动态搜索算法求解时间依赖型旅行商问题研究

时间依赖型旅行商问题(TDTSP)是旅行商问题(TSP)的延伸.在该问题中,任意两节点间的旅行时间(成本)不仅取决于节点间的距离,还依赖于一天中具体时段或节点在哈密顿圈中所处的具体位置.对基于节点所处哈密顿圈中具体位置的TDTSP问题建立相应的数学模型,并提出求解该问题的动态搜索算法.通过实验仿真,验证了动态搜索算法优于目前在邻域搜索领域求解该问题最有效的动态规划启发式算法.

     

用并行回溯搜索算法求解TSP问题

对求解旅行商问题的回溯搜索算法进行并行化的设计和改进,对该并行算法进行了详细描述。在MPI并行计算环境下应用该并行算法进行计算,求出了旅行商问题的最优解。实验结果表明,该并行算法适合求解小规模旅行商问题。     

牛奶配送问题的两阶段平衡TSP优化算法研究

牛奶配送问题中包含访问次数不同的节点,该问题可以当做两阶段旅行商问题进行求解。为有效地求解节点个数处于平衡条件下的牛奶配送问题的两阶段旅行商问题,提出了一种启发式优化求解方法,有助提高目标问题的求解效率和性能。针对节点数量平衡性和节点访问次数不同的特点,提出一种基于节点划分的动态规划优化。通过对实例进行计算和比较,结果验证了所提方法的有效性和优越性。     

动态旅行商问题的研究

传统的旅行商问题都是静态的,但在现实中许多问题是动态的。该文提出动态旅行商问题,问题的规模随时间不断变化。实时问题对算法的求解效率要求很高,为此设计了基于模糊规则的在线遗传算法,可以根据求解问题的变化,在线精炼模糊控制规则来控制算法的参数。仿真实验验证了算法的有效性。     

最小比率旅行商问题的引力搜索算法求解

经典旅行商问题的目标函数是总路程最小,而在实际情况中往往会考虑旅行商的收益问题,研究了以总路程和总收益之比为目标函数的最小比率旅行商问题.由于该问题的目标函数是非线性的,比求解目标函数是线性的旅行商问题更为困难,为有效求解该问题,提出一种引力搜索算法.算法基于万有引力定律和牛顿第二定律进行寻优,并采用速度和位置的计算模型.同时结合随机键的编码方法,将搜索个体的连续位置转换为离散的城市访问顺序.给出了算法的具体实现方案,并通过仿真和比较实验验证算法的优化性能.实验结果表明该算法可以有效求解最小比率旅行商问题.     

动态商拓扑模型及其在路径查找中的应用

为解决动态环境下的问题求解,针对拓扑结构随时间变化的情况,文中借鉴社会学中的信任模型扩展传统的商空间理论,利用贝叶斯方法评估节点的可信度,提出一种基于信任机制的动态商拓扑模型.将该模型应用于最佳路径查找.仿真结果证实,该模型能以较小的时间花费为代价,有效提高路径可靠性,实现动态问题求解.     

一种混合局部搜索算法的嵌套分区算法

提出了一种混合多种局部搜索算法的嵌套分区算法用于求解中小规模旅行商问题.该算法使用加权抽样法产生初始最可能域,用带约束的3-opt局部搜索算法搜索每个子域的最优解,然后对Lin-Kemighan算法进行了改进,并且用改进的Lin-Kemighan算法搜索每个裙域的最优解,最后通过实验分析法确定了子域和裙域最优的抽样个数及初始最可能域的长度.对TSPLIB中15个问题实例的仿真结果表明,所提出的混合局部搜索算法的改进嵌套分区算法在求解旅行商问题时可以获得高质量的解.     

基于基因库求解旅行商问题的遗传算法

针对传统遗传算法(genetic algorithm, GA)求解旅行商问题(traveling salesman problem, TSP)存在寻优效率低、实验结果缺乏一致性等问题,提出了一种基于基因库的遗传算法(genetic algorithm based on genes pool, GPGA)。GPGA从种群中搜索减小哈密顿圈长度的边,并当做优良基因构成基因库。父代哈密顿圈在基因库引导下产生更优的子代哈密顿圈,基因库也随着种群的不断进化而同步更新,引导种群个体逐步向最优解靠近。算例结果表明在同样条件下,GPGA比传统遗传算法和几种改进遗传算法的性能更优。     

改进的麻雀搜索算法及其求解旅行商问题

旅行商问题(TSP)是经典的NP难问题,对该问题的研究从未停止,也得到了很多的近似求解算法,但每一种算法都各有特色,正因如此,对旅行商问题总有新的算法在提出.麻雀算法是新近提出的算法,本文对麻雀搜索算法(SSA)的原理、搜索策略以及算法的基本流程进行研究分析,针对SSA搜索接近全局最优时,种群的多样性减少,容易陷入局部...     

一种求解TSP问题的ACO&SS算法设计

提出一种求解旅行商(TSP)问题的新型分散搜索算法.将蚁群算法(ACO)的构解方法引入分散搜索(SS)算法,在搜索过程中既考虑解的质量,又考虑解的分散性.采用一种将蚁群算法的信息素更新技术与分散搜索的组合机制相结合的新型子集组合成新解的构解机制,同时采用动态更新参考集与临界准则策略来加快收敛速度.实验结果表明,该算法优于其他现有的方法,获得了较好的结果.     

汽车同步装配线生产计划与调度集成优化汽车同步装配线生产计划与调度集成优化

为克服传统的"自顶向下"方式下生产计划与调度不协调的缺陷,针对汽车同步装配线,构造了生产计划与调度集成优化混合整数规划模型,并采用拉格朗日松弛法将其分解为批量计划及调度等子问题.将调度子问题转化为与时间相关的旅行商问题,并采用dynasearch算法求解.对于拉格朗日对偶问题,采用均衡方向策略法求解.仿真实验结果验证了模型及算法的有效性.     

Online and Offline Algorithms for the Time-Dependent TSP with Time Zones

The time-dependent traveling salesman problem (TDTSP) is a variant of TSP with time-dependent edge costs. We study some restrictions of TDTSP where the number of edge cost changes are limited. We find competitive ratios for online versions of TDTSP. From these we derive polynomial time approximation algorithms for graphs with edge costs one and two. In addition, we present an approximation algorithm for the orienteering problem with edge costs one and two.     

Efficient approximation algorithms for the routing open shop problem

We consider the routing open shop problem being a generalization of two classical discrete optimization problems: the open shop scheduling problem and the metric traveling salesman problem. The jobs are located at nodes of some transportation network, and the machines travel on the network to execute the jobs in the open shop environment. The machines are initially located at the same node (depot) and must return to the depot after completing all the jobs. It is required to find a non-preemptive schedule with the minimum makespan. The problem is NP-hard even on the two-node network with two machines. We present new polynomial-time approximation algorithms with worst-case performance guarantees.     

A novel discretization scheme for the close enough traveling salesman problem

This paper addresses a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood set of that node. The problem is known as the close-enough traveling salesman problem. We introduce a new effective discretization scheme that allows us to compute both a lower and an upper bound for the optimal solution. Moreover, we apply a graph reduction algorithm that significantly reduces the problem size and speeds up computation of the bounds. We evaluate the effectiveness and the performance of our approach on several benchmark instances. The computational results show that our algorithm is faster than the other algorithms available in the literature and that the bounds it provides are almost always more accurate.     

Visiting convex regions in a polygonal map

This paper is concerned with a variant of the multi-goal path planning in which goals are represented as convex polygons. The problem is to find a closed shortest path in a polygonal map such that all goals are visited. The proposed solution is based on a self-organizing map (SOM) algorithm for the traveling salesman problem. Neurons’ weights are considered as nodes inside the polygonal domain and connected nodes represent a path that evolves according to the proposed adaptation rules. In addition, a reference algorithm based on the solution of the traveling salesman problem and the consecutive touring polygons problem is provided to find high quality solutions of the created set of problems. The problems are designed to represent various inspection and patrolling tasks and can form a kind of benchmark set for multi-goal path planning algorithms. The performance of the algorithms is examined in this problem set, which includes an instance of the watchman route problem with restricted visibility range. The proposed SOM based algorithms provide a unified approach to solve various visibility based routing problems in polygonal maps while they provide a competitive quality of solutions to the reference algorithm with significantly lower computational requirements.     

Branch-and-cut for the pickup and delivery traveling salesman problem with FIFO loading

This paper introduces a branch-and-cut algorithm for a variant of the pickup and delivery traveling salesman problem in which pickups and deliveries must obey the first-in-first-out policy. We propose a new mathematical formulation of the problem and several families of valid inequalities which are used within the branch-and-cut algorithm. Computational experiments on instances from the literature show that this algorithm outperforms existing exact algorithms, and that some instances with up to 25 requests (50 nodes) can be solved in reasonable computing time.     

Load-dependent and precedence-based models for pickup and delivery problems

We address the one-to-one multi-commodity pickup and delivery traveling salesman problem (m-PDTSP) which is a generalization of the TSP and arises in several transportation and logistics applications. The objective is to find a minimum-cost directed Hamiltonian path which starts and ends at given depot nodes and such that the demand of each given commodity is transported from the associated source to its destination and the vehicle capacity is never exceeded. In contrast, the many-to-many one-commodity pickup and delivery traveling salesman problem (1-PDTSP) just considers a single commodity and each node can be a source or target for units of this commodity. We show that the m-PDTSP is equivalent to the 1-PDTSP with additional precedence constraints defined by the source–destination pairs for each commodity and explore several models based on this equivalence. In particular, we consider layered graph models for the capacity constraints and introduce new valid inequalities for the precedence relations. Especially for tightly capacitated instances with a large number of commodities our branch-and-cut algorithms outperform the existing approaches. For the uncapacitated m-PDTSP (which is known as the sequential ordering problem) we are able to solve to optimality several open instances from the TSPLIB and SOPLIB.     

求解旅行商问题的自学习粒子群优化算法

针对旅行商问题,提出了一种带自学习算子的粒子群优化算法,根据旅行商问题及离散量运算的特点,对粒子的位置、速度等量及其运算规则进行了重新定义,为抑制早熟停滞现象,定义了变异速度来保持粒子群的多样性,使用自学习算子来提高算法的局部求精能力,使算法在空间探索和局部求精间取得了较好的平衡,与领域中的其它典型算法进行了仿真比较,结果表明,该算法具有良好的性能.     

Improving Combinatorial Optimization Algorithms through Record Keeping in Constructive Multistart Search

Constructive multistart search algorithms are commonly used to address combinatorial optimization problems; however, constructive multistart search algorithm performance is fundamentally affected by two factors: (i) The choice of construction algorithm utilized and (ii) the rate of state space search redundancy. Construction algorithms are typically specific to a particular combinatorial optimization problem; therefore, we first investigate construction algorithms for iterative hill climbing applied to the traveling salesman problem and experimentally determine the best performing algorithms. We then investigate the more general problem of utilizing record‐keeping mechanisms to mitigate state space search redundancy. Our research shows that a good choice of construction algorithm paired with effective record keeping significantly improves the quality of traveling salesmen problem solutions in a constant number of state explorations. Particularly, we show that Bloom filters considerably improve time performance and solution quality for iterative hill climbing approaches to the traveling salesman problem.     

指针网络改进遗传算法求解旅行商问题

虽然遗传算法相较于其他算法能够更好地求解旅行商问题,但这种算法在使用的过程中容易陷入局部最优的问题,进而导致问题求解遭遇困境。文章在简要介绍旅行商问题的基础上,介绍了遗传算法求解旅行商问题的思路和方法,并明确算法应用中存在的不足。在此基础上提出基于指针网络改进遗传算法求解旅行商问题的新思路,为弥补遗传算法的缺陷提供相应的原理支持。