain satisfactory optimization solutions.3.The design of a dynamic self-organizing MOPSO.In order to solve DMOPs that the number of targets changing with time,which can't be solved by the basic MOPSO effectively,a dynamic self-organizing MOPSO(DSOMOPSO)is proposed.Firstly,a set of quantitative metrics,based on the Chebyshev distance,is developed to obtain the evolutionary states of the population when the number of objective changes.Secondly,based on the evolutionary states,a self-organizing method of population size is designed to adjust the population size of MOPSO adaptively.Finally,an update mechanism of external archive is designed to solve the problem that the non-dominated solutions in the external archive can't match the current number of objectives.Experimental results applied to the benchmark functions show that DSOMOPSO has better performance.4.DSOMOPSO-based optimal control for WWTP.It is difficult to solve the problem that the optimal control of WWTP in real time.In order to solve this problem,an optimization controller(SOMOPSO-OC)based on DSOMOPSO is proposed.Firstly,the optimization objectives of urban WWTP is established by analyzing the dynamic characteristics of urban WWTP.Secondly,based on the time-varying characteristics of the optimization objective number in urban WWTP,DSOMOPSO is used to solve this optimization objective to obtain optimal set-points of dissolved oxygen and nitrate nitrogen concentration.Finally,the proposed DSOMOPSO-OC is applied to the benchmark simulation model 1(BSM1),the experimental results show that DSOMOPSO-OC can improve the optimal control performance of urban WWTP effectively.