Hierarchy and Adaptive Size Particle Swarm Optimization Algorithm for Solving Geometric Constraint Problems

Abstract

Geometric constraint problems are equivalent to a series of nonlinear equations which are constraint-meeting. Thus, it is a significant issue to improve solving efficiency of the nonlinear equations. This paper proposes Hierarchy and Adaptive Size Particle Swarm Optimization (HASPSO) algorithm for solving geometric constraint problems, and its aim is to greatly improving solving efficiency. This is the basic idea: according to individual extremum, making a comparison between each particle and its members in the direct next hierarchy, then based on transmission principle, taking the best particle’s personal optimal position as its own to do subsequent iterations. Meanwhile, it depends on the natural principle of Fibonacci sequence, by simulating biological reproduction behavior, to make the algorithm adaptively expand its population size from a single individual to appropriate numbers of ones for subsequent hierarchies. If a particle still has not found precision-meeting optimal solution after a T times of iterations, then our approach judge whether the particle is new reproduced individual before the iterations, if so, it continues next T times of iterations, otherwise it produces one new individual in its direct next hierarchy, and reinitializes its position and velocity. HASPSO is able to rank population based on the form of adaptively increasing size by degrees. Theoretical Analysis and experiment show that compared with traditional particle swarm optimization (PSO) algorithm, it can make solution efficiency greatly improved and is an effective method for solving geometric constraint problems.