Research On The Divisional Particle Swarm Optimization Algorithm For Solving Function Optimization Problems

Continuous optimization is widely used in all walks of life, has always been a hotspot. In continuous domain to solve optimization problems, when the objective function or its parameter doesn't change over time, it is known as a static environment optimization, conversely known as dynamic environment optimization. To solve this kind of optimization problems, the traditional optimization method is always based on gradient information and requires the object function to be continuous and differentiable. In this computing architecture, it can't be widely and accurately solve optimization problems. For this reason, researchers have tried to use heuristic algorithms based on swarm intelligence to handle these problems. Particle Swarm Optimization (PSO) is a new type of swarm intelligent bionic algorithm, which simulates some intelligent colony behaviors in the nature and can able to optimize the problem with uncertain information. With its simple structure, easy to be realized, few parameters need to be tuned and high effective, it has been applied successfully to continuous optimization problems. But using original PSO to handle complex functions with high-dimension and multi-modal has the problems of low convergence speed and sensitivity to local convergence. Therefore, this paper proposed a divisional PSO algorithm, named grouping PSO (GPSO). This algorithm divide function domain into several subspaces, each subspace will be randomly allocated some particles. Particles in each group search independently in their own space respectively. In order to guarantee each species diversity and ergodicity of searching, chaotic sequence is used to initiate individual position for each group. By proper dividing, experimental results on several typical complex multi-modal function show that the algorithm can rapidly find the optimal solution which is quite satisfactory.When using standard PSO to handle dynamic continuous optimization problem, the algorithm can't adapt to the dynamic environment because of the solving process that gradually converge to the optimal solution and lack of species diversity in the later evolution. Most improved algorithms have the problem of enormous computation and low precision etc. Accordingly, this paper proposed a novel grouping and layering dynamic PSO (GLDPSO). Taking into account the optimization goal is to track changing of the extreme point, that is to say the optimum dynamic changes in the global space. Taking into account the optimization goal is to track changing of the extreme point, this function domain is divided into several subspaces, each subspace will be randomly allocated some particles and all the particles as the first layer particles search the object space. To enhance the ability of particles in every group to learn from each other, the best particles in each group form into the second layer particles, and also search the object space. The results of searching will exert positive effects on the movement of the other particles in each group. At the meantime, to enhance the ability of the algorithm to adapt dynamic environment, improved detection method based on the optimum in each group itself information and response method based on the diversity computation are proposed. Then the improved algorithm updates the particle position selectively and directionally. The experimental results demonstrate that the new algorithm adapt dynamic environment quickly and track the movement of the optimum with changeable environment.