基于微粒群优化算法的空间优化决策

Spatial Optimal Search Based on Particle Swarm Optimization

空间优化决策是GIS应用中复杂而又常见的问题。由于涉及到大量的组合,使用穷举法等方法难以找到最优的解决方案,因此需要运用新的理论方法来解决这类问题。微粒群优化算法是近年来新兴的一种优化技术,与GIS相结合可解决空间优化决策问题。首先,对微粒群优化算法和空间优化决策问题作了简单介绍;然后,基于人口密度、最短距离约束条件下,通过GIS技术,对微粒群优化算法用于空间优化决策的方法、实施过程作了详细阐述;接着,用4×4方格单元对PSO方法的正确性、有效性进行了验证;最后,以广州市芳村区为例,对该方法进行实例验证。通过实验,证明微粒群优化算法具有较好的收敛速度、较高的结果精度,是解决空间优化决策问题的一种有效方法。

The solutions to spatial optimal search are complex and important. Since combinatorial optimal problems are computationally difficult, brute-force search can hardly solve the problems. As a result, a novel approach is necessary to deal with them. Particle swarm optimization （PSO） is a new kind of optimal technique, which can solve complex nonlinear spatial optimal problems. This paper demonstrates that PSO solves the spatial optimal search based on GIS under the constraint conditions of population distribution and shortest path. The PSO treats each solution as a particle searching in D-dimensional hyperspace. Different from other optimal problems, the spatial optimal search is in 2-dimensional geographic space, in which each point includes X, Y coordinates. D is equal to 2n. Where n is the number of marketplaces. So the position vector of the particle i is （xi1,, yi1, xi2, yi2,…, xin, yin. Each particle flies over search space and its velocity vector is （vxi1, vyi1, vxi2, vyi2, …, vxin, vyin）. The particles can adjust their positions and velocities according to the current optimal value p （t） and global optimal value pg. The work in this paper makes use of the control MapObject2.3 to extract the centroid coordinates, area and population density of each cell in the map of population distribution by means of the computer programming language. It initializes the parameters, computes the fitness value of each particle and finds the current optimal value and global optimal value which adjust the position and velocity of each particle until they satisfy the condition of maximal number of iterations or precision. Finally, it identifies the position of the particle with the global optimal value is the optimal location of the marketplaces. The contents of this paper include： first, this paper introduces the characteristic and research progress about PSO and spatial search. Secondly, the paper elaborates on the implementing procedure and method of spatial optimal search by using PSO and GIS under the constraint condition of population distribution and shortest path. Thirdly, the paper utilizes the 4×4 spatial regions as an example to prove the correctness and effectiveness of the proposed method. Finally, the paper further verifies this method by a case of Fangcun District, Guangzhou. It is concluded that particle swarm optimization is a robust method of solving spatial optimal search under complex conditions.