Design And Application Of Dynamic Multiobjective Particle Swarm Optimization Algorithm

Multiobjective particle swarm optimization(MOPSO)algorithm is a populationbased stochastic searching evolutionary algorithm.Because of its fast convergence and easy implementation,MOPSO algorithm has been widely used to solve the multiobjective optimization problems in process industries,discrete manufacturing and other fields.However,in pratical applications,the multiobjective optimization problems not only conflict with each other,but also have time-varying objective functions,and the existing MOPSO algorithms can not obtain the satisfactory optimization effects.Therefore,it is ugent to study a MOPSO algorithm which can solve the dynamic multiobjective problem.To obtain the effective optimal solutions of the dynamic multiobjective optimization problems,a dynamic MOPSO(DMOPSO)algorithm is proposed in this paper.By analyzing the flight process of particles,the proposed DMOPSO algorithm is designed to obtain the characteristics of particle evolution.Meanwhile,a dynamic global best selection mechanism is designed to adjust the evolutionary direction and the dynamic multiobjective optimization problem is solved accurately.Finally,the proposed DMOPSO algorithm is applied to the wastewater treatment process(WWTP).A dynamic optimal controller(DMOPSO-OC),based on the proposed DMOPSO algorithm,is developed to obtain the dynamic optimal control of WWTP.Paper main research work and innovation are as follows:1.The design of an adaptive MOPSO algorithm.To solve the speed problem of MOPSO algorithm that the evolutionary direction of the particles,an adaptive MOPSO algorithm is designed around the direction of the particle evolution.First,the flight process of the particles can be analyzed and the evolutionary characteristics of particles can be obtained.Next,the distribution of optimal solutions in the archive is evaluated by the non-dominated solution diversity information,and an adaptive global best selection mechanism is proposed to obtain the evolutionary state of the population.Then,an adaptive flight parameter mechanism,based on the population diversity information,is designed to enhance the global exploration ability.Finally,the adaptive MOPSO algorithm is applied to the standard test experiments.And the experimental results demonstrated that the proposed adaptive MOPSO algorithm can accurately select the evolutionary direction of particles and can be faster to catch the Pareto front.2.The design of a dynamic MOPSO algorithm.In order to obtain the optimal solutions of the dynamic multiobjective optimization problems with time-varying objective functions,a DMOPSO algorithm is designed in this paper.First,a solution distribution entropy method is developed to describe the distribution state of the nondominated solutions in the archive.Next,a dynamic global best selection mechanism,based on the solution distribution entropy,is designed to adjust the evolutionary direction of the particles.Then,a dynamic flight parameter adjustment mechanism,based on the population spacing information,is proposed to obtain the distribution state and balance the global exploration and local exploitation abilities of the particles.Finally,the experimental results validate the effectiveness of the proposed DMOPSO algorithm,as well as demonstrate that DMOPSO outperforms other MOPSO algorithms in solving complex multiobjective optimization problems and obtain satisfactory optimal solutions.3.DMOPSO-based Optimal Control for WWTP.Around the typical dynamic multiobjective optimization problem,the operation of WWTP,an optimal controller(DMOPSO-OC)based on a DMOPSO algorithm is proposed in this paper.An optimization framework,containing the multiple conflicting criteria,is designed by the analysis of the complex and time-varying characteristics in WWTP.Meanwhile,the DMOPSO algorithm was used to optimize the multiobjective function and obtain the accurate optimal set-points of WWTP.Then,the dissolved oxygen and nitrate nitrogen were controlled by the proposed DMOPSO-OC method.Finally,the proposed DMOPSO-OC method is tested in the benchmark simulation model 1(BSM1)and implemented in a real WWTP.Comparative experimental results demonstrate that the proposed DMOPSO-OC facilitates better optimization and control of process performance in comparison with the related existing optimal controllers.