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1.
旅行商问题的交叉粒子群优化算法   总被引:1,自引:0,他引:1  
本文将粒子群优化算法(PSO)应用于求解旅行商问题(TSP),结合遗传算法的交叉算子,建立了求解此问题的交叉粒子群优化算法,数值模拟结果表明了该算法的有效性.  相似文献   

2.
在确定型TSP问题的基础上,融合灰色系统的思想提出了灰色TSP问题,构建了灰色TSP问题的动态规划模型,结合动态规划方法利用可能度及排序方法给出了求解灰色TSP问题的算法,并结合数值实例,对算法进行了说明.  相似文献   

3.
本文从代数及组合两个方面论证了NP完全问题存在多项式时间算法 .以往利用线性规划 (LP)技术来分析NP完全问题中的TSP问题 ,因其存在子环游问题 ,从而使问题得不到有效解决 .文中发展一分层网络 ,在求解TSP问题时 ,存在另一类(不完全 )子环游问题 .但两模型允许解集的交集避免了两类子环游基本可行解 ,从而使TSP问题可利用LP技术多项式时间内得以解决 ,同时给出了求哈密尔顿回路的多项式标记证明方法 ,开创了NPC问题研究的新局面 .  相似文献   

4.
利用李小平等提出的相邻工件加工结束时间差矩阵,将求解无等待流水调度问题的最小最大完工时间(Makespan)问题映射为TSP问题,构造对应的能量函数,进而得到随机混沌神经网络(SCSA)算法.实验结果证明该混沌神经网络优化算法优于RAJ算法和GANRAJ算法.  相似文献   

5.
旅行商问题(TSP)是运筹学中最典型的NP难题之一.研究了非对称TSP最优路程下界如何确定的问题.为了更加突出TSP问题非对称的特性,提出了入边和出边等概念,给出了确定TSP问题最优路程下界的有关定理,又给出了路程调整值的计算方法,从而得到了最优路程更精确的下界,更好地刻画了路程的逼近程度,最后结合实例对定理进行了说明,它表明给出的方法是有效的.  相似文献   

6.
针对蚁群算法在寻优过程中容易出现停滞现象,同意在该算法中引入免疫机制,将待求解问题看成抗原,而问题的解看成抗体,通过基于浓度的选择机制和多样性保持策略来提高蚁群算法的全局搜索能力和避免停滞现象.对TSP问题的仿真实验结果表明,该算法极大地提高了搜索能力和避免了停滞现象.  相似文献   

7.
用嵌套插队算法解决TSP问题   总被引:1,自引:0,他引:1  
本提出了一种求解TSP问题的近似算法—嵌套插队算法。这种算法结合了启发式算法和随机化算法以及局部寻优的思想。实验结果表明对于较小规模的。TSP问题,直接用插队算法(QJA)就能以很大的概率获得已知最优解。对于规模较大的问题实例。嵌套插队算法(NQJA)能获得质量高于名的启发式算法的解。另外,用嵌套插队算法找到的China144的最短路径优于目前已知的最短路径。嵌套插队算法是专门针对TSP问题而提出的,但其思想也可以给求解其他NP难解的组合优化问题以启发。  相似文献   

8.
蚂蚁算法是一种新型的模拟进化算法,也是一种随机型智能搜索算法.较为系统的总结了算法的基本理论,分析了其基本算法解决TSP问题的模型,给出基于熵的变系数改进蚂蚁算法,并针对TSP问题进行优化性能的比较分析.  相似文献   

9.
本文提出了一种新的求解旅行商问题(TSP)的离散人工蜂群算法(DABC)。以基本人工蜂群算法为框架,采用路径编码的方式,综合运用离散交叉算子,逆转算子,免疫算子和单/多步2-opt算子以帮助雇佣蜂,观察蜂和侦察蜂产生新食物源。选择TSPLIB中典型的TSP实例进行仿真实验,运用多项性能指标对DABC算法进行评估。实验结果表明本文算法是解决TSP问题的一种非常有效的新方法。  相似文献   

10.
介绍了一种求解TSP问题的算法—改进的蚁群算法,算法通过模拟蚁群搜索食物的过程,可用于求解TSP问题,算法的主要特点是:正反馈、分布式计算、与某种启发式算法相结合.通过对传统蚁群算法的改进可以得到较好的结果.计算机仿真结果表明了该算法的有效性.  相似文献   

11.
在遗传算法能够有效解决TSP问题的基础上,根据遗传算法——通过搜索大规模,多样化的种群,在种群间交换个体所携带的遗传信息,保留种群中个体的优越遗传信息——的思想,设计了求解分组TSP问题的遗传算法。算法中染色体表示、评价函数的构造、杂交变异算子的设计经过实例计算的检验被证明较为可靠;算法运算速度快,容易获得有效解。  相似文献   

12.
We propose a framework of lower bounds for the asymmetric traveling salesman problem (TSP) based on approximating the dynamic programming formulation with different basis vector sets. We discuss how several well-known TSP lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between cities. We then introduce an exact reformulation that generates a family of successively tighter lower bounds, all solvable in polynomial time. We show that the base member of this family yields a bound greater than or equal to the well-known Held-Karp bound, obtained by solving the linear programming relaxation of the TSP’s integer programming arc-based formulation.  相似文献   

13.
The traveling salesman problem is an important combinatorial optimization problem due to its significance in academic research and its real world applications. The problem has been extensively studied and much is known about its polyhedral structure and algorithms for exact and heuristic solutions. While most work is concentrated on solving the deterministic version of the problem, there also has been some research on the stochastic TSP. Research on the stochastic TSP has concentrated on asymptotic properties and estimation of the TSP-constant. Not much is, however, known about the probability distribution of the optimal tour length. In this paper, we present some empirical results based on Monte Carlo simulations for the symmetric Euclidean and Rectilinear TSPs. We derive regression equations for predicting the first four moments of the distribution of estimated TSP tour lengths using heuristics. We then show that a Beta distribution gives excellent fits for small to moderate sized TSP problems. We derive regression equations for predicting the parameters of the Beta distribution. Finally we predict the TSP constant using two alternative approaches.  相似文献   

14.
《Optimization》2012,61(5):691-704
In 1972 Christofides introduced a lower bound for the Traveling Salesman Problem (TSP). The bound is based on solving repeatedly a Linear Assignment Problem. We relate the bound to the Complete Cycle Problem; as a consequence the correctness of the bound is easier to prove.

Further we give improvements for the bound in the symmetric case and we deal with the influence of the triangle equation together with the identification of non-optimal edges for the TSP. The improvements are illustrated by examples and computational results for large problems.  相似文献   

15.
The time dependent traveling salesman problem (TDTSP) is a generalization of the classical traveling salesman problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet-defining cuts. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving almost all instances from the TSPLIB with up to 107 vertices.  相似文献   

16.
This paper introduces a new problem that is an extension of the travelling salesman problem (TSP) in which the travelling times are resource dependent and the objective is to maximize the profit per unit of time. We present an optimal solution approach comprised of three main steps: (1) calculating the optimal amount of total resource required (regardless of the selected tour); (2) constructing the tour; and (3) assigning the optimal resource to each connection between vertices using the equivalent load method. This solution approach finds the optimal solution with the same computational complexity for solving the classic TSP.  相似文献   

17.
In this paper, we deal with the sequencing and routing problem of order pickers in conventional multi-parallel-aisle warehouse systems. For this NP-hard Steiner travelling salesman problem (TSP), exact algorithms only exist for warehouses with at most three cross aisles, while for other warehouse types literature provides a selection of dedicated construction heuristics. We evaluate to what extent reformulating and solving the problem as a classical TSP leads to performance improvements compared to existing dedicated heuristics. We report average savings in route distance of up to 47% when using the LKH (Lin–Kernighan–Helsgaun) TSP heuristic. Additionally, we examine if combining problem-specific solution concepts from dedicated heuristics with high-quality local search features could be useful. Lastly, we verify whether the sophistication of ‘state-of-the-art’ local search heuristics is necessary for routing order pickers in warehouses, or whether a subset of features suffices to generate high-quality solutions.  相似文献   

18.
模糊蚁群算法及其在TSP中的应用   总被引:1,自引:0,他引:1  
在传统蚁群算法的基础上加入了使用模糊规则表更新信息素的策略,提出了一种新的算法——模糊蚁群算法.算法结合了模糊控制中输入输出的模糊化处理和蚁群寻优的特点,为实际问题提供了新的解决手段.文中将模糊蚁群算法应用于TSP问题,通过对中国31个省会城市等实例数据进行的测试,验证表明了新算法具有良好的有效性和鲁棒性.  相似文献   

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