The generalized covering traveling salesman problem

In this paper we develop a problem with potential applications in humanitarian relief transportation and telecommunication networks. Given a set of vertices including the depot, facility and customer vertices, the goal is to construct a minimum length cycle over a subset of facilities while covering a given number of customers. Essentially, a customer is covered when it is located within a pre-specified distance of a visited facility on the tour. We propose two node-based and flow-based mathematical models and two metaheuristic algorithms including memetic algorithm and a variable neighborhood search for the problem. Computational tests on a set of randomly generated instances and on set of benchmark data indicate the effectiveness of the proposed algorithms.     

Improving the quality of heuristic solutions for the capacitated vertex p-center problem through iterated greedy local search with variable neighborhood descent

The capacitated vertex p-center problem is a location problem that consists of placing p facilities and assigning customers to each of these facilities so as to minimize the largest distance between any customer and its assigned facility, subject to demand capacity constraints for each facility. In this work, a metaheuristic for this location problem that integrates several components such as greedy randomized construction with adaptive probabilistic sampling and iterated greedy local search with variable neighborhood descent is presented. Empirical evidence over a widely used set of benchmark data sets on location literature reveals the positive impact of each of the developed components. Furthermore, it is found empirically that the proposed heuristic outperforms the best existing heuristic for this problem in terms of solution quality, running time, and reliability on finding feasible solutions for hard instances.     

Insertion based Lin–Kernighan heuristic for single row facility layout

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is known to be NP-hard. In this paper, we present a neighborhood search heuristic called LK-INSERT which uses a Lin–Kernighan neighborhood structure built on insertion neighborhoods. To the best of our knowledge this is the first such heuristic for the SRFLP. Our computational experiments show that LK-INSERT is competitive for most instances, and it improves the best known solutions for several large sized benchmark SRFLP instances.     

Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like models

Companies frequently decide on the location and design for new facilities in a sequential way. However, for a fixed number of new facilities, the company might be able to improve its profit by taking its decisions for all the facilities simultaneously. In this paper we compare three different strategies: simultaneous location and independent design of two facilities in the plane, the same with equal designs, and the sequential approach of determining each facility in turn. The basic model is profit maximization for the chain, taking market share, location costs and design costs into account. The market share captured by each facility depends on the distance to the customers (location) and its quality (design), through a probabilistic Huff-like model. Recent research on this type of models was aimed at finding global optima for a single new facility, holding quality fixed or variable, but no exact algorithm has been proposed to find optimal solutions for more than one facility. We develop such an exact interval branch-and-bound algorithm to solve both simultaneous location and design two-facility problems. Then, we present computational results and exhibit the differences in locations and qualities of the optimal solutions one may obtain by the sequential and simultaneous approaches.     

Heuristics for the capacitated dispersion problem

In this paper, we investigate the adaptation of the greedy randomized adaptive search procedure (GRASP) and variable neighborhood descent (VND) methodologies to the capacitated dispersion problem. Dispersion and diversity problems arise in the placement of undesirable facilities, workforce management, and social media, among others. Maximizing diversity deals with selecting a subset of elements from a given set in such a way that the distance among the selected elements is maximized. We target here a realistic variant with capacity constraints for which a heuristic with a performance guarantee was previously introduced. In particular, we propose a hybridization of GRASP and VND implementing within the strategic oscillation framework. To evaluate the performance of our heuristic, we perform extensive experimentation to first set key search parameters, and then compare the final method with the previous heuristic. Additionally, we propose a mathematical model to obtain optimal solutions for small‐sized instances, and compare our solutions with the well‐known LocalSolver software.     

An efficient variable neighborhood search heuristic for very large scale vehicle routing problems

In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.     

Variable neighborhood search for the bi-objective post-sales network design problem: A fitness landscape analysis approach

Post-sales services are important markets in electronics industry due to their impact on marginal profit, market share, and their ability to retain customers. In this study, designing a multi-product four-layer post-sales reverse logistics network operated by a 3PL is investigated. A bi-objective MILP model is proposed to minimize network design costs as well as total weighted tardiness of returning products to customers. To solve the proposed model, a novel multi-start variable neighborhood search is suggested that incorporates nine neighborhood structures and three new encoding–decoding mechanisms. In particular, a fitness landscape measure is employed to select an effective neighborhood order for the proposed VNS. Extensive computational experiments show the effectiveness of the proposed heuristic and the three encoding–decoding mechanisms. The proposed method finds significantly better Pareto optimal sets in comparison with the original Priority method based on the number and the quality of obtained Pareto optimal solutions. In addition, it shows high efficiency by finding near-optimal solutions for the single objective versions of the problem.     

Heuristics for the single source capacitated multi-facility Weber problem

The Single Source Capacitated Multi-facility Weber Problem (SSCMWP) is concerned with locating I capacitated facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost of a single commodity such that each customer satisfies all its demand from exactly one facility. The SSCMWP is a non-convex optimization problem and difficult to solve. In the SSCMWP, customer locations, customer demands and facility capacities are known a priori. The transportation costs are proportional to the distance between customers and facilities. We consider both the Euclidean and rectilinear distance cases of the SSCMWP. We first present an Alternate Location and Allocation type heuristic and its extension by embedding a Very Large Scale Neighborhood search procedure. Then we apply a Discrete Approximation approach and propose both lower and upper bounding procedures for the SSCWMP using a Lagrangean Relaxation scheme. The proposed heuristics are compared with the solution approaches from the literature. According to extensive computational experiments on standard and randomly generated test sets, we can say that they yield promising performance.     

A bilevel fixed charge location model for facilities under imminent attack

We investigate a bilevel fixed charge facility location problem for a system planner (the defender) who has to provide public service to customers. The defender cannot dictate customer-facility assignments since the customers pick their facility of choice according to its proximity. Thus, each facility must have sufficient capacity installed to accommodate all customers for whom it is the closest one. Facilities can be opened either in the protected or unprotected mode. Protection immunizes against an attacker who is capable of destroying at most r unprotected facilities in the worst-case scenario. Partial protection or interdiction is not possible. The defender selects facility sites from m candidate locations which have different costs. The attacker is assumed to know the unprotected facilities with certainty. He makes his interdiction plan so as to maximize the total post-attack cost incurred by the defender. If a facility has been interdicted, its customers are reallocated to the closest available facilities making capacity expansion necessary. The problem is formulated as a static Stackelberg game between the defender (leader) and the attacker (follower). Two solution methods are proposed. The first is a tabu search heuristic where a hash function calculates and records the hash values of all visited solutions for the purpose of avoiding cycling. The second is a sequential method in which the location and protection decisions are separated. Both methods are tested on 60 randomly generated instances in which m ranges from 10 to 30, and r varies between 1 and 3. The solutions are further validated by means of an exhaustive search algorithm. Test results show that the defender's facility opening plan is sensitive to the protection and distance costs.     

GRASP and hybrid GRASP-Tabu heuristics to solve a maximal covering location problem with customer preference ordering

In this study, a maximal covering location problem is investigated. In this problem, we want to maximize the demand of a set of customers covered by a set of p facilities located among a set of potential sites. It is assumed that a set of facilities that belong to other firms exists and that customers freely choose allocation to the facilities within a coverage radius. The problem can be formulated as a bilevel mathematical programming problem, in which the leader locates facilities in order to maximize the demand covered and the follower allocates customers to the most preferred facility among those selected by the leader and facilities from other firms. We propose a greedy randomized adaptive search procedure (GRASP) heuristic and a hybrid GRASP-Tabu heuristic to find near optimal solutions. Results of the heuristic approaches are compared to solutions obtained with a single-level reformulation of the problem. Computational experiments demonstrate that the proposed algorithms can find very good quality solutions with a small computational burden. The most important feature of the proposed heuristics is that, despite their simplicity, optimal or near-optimal solutions can be determined very efficiently.     

A TABU search heuristic for the team orienteering problem

This paper describes a tabu search heuristic for the Team Orienteering Problem (TOP). The TOP is a variant of the well-known Vehicle Routing Problem in which a set of vehicle tours are constructed such that the total collected reward received from visiting a subset of customers is maximized and the length of each vehicle tour is restricted by a pre-specified limit. The tabu search heuristic is embedded in an adaptive memory procedure that alternates between small and large neighborhood stages during the solution improvement phase. Both random and greedy procedures for neighborhood solution generation are employed and infeasible, as well as feasible, solutions are explored in the process. Results from computational experiments conducted on a set of published test problems show that the proposed technique consistently produces high-quality solutions and outperforms other published heuristics for the TOP.     

基于混合需求的设施选址问题研究

研究网络中设施的需求一部分来自于网络节点, 一部分来自于过往流量的基于混合需求的设施选址问题。引入引力模型, 以新建设施获得总利润最大为目标建立非线性整数规划模型, 并构造启发式算法, 通过MATLAB进行仿真实验, 将求解结果与GPAH算法及精确算法的结果进行比较。比较结果表明, 提出的算法求解质量高、运行速度快, 可用于大中型网络设施的选址问题。     

A leader-follower game in competitive facility location

We address the problem of locating new facilities of a firm or franchise that enters a market where a competitor operates existing facilities. The goal of the new entrant firm is to decide the location and attractiveness of its new facilities that maximize its profit. The competitor can react by opening new facilities, closing existing ones, and adjusting the attractiveness levels of its existing facilities, with the aim of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the new facilities of both the firm and the competitor can be located at predetermined candidate sites. We employ the gravity-based rule in modeling the behavior of the customers where the probability that a customer visits a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. We propose heuristics that combine tabu search with exact solution methods.     

定位2运输路线安排问题的两阶段启发式算法

重点研究了集成化物流中一类特殊的定位一运输路线安排问题(LRP)的解决方法．LRP问题包括设施定位和运输路线优化两方面决策，属于NP-hard难题．由于问题的复杂性，提出基于假设前提的LRP模型及其两阶段启发式求解算法．该方法分两步实现：首先，采用基于最小包络聚类分析的启发式方法确定被选择的潜在设施及由每一个选中的设施所要提供服务的客户群；其次，运用带有控制开关的遗传算法求解每一确定客户类中的优化运输路线．提出利用两阶段启发式算法求解LRP问题，此方法实现容易、运算简单，一定程度上避免了遗传算法中的“局部最优现象”．仿真实验证明了该算法求解单目标LRP的有效性和准确性．     

An adaptive tabu search algorithm for the capacitated clustering problem

In the Capacitated Clustering Problem, a given set of customers with distinct demands must be partitioned into p clusters with limited capacities. The objective is to find p customers, called medians, from which the sum of the distances to all other customers in the cluster is minimized. In this article, a new adaptive tabu search approach is applied to solve the problem. Initial solutions are obtained by four constructive heuristics that use weights and distances as optimization criteria. Two neighborhood generation mechanisms are used by the local search heuristic: pairwise interchange and insertion . Computational results from 20 instances found in the literature indicate that the proposed method outperforms alternative metaheuristics developed for solving this problem.     

An integer programming-based local search for the covering salesman problem

We consider a generalized version of the well known Traveling Salesman Problem called Covering Salesman problem. In this problem, we are given a set of vertices while each vertex i can cover a subset of vertices within its predetermined covering distance r_i. The goal is to construct a minimum length Hamiltonian cycle over a subset of vertices in which those vertices not visited on the tour has to be within the covering distance of at least one vertex visited on the tour. The paper proposes an Integer Linear Programming based heuristic method which takes advantage of Integer Linear Programming techniques and heuristic search to improve the quality of the solutions. Extensive computational tests on the standard benchmark instances and on a new set of large sized datasets show the effectiveness of the proposed approach.     

Less is more approach: basic variable neighborhood search for the obnoxious p‐median problem

The goal of the less is more approach (LIMA) for solving optimization problems that has recently been proposed in Mladenovi? et al. (2016) is to find the minimum number of search ingredients that make a heuristic more efficient than the currently best. In this paper, LIMA is successfully applied to solve the obnoxious p‐median problem (OpMP). More precisely, we developed a basic variable neighborhood search for solving the OpMP, where the single search ingredient, the interchange neighborhood structure, is used. We also propose a new simple local search strategy for solving facility location problems, within the interchange neighborhood structure, which is in between the usual ones: first improvement and best improvement strategies. We call it facility best improvement local search. On the basis of experiments, it appeared to be more efficient and effective than both first and best improvement. According to the results obtained on the benchmark instances, our heuristic turns out to be highly competitive with the existing ones, establishing new state‐of‐the‐art results. For example, four new best‐known solutions and 133 ties are claimed in testing the set with 144 instances.     

A biased‐randomized metaheuristic for the capacitated location routing problem

The location routing problem (LRP) involves the three key decision levels in supply chain design, that is, strategic, tactical, and operational levels. It deals with the simultaneous decisions of (a) locating facilities (e.g., depots or warehouses), (b) assigning customers to facilities, and (c) defining routes of vehicles departing from and finishing at each facility to serve the associated customers’ demands. In this paper, a two‐phase metaheuristic procedure is proposed to deal with the capacitated version of the LRP (CLRP). Here, decisions must be made taking into account limited capacities of both facilities and vehicles. In the first phase (selection of promising solutions), we determine the depots to be opened, perform a fast allocation of customers to open depots, and generate a complete CLRP solution using a fast routing heuristic. This phase is executed several times in order to keep the most promising solutions. In the second phase (solution refinement), for each of the selected solutions we apply a perturbation procedure to the customer allocation followed by a more intensive routing heuristic. Computational experiments are carried out using well‐known instances from the literature. Results show that our approach is quite competitive since it offers average gaps below 0.4% with respect to the best‐known solutions (BKSs) for all tested sets in short computational times.     

A fast two-level variable neighborhood search for the clustered vehicle routing problem

In this paper, we present an improved two-level heuristic to solve the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the classical capacitated vehicle routing problem (CVRP) in which customers are grouped into predefined clusters, and all customers in a cluster must be served consecutively by the same vehicle. This paper contributes to the literature in the following ways: (i) new upper bounds are presented for multiple benchmark instances, (ii) good heuristic solutions are provided in much smaller computing times than existing approaches, (iii) the CluVRP is reduced to its cluster level without assuming Euclidean coordinates or distances, and (iv) a new variant of the CluVRP, the CluVRP with weak cluster constraints, is introduced. In this variant, clusters are allocated to vehicles in their entirety, but all corresponding customers can be visited by the vehicle in any order.The proposed heuristic solves the CluVRP by combining two variable neighborhood search algorithms, that explore the solution space at the cluster level and the individual customer level respectively. The algorithm is tested on different benchmark instances from the literature with up to 484 nodes, obtaining high quality solutions while requiring only a limited calculation time.     

多目标同时取送货选址–路径问题的多起点变邻域搜索算法

为使同时取送货的选址–路径问题(LRPSPD)的总成本和各路径间最大长度差最小化, 建立同时考虑车辆 容量和行驶里程约束的LRPSPD双目标模型. 采用多蚁群算法构造多个以信息素为关联的初始解, 作为多目标变邻 域搜索算法搜索的多个起点, 构造四类邻域结构进行变邻域搜索, 并根据最新获得的最优邻域解更新蚂蚁信息素, 从而使蚁群算法产生的多个初始解间、以及初始解与变邻域搜索产生的解之间均存在正向影响关系. 用该算法求 得文献中4组共128个算例的近似Pareto解集, 结果证明了最小化路径间最大长度差目标对于节点及需求分布不集 中算例的重要意义. 以绝对偏向最小化总成本的解与文献中仅最小化总成本的几种算法的算例结果进行比较, 结果 表明算法可在极短的运行时间里求得权衡各目标的Pareto解, 并使最小总成本目标值具有竞争性.