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
Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for...Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.展开更多
We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability o...We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to average-case reductions; pseudorandomness and extractor constructions; and Valiant＇s new theory of holographic algorithms and reductions.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.
文摘Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years I we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.
文摘We briefly survey a number of important recent uchievements in Theoretical Computer Science （TCS）, especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to average-case reductions; pseudorandomness and extractor constructions; and Valiant＇s new theory of holographic algorithms and reductions.
