Particle Swarm and Ant Colony Algorithms and Their Applications in Chinese Traveling Salesman Problem

Abstract

Intelligent heuristic optimization methods have increasingly attracted the attentions and interests of many scholars in recent years. Such as genetic algorithm, ant colony algorithm, particle swarm optimization, simulated annealing, etc.. They have become effective tools to solve the TSP and other NP-hard combinatorial optimization problems. The particle swarm optimization (PSO) algorithm is a population-based evolutionary algorithm which was proposed by Eberhart and Kennedy in 1995 (Eberhart & Kennedy, 1995). The PSO simulates the behaviors of bird flocking. Suppose the following scenario: a group of birds are randomly searching food in an area. There is only one piece of food in the area being searched. No bird knows where the food is. But they know how far the food is in each iteration. So what’s the best strategy to find the food? An effective one is to follow the birds which are nearest to the food. The PSO firstly generates a random initial population, the population contains numbers of particles, each particle represents a potential solution of system, each particle is represented by three indexes: position, velocity, fitness. Firstly endows each particle a random velocity, in flight, it dynamically adjusts the velocity and position of particles through their own flight experience (personal best position), as well as their companions’ (global best position). The evolutions of particles have a clear direction, the whole group will fly to the search region with higher fitness through continuous learning and updating. This process will be repeated until reach the default maximum iterations or the predetermined minimum fitness. The PSO is therefore in essence a fitnessbased and group-based global optimization algorithm, whose advantage lies in the simplicity of algorithm, easy implementing, fast convergence and less parameters. Presently, the PSO has been widely applied in function optimization, neural network training, pattern classification, fuzzy system control and other applications. Whereas, like other intelligent optimization algorithms, the PSO may occur the phenomenon that particle oscillates in the vicinity of optimal solution during searching in the search space, therefore the entire particle swarm performs a strong convergence, and it is easily trapped in local minimum points, which makes the swarm lose diversity. Thus it has the weakness of solving complex problems, and it is difficult to obtain a more accurate solution in the late evolution. Many scholars proposed some improved algorithms (Yuan et al., 2007; Xu et al., 2008; Lovbjerg, 2001), which improve the search capabilities of the elementary PSO in different aspects.