The Knapsack Sharing Problem: An Exact Algorithm

In this paper, we propose an exact algorithm for the knapsack sharing problem. The proposed algorithm seems quite efficient in the sense that it solves quickly some large problem instances. The problem is decomposed into a series of single constraint knapsack problems; and by applying the dynamic programming and another strategy, we solve optimally the original problem. The performance of the exact algorithm is evaluated on a set of medium and large problem instances (a total of 240 problem instances). This algorithm is parallelizable and this is one of its important feature.     

有时间窗车辆路径问题的模型及其改进模拟退火算法研究

论文在对有时间窗车辆路径问题进行描述的基础上,建立了该问题的基于直观描述的数学模型.论文还根据有时间窗车辆路径问题的特点构造了求解该问题的改进模拟退火算法,并进行了实验计算.计算结果表明,用本文设计的改进模拟退火算法求解有时间窗车辆路径问题,不仅可以取得很好的计算结果,而且算法的计算效率较高,收敛速度较快,计算结果也较稳定.     

最短时限运输问题及解法

提出了存在于实际中的最短时限运输问题,研究了其解的最优性充分条件,并给出了求解这一问题的具体步骤,最后用实例说明了解法的可操作性,该解法是解决这一类问题的一个好算法。     

用混合遗传算法求解物流配送路径优化问题的研究

论文建立了物流配送路径优化问题的数学模型,并针对遗传算法在局部搜索能力方面的不足,提出将爬山算法与遗传算法相结合,从而构造了求解物流配送路径优化问题的混合遗传算法,并进行了实验计算。计算结果表明,用混合遗传算法求解物流配送路径优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足,从而得到质量较高的解。     

具有模糊预约时间的VRP混合遗传算法

在对具有模糊预约时间的多对多货物收发情况下的车辆路径问题进行简单描述的基础上,构建了该问题的多目标数学规划模型,提出了解决该问题的一种基于插入启发式算法、并用修正的推—碰—掷过程进行改进的混合遗传算法,最后,给出了该问题的一个计算实例,并与改进的Solomon插入启发式算法进行了比较.     

车辆路径问题的禁忌搜索算法研究

论文在对车辆路径问题进行简单描述的基础上,通过设计一种新的解的表示方法构造了求解该问题的一种新的禁忌搜索算法,并进行了实验计算。计算结果表明,用本文设计的禁忌搜索算法求解车辆路径问题,不仅可以取得很好的计算结果,而且算法的计算效率较高,收敛速度较快,计算结果也较稳定。     

运输问题时间优化算法

运输问题是线性规划中的一类特殊问题。适用于求解目标函数符合线性叠加关系的费用或距离问题,对于实际运输问题中的运输时间优化问题则难以给出优化解。本文结合科研实践提出了运输问题中有关时间优化的迭代算法模型,此模型可给出整体运输时间最优的运输方案。通过实际检验证明,此算法简便、稳定、计算结果符合实际情况。     

Exact approaches for the pickup and delivery problem with loading cost

In this paper, we propose a branch-and-cut algorithm and a branch-and-price algorithm to solve the pickup and delivery problem with loading cost (PDPLC), which is a new problem derived from the classic pickup and delivery problem (PDP) by considering the loading cost in the objective function. Applications of the PDPLC arise in healthcare transportation where the objective function is customer-centric or service-based. In the branch-and-price algorithm, we devise an ad hoc label-setting algorithm to solve the pricing problem and employ the bounded bidirectional search strategy to accelerate the label-setting algorithm. The proposed algorithms were tested on a set of instances generated by a common data generator in the literature. The computational results showed that the branch-and-price algorithm outperformed the branch-and-cut algorithm by a large margin, and can solve instances with 40 requests to optimality in a reasonable time frame.     

无人仓系统储位分配问题的优化模型与算法

考虑到无人仓系统补货阶段货架上只有部分空余储位的特点，研究了补货商品储位分配问题的优化模型与算法。以同一货架上存放的商品之间关联度之和最大化为目标建立了混合整数规划模型；结合贪婪算法和邻域搜索算法设计了求解模型的两阶段方法。第一阶段利用贪婪算法求初始可行解；第二阶段利用邻域搜索算法对初始可行解进行优化。利用一个具体算例验证了邻域搜索算法的优化效果，结果显示，通过邻域搜索算法对初始可行解的优化，可以使目标函数值至少提升27%。进一步利用多个小规模算例分析了两阶段算法的近似比和求解速度，验证了算法的快速有效性。本文的研究结果不仅解决了货架初始状态非空情况下的储位分配问题，同样适合解决货架初始状态为空的情况，因此更加符合实际场景，可以作为无人仓管理信息系统的核心模型和算法。     

A hard clustering approach to the part family formation problem

The part family problem in group technology can be stated as the problem of finding the best grouping of parts into families such that the parts within each family are as similar to each other as possible. In this paper, the part family formation problem is considered. The problem is cast into a hard clustering model, and the k-means algorithm is proposed for solving it. Preliminary computational experience on the algorithm is very encouraging and it shows that real-life problems of large sizes can efficiently be handled by this approach.     

A Parametric Approach for a Nonlinear Discrete Location Problem

A discrete location problem is formulated for the design of a postal service network. The cost objective of this problem includes a nonlinear concave component. A parametric integer programming algorithm is developed to find an approximate solution to the problem. The algorithm reduces the problem into a sequence of p-median problems and deals with the nonlinear cost by a node-replacement scheme. Preliminary computational results are presented.     

From theory to practice: maximizing revenues for on-line dial-a-ride

We consider the on-line dial-a-ride problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter. We also provide experimental results for the complete and complete bipartite graphs. Our simulations support our theoretical findings and demonstrate that our algorithms perform well under settings that reflect realistic dial-a-ride systems.     

基于混合蚁群算法的冷链物流配送路径优化研究

基于绿色物流发展理念，为企业寻求经济与环境达到双赢的局面，本研究将节能减排转化为绿色成本，融入路径优化问题中，建立以总成本最小为研究目标的冷链物流路径优化数学模型。针对蚁群算法初始阶段由于信息素不足导致收敛速度慢的问题，将A*算法与蚁群算法相结合，利用A*算法的全局收敛性和蚁群算法的正反馈性构造了一种混合蚁群算法。通过对实例进行仿真优化与对比分析，验证了模型和算法的有效性。     

有限缓冲区的多节点订单接受模型与算法

订单接受问题广泛存在于生产管理中,而现有多节点订单接受问题中大多不考虑缓冲区约束对订单接受的影响。针对这一问题,以缓冲区约束的多节点生产为背景,建立了订单接受模型。利用改进NEH算法、离散和声搜索算法和变邻域搜索的混合算法对模型进行求解。实验结果显示,当问题规模较小时,算法取得较好的计算效果。问题规模较大时,求解效果一般。缓冲区的大小对订单完工时间影响较小,与无限缓冲区的计算结果相似。混合算法具有较好的求解速度,能够有效求解问题模型。     

A successive approximation algorithm for the multiple knapsack problem

It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective algorithm for the 0-1 knapsack problem. This paper considers such an approximation algorithm that packs the knapsacks in the nondecreasing order of their capacities. We analyze this algorithm for 2 and 3 knapsack problems by the worst-case analysis method and give all their error bounds.     

Minimizing number of tardy jobs on a single machine subject to periodic maintenance

This paper considers a single-machine scheduling problem with periodic maintenance. In this study, a schedule consists of several maintenance periods and each maintenance period is scheduled after a periodic time interval. The objective is to find a schedule that minimizes the number of tardy jobs subject to periodic maintenance and nonresumable jobs. Based on the Moore's algorithm, an effective heuristic is developed to provide a near-optimal schedule for the problem. A branch-and-bound algorithm is also proposed to find the optimal schedule. Some important theorems associated with the problem are implemented in the algorithm. Computational results are presented to demonstrate the effectiveness of the proposed heuristic.     

基于Lagrange松弛分解法的供应链生产-定位-路径集成问题优化

本文研究了集成生产批量、配送中心定位和车辆运输路径问题的一个复杂大系统,并建立了相应的数学模型。为了便于理解和求解这一大系统,将这一系统运用Lagrange松弛法分解成了生产、配送中心和定位-路径等三个相对独立的子系统。基于次梯度优化算法提出了一种优化协调机制,实现了系统的整体优化,并进行了数值实验分析。     

The optimum traversal of a graph

For a given graph (network) having costs [c_ij] associated with its links, the present paper examines the problem of finding a cycle which traverses every link of the graph at least once, and which incurs the minimum cost of traversal. This problem (called thegraph traversal problem, or theChinese postman problem [9]) can be formulated in ways analogous to those used for the well-known travelling salesman problem, and using this apparent similarity, Bellman and Cooke [1] have produced a dynamic programming formulation. This method of solution of the graph traversal problem requires computational times which increase exponentially with the number of links in the graph. Approximately the same rate of increase of computational effort with problem size would result by any other method adapting a travelling salesman algorithm to the present problem.This paper describes an efficient algorithm for the optimal solution of the graph traversal problem based on the matching method of Edmonds [5, 6]. The computational time requirements of this algorithm increase as a low order (2 or 3) power of the number of links in the graph. Computational results are given for graphs of up to 50 vertices and 125 links.The paper then discusses a generalised version of the graph traversal problem, where not one but a number of cycles are required to traverse the graph. In this case each link has (in addition to its cost) a quantity q_ij associated with it, and the sum of the quantities of the links in any one cycle must be less than a given amount representing the cycle capacity. A heuristic algorithm for the solution of this problem is given. The algorithm is based on the optimal algorithm for the single-cycle graph traversal problem and is shown to produce near-optimal results.There is a large number of possible applications where graph traversal problems arise. These applications include: the spraying of roads with salt-grit to prevent ice formation, the inspection of electric power lines, gas, or oil pipelines for faults, the delivery of letter post, etc.     

The hierarchical model for load balancing on two machines

Following previous work, we consider the hierarchical load balancing model on two machines of possibly different speeds. We first focus on maximizing the minimum machine load and show that no competitive algorithm exists for this problem. We overcome this barrier in two ways, both related to previously known models. The first one is fractional assignment, where each job can be arbitrarily split between the machines. The second one is a semi-online model where the sum of jobs is known in advance. We design algorithms of best possible competitive ratios for both these cases. Furthermore, we show that the combination of the two models leads to the existence of an optimal algorithm (i.e., an algorithm of competitive ratio 1). This algorithm is clearly optimal for the makespan minimization problem as well. For the latter problem, we consider the fractional assignment model and design an algorithm of best possible competitive ratio for it. This work was submitted as the M.Sc. thesis of the first author.     

Pareto mimic algorithm: An approach to the team orienteering problem

The team orienteering problem is an important variant of the vehicle routing problem. In this paper, a new algorithm, called Pareto mimic algorithm, is proposed to deal with it. This algorithm maintains a population of incumbent solutions which are updated using Pareto dominance. It uses a new operator, called mimic operator, to generate a new solution by imitating an incumbent solution. Furthermore, to improve the quality of a solution, it employs an operator, called swallow operator which attempts to swallow (or insert) an infeasible node and then repair the resulting infeasible solution. A comparative study supports the effectiveness of the proposed algorithm, especially, our algorithm can quickly find new better results for several large-scale instances. We also demonstrate that Pareto mimic algorithm can be generalized to solve other routing problems, e.g., the capacitated vehicle routing problem.