In solving small- to medium-scale travelling salesman problems （TSPs） of both symmetric and asymmetric types, the traditional ant colony optimization （ACO） algorithm could work well, providing high accuracy and sa...In solving small- to medium-scale travelling salesman problems （TSPs） of both symmetric and asymmetric types, the traditional ant colony optimization （ACO） algorithm could work well, providing high accuracy and satisfactory efficiency. However, when the scale of the TSP increases, ACO, a heuristic algorithm, is greatly challenged with respect to accuracy and efficiency. A novel pheromone-trail updating strategy that moderately reduces the iteration time required in real optimization problem-solving is proposed. In comparison with the traditional strategy of the ACO in several experiments, the proposed strategy shows advantages in performance. Therefore, this strategy of pheromone-trail updating is proposed as a valuable approach that reduces the time-complexity and increases its efficiency with less iteration time in real optimization applications. Moreover, this strategy is especially applicable in solving the moderate large-scale TSPs based on ACO.展开更多
Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional pa...Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(2015XZD15)the Soft Science Research Project of Guangdong Province(2015A070704015)+1 种基金the Guangdong Province Key Laboratory Open Foundation(2011A06090100101B)the Technology Trading System and Science&Technology Service Network Construction Project of Guangdong Province(2014A040402003)
文摘In solving small- to medium-scale travelling salesman problems （TSPs） of both symmetric and asymmetric types, the traditional ant colony optimization （ACO） algorithm could work well, providing high accuracy and satisfactory efficiency. However, when the scale of the TSP increases, ACO, a heuristic algorithm, is greatly challenged with respect to accuracy and efficiency. A novel pheromone-trail updating strategy that moderately reduces the iteration time required in real optimization problem-solving is proposed. In comparison with the traditional strategy of the ACO in several experiments, the proposed strategy shows advantages in performance. Therefore, this strategy of pheromone-trail updating is proposed as a valuable approach that reduces the time-complexity and increases its efficiency with less iteration time in real optimization applications. Moreover, this strategy is especially applicable in solving the moderate large-scale TSPs based on ACO.
基金Supported by National Natural Science Foundation of China under Grant Nos.11071278,111471004the Fundamental Research Funds for the Central Universities of GK201302026 and GK201102007
文摘Motivated by the widely used ans¨atz method and starting from the modified Riemann–Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
