Studies On Multi-objective Particle Swarm Optimization Algorithm And Its Applications In Water Distribution Network

The related studies of multi-objective optimization problems(MOPs)have attracted the attention of scholars due to its prevalence in engineering applications.Since metaheuristic algorithms are consistent with the demand of solving MOPs,it has been developed rapidly in the past few decades.Particle swarm optimization algorithm has evolved as one of the most popular options for MOPs on account of its efficient optimization mechanism and easy-to-implement.Although the multi-objective particle swarm optimization(MOPSO)algorithm has been improved continuously,there are still some problems that are difficult to solve.With the increasing demand for solving MOPs,appropriate improvements are needed to further enhance the performance of MOPSO urgently.Therefore,the related studies about adaptive MOPSO and its application are conducted in this thesis.The main contents are summarized as follows.(1)The optimization mechanism of MOPSO is improved and a multi-strategy optimization scheme based on population partition is proposed.Most improved MOPSO algorithm just rely on a single search strategy without considering the optimization conditions of particles with different performances.The algorithm shows insufficient convergence and diversity when solving complex MOPs.To solve this problem,the population partition is proposed,and corresponding optimization strategies are designed according to the characteristics of particles in different partition to improve the poor performance of MOPSO due to its single optimization mechanism.Moreover,the employment of multiple strategies provides a clear division of labor for the particles,maximizes the optimization potential of the particles in different partitions,and promotes the particle utilization rate,which provide the foundation for the algorithm to achieve excellent convergence and diversity.(2)A complete particle evaluation system is established under the background of MOPs to consummate the proposed algorithm framework.The guidance that the optimal positions participate in MOPSO optimization process,makes a complete particle evaluation system is of great necessity to establish in the background of MOPs.The evaluation system,including the convergence index,the diversity index,and the fusion index of dual performance,are proposed to improve the performance distinction of nondominated solutions.Moreover,a reliable personal optimal position selection scheme is proposed by equipping particles with a memory interval.(3)Further studies on algorithm theory.The adaptive strategy based on energy conversion and the explosion mutation mechanism are proposed.The influence of flight parameters on the performance of MOPSO is crucial.The parameters fixed manually can hardly cope with the varying evolutionary environment,and the algorithm is difficult to exert full performance.Adaptive strategy is one of the most effective schemes to solve the parameter problem of MOPSO.Different from the existing mechanisms,a novel adaptive strategy is proposed from the perspective of force analysis and energy conversion.The evolutionary environment of the proposed algorithm is detected by the variation of particles’ energy,and then the corresponding adaptive strategy can be formulated.Furthermore,inspired by fireworks explosion,a multistrategy explosive mutation is proposed in combination with the population partition to improve the efficiency of optimization and mutation effectiveness.(4)The convergence of the proposed MOPSO is analyzed and proved theoretically.Guaranteeing that the proposed algorithm can effectively converge to the Pareto optimal set is the basis and prerequisite for the algorithm to be applied in MOPs.A comprehensive convergence analysis of the proposed MOPSO algorithm has conducted in this thesis.The optimization is divided into two stages according to the position updating of particles,and the convergence of two stages is proved progressively.Then,the overall convergence of the proposed algorithm can be obtained.(5)Application of the proposed algorithm to water distribution system optimization.The proposed algorithm is applied to the optimal design of water distribution networks(WDNs)based on substantial benchmark experiments.The objectives of WDNs are determined by the cost and the variance of node surplus head,and the constraints are provided according to hydraulic analysis and engineering conditions.A multi-objective optimization model of WDNs is established finally.Two-loop network and Hanoi network are conducted to verify the effectiveness of the proposed algorithm in practical MOPs.