Concerning the drawbacks of the Ant Colony Optimization (ACO) algorithm such as low convergence rate and being easy to fall into local optimum solutions, an ACO algorithm based on Improved Pheromones Double Updating and Local Optimization (IPDULACO) was proposed. Double updating was performed on the pheromones of subpaths whose path contribution degrees to the current global optimal solution obtained by colony were bigger than the prescribed path contribution threshold. The selected probability of the subpaths which were used to constitute the potential optimal solution was increased and the convergence rate of the proposed algorithm was accelerated. Then, when the ant colony fell into the local optimal solution in the search process, the random insertion method was utilized to change the city sequences of the current local optimal solution in order to enhance the algorithm's ability of jumping out of local optimal solution. The improved algorithm was applied to several classical Traveling Salesman Problem (TSP) instances in the simulation experiments. The experimental results show that, for small-size TSP instances, the IPDULACO can obtain the known optimal solution in less number of iterations. For relatively large-size TSP instances, the IPDULACO can obtain the optimal solution with higher accuracy in less number of iterations. Therefore, the IPDULACO has the stronger ability of searching for the global optimal solution and faster convergence rate, and it can be used for solving TSP effectively.

To solve the problem that basic discrete Particle Swarm Optimization (PSO) algorithm often leads the computation process into local optimum and premature convergence when applied to Traveling Salesman Problem (TSP), a PSO based on Self-adaptive Excellence Coefficients (SECPSO) algorithm was proposed. To improve the global search ability, heuristic information was further utilized to modify the static excellence coefficients of paths based on previous work, so that these coefficients could be adjusted adaptively and dynamically according to the process of searching for the solutions. Furthermore, a 3-opt search mechanism was added to improve the accuracy of the solution and the convergence rate of the algorithm. Through simulation experiments with Matlab, the performance of the proposed algorithm was evaluated using several classical examples in the international general TSP database (TSPLIB). The experimental results indicate that the proposed SECPSO algorithm performs better in terms of global search ability and convergence rate compared with several other algorithms, and thus is a potential intelligent algorithm for solving TSP.

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.

To overcome the problem of easily trapping into local optima of standard Artificial Bee Colony (ABC) algorithm, the roulette selection strategy of ABC was modified and an improved ABC based on dynamic evaluation selection strategy (DSABC) algorithm was proposed. Firstly, the quality of each food source position was evaluated dynamically according to the times that the food source position had been continuously updated or stagnated within a certain number of iterations so far. Then, onlooker bees were recruited for the food source according to the obtained value of the evaluation function. The experimental results on six benchmark functions show that, compared with standard ABC algorithm, the proposed dynamic evaluation selection strategy modifies the selection strategy of ABC algorithm, and greatly improves the quality of solution of DSABC algorithm, especially for function Rosenbrock with different dimensions, the absolute error of the best solution reduces from 0.0017 and 0.0013 to 0.000049 and 0.000057, respectively; Moreover, DSABC algorithm can avoid the premature convergence caused by the decrease of population diversity at later stage and improve the accuracy and stability of solutions, thus provides an efficient and reliable solution method for function optimization.