针对基本离散粒子群优化(DPSO)算法收敛速度慢、易于陷入局部最优等问题,提出了一种基于优秀系数的局部搜索混沌离散粒子群优化(ILCDPSO)算法并用于求解旅行商问题(TSP)。基于轮盘赌选择原理,给每段路径设定一个合理的优秀系数,以提高短边被选择的概率,从而有利于提高算法的寻优能力和收敛速度;为了进一步提高解的精确性,在算法机制中添加了局部搜索策略,通过调整每个城市在给定邻域内的城市路径,提高算法的局部搜索能力;另外,在算法的迭代公式中加入了混沌序列来提高粒子的随机性和多样性,增强了算法的全局搜索能力。最后用国际通用的TSP数据库(TSPLIB)中的若干经典实例对算法进行了测试,并与粒子群优化(PSO)算法、改进的PSO(IPSO)算法和混沌PSO(CPSO)算法等进行了比较。实验数据显示,在相同的实验条件下,与其他算法相比,ILCDPSO算法获得最优解的平均迭代次数较少且获得最优解的次数比例最高。研究结果表明,加入优秀系数后,ILCDPSO算法在收敛速度、全局寻优能力以及稳定性方面均优于其他算法。
In view of the drawbacks of the standard Discrete Particle Swarm Optimization( DPSO) algorithm such as slow convergence speed and easily trapping into local optima, an Improved Local-search-based Chaotic Discrete Particle Swarm Optimization( ILCDPSO) algorithm based on excellence coefficient was proposed and then applied to Traveling Salesman Problem( TSP). In this algorithm, each edge was assigned an appropriate excellence coefficient based on the principle of roulette selection. This helped to improve the selection probability of short edge, thus improving the optimization ability and convergence speed of the algorithm. In order to further improve the accuracy of solution, a local search strategy was employed such that the exploration ability of the algorithm could be improved by adjusting the routes of cities in the given neighborhood for each city. Moreover, a chaotic sequence was integrated into the iteration formula to enhance the randomness and diversity of particles and hence increasing the global searching ability of the proposed algorithm. Finally the algorithm was evaluated by some typical instances in the internationally commonly used library of TSP( TSPLIB) and compared with Particle Swarm Optimization( PSO) algorithm, Improved Particle Swarm Optimization( IPSO) algorithm, and Chaotic Particle Swarm Optimization( CPSO) algorithm, etc. The experiment data show that, under the same experimental conditions, ILCDPSO can achieve optimal solutions with less average iterations than other algorithms and has the highest ratio of number for obtaining optimal solutions. The research results indicate that ILCDPSO algorithm performs better than other algorithms in terms of convergence speed, global optimization ability and stability, and it is a comparatively potential intelligent algorithm for solving TSP.