A branch-price-and-cut algorithm for the commodity constrained split delivery vehicle routing problem

We consider the Commodity constrained Split Delivery Vehicle Routing Problem (C-SDVRP), a routing problem where customers may request multiple commodities. The vehicles can deliver any set of commodities and multiple visits to a customer are allowed only if the customer requests multiple commodities. If the customer is visited more than once, the different vehicles will deliver different sets of commodities. Allowing the splitting of the demand of a customer only for different commodities may be more costly than allowing also the splitting of each individual commodity, but at the same time it is easier to organize and more acceptable to customers. We model the C-SDVRP by means of a set partitioning formulation and present a branch-price-and-cut algorithm. In the pricing phase, the ng-path relaxation of a constrained elementary shortest path problem is solved with a label setting dynamic programming algorithm. Capacity cuts are added in order to strengthen the lower bound. We solve to optimality within 2 h instances with up to 40 customers and 3 commodities per customer.     

基于粒计算的多标签懒惰学习算法

多标签学习用于处理一个样本同时拥有多个标签的问题。已有的多标签懒惰学习算法IMLLA未充分考虑样本分布的特点,即在构建样本的近邻点集时,近邻点个数取固定值,这可能会将相似度高的点排除在近邻集之外,或者将相似度低的点包括在近邻集内,影响分类方法的性能。针对IMLLA的缺陷,将粒计算的思想加入近邻集的构建,提出一种基于粒计算的多标签懒惰学习算法(GMLLA)。该方法通过粒度控制,确定样本近邻点集,使得近邻集内的样本具有高相似度。实验结果表明,本算法的性能优于IMLLA。     

A genetic algorithm-based approach for solving the resource-sharing and scheduling problem

We introduce a heuristic that is based on a unique genetic algorithm (GA) to solve the resource-sharing and scheduling problem (RSSP). This problem was previously formulated as a continuous-time mixed integer linear programming model and was solved optimally using a branch-and-bound (B&B) algorithm. The RSSP considers the use of a set of resources for the production of several products. Producing each product requires a set of operations with precedence relationships among them. Each operation can be performed using alternative modes which define the subset of the resources needed, and an operation may share different resources simultaneously. The problem is to select a single mode for each operation and accordingly to schedule the resources, while minimizing the makespan time. The GA we propose is based on a new encoding schema that adopts the structure of a DNA in nature. In our experiments we compared the effectiveness and runtime of our GA versus a B&B algorithm and two truncated B&B algorithms that we developed on a set of 118 problem instances. The results demonstrate that the GA solved all the problems (10 runs each), and reaches optimality in 75% of the runs, had an average deviation of less than 1% from the optimal makespan, and a runtime that was much less sensitive to the size of the problem instance.     

基于密度峰值聚类和径向基函数的过采样算法

现有的大多数过采样算法在采样过程中只考虑少数类样本的分布而忽略多数类样本的分布,且数据集除了存在类间不平衡问题之外,还存在类内不平衡问题。针对这些问题,提出一种基于密度峰值聚类和径向基函数的过采样方法。该方法首先利用改进的密度峰值聚类算法自适应地为少数类聚类,获得多个子簇;利用聚类过程计算所得的局部密度为各子簇分配权重,并根据权重确定各子簇的过采样量;用径向基函数计算少数类样本的相互类势,以相互类势为依据对少数类进行过采样。将算法与不同分类器结合进行实验,用不同指标评价分类效果,实验表明,该算法的分类效果较优。     

The labeled maximum matching problem

Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the labeled maximum matching problem. It is a relatively new problem whose application is related to the timetabling problem. We prove it is NP-complete and present four different mathematical formulations. Moreover, we propose an exact algorithm based on a branch-and-bound approach to solve it. We evaluate the performance of our algorithm on a wide set of instances and compare our computational times with the ones required by CPLEX to solve the proposed mathematical formulations. Test results show the effectiveness of our procedure, that hugely outperforms the solver.     

通过评估示例中概念的重要性来解决多示例学习问题

在多示例学习问题中,训练数据集里面的每一个带标记的样本都是由多个示例组成的包,其最终目的是利用这一数据集去训练一个分类器,使得可以利用该分类器去预测还没有被标记的包。在以往的关于多示例学习问题的研究中,有的是通过修改现有的单示例学习算法来迎合多示例的需要,有的则是通过提出新的方法来挖掘示例与包之间的关系并利用挖掘的结果来解决问题。以改变包的表现形式为出发点,提出了一个解决多示例学习问题的算法——概念评估算法。该算法首先利用聚类算法将所有示例聚成d簇,每一个簇可以看作是包含在示例中的概念;然后利用原本用于文本检索的TF-IDF(Term Frequency-Inverse Document Frequency)算法来评估出每一个概念在每个包中的重要性;最后将包表示成一个d维向量——概念评估向量,其第i个位置表示第i个簇所代表的概念在某个包中的重要程度。经重新表示后,原有的多示例数据集已不再是"多示例",以至于一些现有的单示例学习算法能够用来高效地解决多示例学习问题。     

A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.     

Multiscale production routing in multicommodity supply chains with complex production facilities

In this work, we introduce the multiscale production routing problem (MPRP), which considers the coordination of production, inventory, distribution, and routing decisions in multicommodity supply chains with complex continuous production facilities. We propose an MILP model involving two different time grids. While a detailed mode-based production scheduling model captures all critical operational constraints on the fine time grid, vehicle routing is considered in each time period of the coarse time grid. In order to solve large instances of the MPRP, we propose an iterative MILP-based heuristic approach that solves the MILP model with a restricted set of candidate routes at each iteration and dynamically updates the set of candidate routes for the next iteration. The results of an extensive computational study show that the proposed algorithm finds high-quality solutions in reasonable computation times, and in large instances, it significantly outperforms a standard two-phase heuristic approach and a solution strategy involving a one-time heuristic pre-generation of candidate routes. Similar results are achieved in an industrial case study, which considers a real-world industrial gas supply chain.     

Integrating employee timetabling with scheduling of machines and transporters in a job-shop environment: A mathematical formulation and an Anarchic Society Optimization algorithm

This paper addresses a ternary-integration scheduling problem that incorporates employee timetabling into the scheduling of machines and transporters in a job-shop environment with a finite number of heterogeneous transporters where the objective is to minimize the completion time of all jobs. The problem is first formulated as a mixed-integer linear programming model. Then, an Anarchic Society Optimization (ASO) algorithm is developed to solve large-sized instances of the problem. The formulation is used to solve small-sized instances and to evaluate the quality of the solutions obtained for instances with larger sizes. A comprehensive numerical study is carried out to assess the performance of the proposed ASO algorithm. The algorithm is compared with three alternative metaheuristic algorithms. It is also compared with several algorithms developed in the literature for the integrated scheduling of machines and transporters. Moreover, the algorithms are tested on a set of adapted benchmark instances for an integrated problem of machine scheduling and employee timetabling. The numerical analysis suggests that the ASO algorithm is both effective and efficient in solving large-sized instances of the proposed integrated job-shop scheduling problem.     

An exact algorithm and a metaheuristic for the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem (GVRP) involves finding a minimum-length set of vehicle routes passing through a set of clusters, where each cluster contains a number of vertices, such that the tour includes exactly one vertex from each cluster and satisfies capacity constraints. We consider a version of the GVRP where the number of vehicles is a decision variable. This paper introduces a new mathematical formulation based on a two-commodity flow model. We solve the problem using a branch-and-cut algorithm and a metaheuristic that is a hybrid of the greedy randomized adaptive search procedure (GRASP) and the evolutionary local search (ELS) proposed in [18]. We perform computational experiments on instances from the literature to demonstrate the performance of our algorithms.     

A GRASP algorithm to solve the unicost set covering problem

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper presents a GRASP algorithm to solve a special SCP case known in the literature as the unicost set covering problem. The algorithm incorporates a local improvement procedure based on the heuristics to solve binary constraint satisfiability problems (SAT). The quality of the proposed algorithm is tested on a set of reference instances, comparing the obtained results with those found in the literature. Our algorithm improves the best-known solutions for many of these instances.     

求解车辆路径问题的人工蜂群算法

采用人工蜂群算法对车辆路径问题进行求解,给出食物源的自然数编码方法,并采用邻域倒位方法生成候选食物源。应用算法求解了多个车辆路径问题的实例,并将结果与其它一些启发式算法进行了比较和分析。计算结果表明,人工蜂群算法可以有效求解车辆路径问题,同时也为算法求解其它一些组合优化问题提供了有益思路。     

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.     

Adaptive memory programming for the vehicle routing problem with multiple trips

The Vehicle Routing Problem with Multiple Trips is an extension of the classical Vehicle Routing Problem in which each vehicle may perform several routes in the same planning period. In this paper, an adaptive memory algorithm to solve this problem is proposed. Computational experience is reported over a set of benchmark problem instances.     

A linear model for compound multicommodity network flow problems

This work proposes a network flow linear program model to solve the problem of minimizing costs of production and distribution of compound multicommodities. In our proposed model, coupling constraints are considered in order to treat the existing proportionality among several flows of different commodities that are necessary to mixture for composing new commodities. The coupling constraint matrix for this type of problem is very large in general. Our formulation reduces the number of proportionality constraints enabling the use of a solution technique based on a specialization of the primal-dual simplex algorithm applied in two distinct phases. As initial solution it is used a basis built through the heuristic method that allocates flows in low cost lanes. To perform the change of basis operation, the working matrix is stored as a product form of the inverse to keep constant its dimension and to preserve sparsity. Experimental results containing around 200,000 constraints and 75,000 arcs applicable to the distribution of multicommodities of a petrochemical industry were accomplished with success. The results obtained show computer efficiency of the developed algorithm and the applicability of the formulated model.     

基于统计学习框架的中文新词检测方法

近邻(Nearest Neighbor,NN)算法是一种简单实用的监督分类算法。但NN算法在分类未知类标的样例时,需要存储整个训练集,还要计算该样例到训练集中每一个样例之间的距离,所以NN算法的计算复杂度非常高。为了克服这一缺点,P.Hart提出了压缩近邻(Condensed Nearest Neighbor,CNN)规则算法,即从整个训练集中找原样例集的一致子集(一致子集是能正确分类训练集中其他样例的子集)。其计算复杂度依然比较高,特别是对于大型数据库,寻找其一致子集是非常耗费时间的。针对这一问题,提出了基于粗糙集技术的压缩近邻规则算法。该算法分为3步,首先利用粗糙集方法求属性约简(特征选择),以将冗余的属性去掉。然后选取靠近边界域的样例,以将冗余的样例去掉。最后从选出的样例中计算一致子集。该算法能同时沿垂直方向和水平方法进行数据约简。实验结果显示,所提出的方法是行之有效的。     

The patient bed assignment problem solved by autonomous bat algorithm

The patient bed assignment problem consists of managing, in the best possible way, a set of beds with particular features and assigning them to a set of patients with special requirements. This assignment problem can be seen an optimization problem, of which the intended aims are usually to minimize the number of internal movements within a unit and to maximize bed usage according to the levels of criticality of the patients, among others. The usual approaches for solving this problem follow a traditional model based on the constraint programming paradigm, mainly using hard constraints. However, in real-life problems, constraints that should ideally be satisfied are often violated. In this paper, we present a new model for the patient bed assignment problem based on the minimum sum of unsatisfied constraints. This technique enables the consideration of soft constraints in the potential solutions that exhibit the best performance. The aim is to find the assignment that minimizes a weighted sum of the unsatisfied constraints. To this end, we use an autonomous binary version of the bat algorithm, which is an optimization technique inspired by the bio-sonar behaviour of microbats, to find the best set of potential solutions without requiring any expert user knowledge to achieve an efficient solution process. To validate our proposal, we use our model to solve problem instances based on data from several hospitals, and we perform a detailed comparative statistical analysis with a traditional constraint programming solver and several well-known optimization algorithms, including the classic bat algorithm. Promising results show that our approach is capable of efficiently solving 30 instances with decreased solution times.     

A graph-based immune-inspired constraint satisfaction search

We propose an artificial immune algorithm to solve constraint satisfaction problems (CSPs). Recently, bio-inspired algorithms have been proposed to solve CSPs. They have shown to be efficient in solving hard problem instances. Given that recent publications indicate that immune-inspired algorithms offer advantages to solve complex problems, our main goal is to propose an efficient immune algorithm which can solve CSPs. We have calibrated our algorithm using relevance estimation and value calibration (REVAC), which is a new technique recently introduced to find the parameter values for evolutionary algorithms. The tests were carried out using randomly generated binary constraint satisfaction problems and instances of the three-colouring problem with different constraint networks. The results suggest that the technique may be successfully applied to solve CSPs.     

Using a SAT-solver to schedule sports leagues

Tournament schedules of sports leagues have to satisfy several types of constraints such as stadium unavailability, fixed matches, forbidden matches, minimum number of breaks. Usually, there is no schedule satisfying all given constraints and, hence, some of the constraints are considered as ‘soft’ ones. There are various models appropriately describing the environment of sport leagues. Only heuristic methods are known from the literature for solving instances of real life dimensions. We consider here a model which satisfies the demands of many sports leagues. We solve our model by reduction to series of instances of the propositional satisfiability problem and adaption of a satisfiability solver for these specific instances. We test our method on two real life examples and solve the problem optimally within our model in each case. Our solver shows good computational results also on generated test instances, which are motivated by real life requirements. It can be easily extended to meet the demands of other sports leagues.     

Determine the optimal carrier selection for a logistics network based on multi-commodity reliability criterion

From the perspective of supply chain management, the selected carrier plays an important role in freight delivery. This article proposes a new criterion of multi-commodity reliability and optimises the carrier selection based on such a criterion for logistics networks with routes and nodes, over which multiple commodities are delivered. Carrier selection concerns the selection of exactly one carrier to deliver freight on each route. The capacity of each carrier has several available values associated with a probability distribution, since some of a carrier's capacity may be reserved for various orders. Therefore, the logistics network, given any carrier selection, is a multi-commodity multi-state logistics network. Multi-commodity reliability is defined as a probability that the logistics network can satisfy a customer's demand for various commodities, and is a performance indicator for freight delivery. To solve this problem, this study proposes an optimisation algorithm that integrates genetic algorithm, minimal paths and Recursive Sum of Disjoint Products. A practical example in which multi-sized LCD monitors are delivered from China to Germany is considered to illustrate the solution procedure.