Interval Particle Swarm Optimization Algorithm For Solving Multimodal Problems And Its Application

There are many complex optimization problems in theoretical research and practical engineering applications,such as uncertainty problems,multimodal problem,multi-objective problems,etc.While the traditional optimization methods mainly focus on simple optimization problems such as deterministic and single peak,which are not effective to solve such complex problems.Therefore,it is of great theoretical significance and application value to carry out research on complex optimization problems.As one of the evolutionary algorithms,particle swarm optimization(PSO)algorithm has the characteristics of simple and easy implementation,less adjustable parameters and fast convergence.It is a good tool for solving complex optimization problems.Interval particle swarm optimization(IPSO)algorithm adds interval analysis theory to PSO,expresses uncertain information by interval particles,and determines the state update and performance comparison of interval particles based on interval mathematics.The uncertainty optimization problem provides an effective way.IPSO has demonstrated strong capabilities in solving uncertainty optimization problems,but it still has the same shortcomings as PSO.The random search characteristics of the algorithm and the rapid decrease in convergence speed in the late iteration make it easy to fall into local optimum,and it is difficult to find and maintain multiple optimal solutions.In order to solve the above problems,this paper proposes two IPSO algorithms for solving multi-peak problems in the case of single target and multi-objective,single niching interval particle swarm optimization(SNIPSO),and multi-objective niching interval particle swarm optimization(MNIPSO),and apply them to the modeling of uncertain systems,which makes the algorithms practical.The research work and innovation of the thesis mainly include the following aspects:(1)Analyzed the IPSO algorithm and proposed a variety of methods to avoid the divergence of results.The IPSO is internally calculated in intervals,and it is inevitable that interval expansion will occur.In order to prevent the result from diverging due to the interval expansion in the algorithm iteration process,the paper uses trend subtraction to improve the position and speed update formula of IPSO,limit the particle width of the population,and constrain the particle speed range.(2)The PSO topology and niche technology are studied,and the IPSO algorithm based on ring topology is determined.Compared with the classical global PSO topology,the ring-shaped PSO has stronger local search ability and is more suitable for solving multi-peak optimization problems.Therefore,the paper proposes a method based on ring topology to construct niche,which does not require any niche parameters,and solves the problem that the parameters in traditional niche algorithms are difficult to determine.(3)Propose a dual file mechanism to maintain the optimal solution through the individual best file PBA and the neighborhood best file NBA.One of the difficulties of the multi-peak optimization problem is how to maintain the multiple optimal solutions found until the end of the algorithm.The particle group has memory ability and the particles interact with each other.According to the characteristics of the particle group,the algorithm proposed two files.To preserve the individual optimal position of the particle and the optimal position of the neighborhood,the global optimal solution found by the algorithm can survive in the subsequent iterations.(4)Under the multi-objective situation,the correspondence between the target space and the decision space is analyzed,and a special crowding distance sorting mechanism based on interval is proposed.In the multi-objective multi-peak optimization problem,it is necessary to consider the distribution of the target space and the decision space at the same time,which increases the difficulty of sorting and selecting the Pareto optimal solution.In this paper,a special crowding degree sorting mechanism based on interval is proposed.Based on the interval fast non-dominant sorting method,the sorting mechanism is used to solve the sorting problem of Pareto optimal solution.(5)Analyzed the research status of uncertain system modeling,put forward the idea of interval modeling,and applied the proposed algorithm to the modeling of uncertain systems.Uncertain systems are very common in industrial control,but due to the existence of uncertain information,modeling of such systems is difficult.In this paper,the Interval Neural Network(INN)is used to model the uncertain system.The algorithm is used to optimize the weight and threshold of INN,which provides an effective method for modeling uncertain systems.