An integrated search heuristic for large-scale flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely hybrid harmony search (HHS) and large neighborhood search (LNS), are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search heuristic, denoted as HHS/LNS, is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that the proposed HHS/LNS shows competitive performance with state-of-the-art algorithms on large-scale FJSP problems, and some new upper bounds among the unsolved benchmark instances have even been found.     

校车路径问题的改进迭代局部搜索算法

针对考虑站点服务时间、学生最大乘车时间约束的校车路径问题(SBRP),提出一种改进迭代局部搜索(ILS)算法以提升求解质量。该算法使用大规模邻域搜索(LNS)算法作为扰动算子;在解的破坏过程中,设计一组解的破坏因子并赋以一定的选择概率,每隔若干次迭代后根据解的质量自适应更改破坏因子的选择概率,进而调整解的破坏程度。为提升ILS解的多样性,算法采用了基于偏差系数的邻域解接受准则。在国际基准测试案例上进行了测试,测试结果表明在ILS算法中使用自适应调整破坏程度的LNS扰动比常规扰动和其他破坏扰动的求解质量有大幅提升;与蚁群算法的比较结果进一步验证了改进算法的有效性。     

求解PDPTW问题的快速LNS算法

提出了一种解决有时间窗口的装卸货问题（PDPTW）的快速大规模领域搜索（LNS）算法。该算法基于大规模邻域搜索理论和随机扰动思想，在第一阶段主要以减少车辆为目标，第二阶段对第一阶段得到的解优化总路程长度。该算法能在较短时间内显著提高初始解的质量．克服了单纯以车辆数目或以总路程长度为目标的算法所得到解的局限性。通过标准算例的测试和同禁忌搜索的比较表明，该算法在求解PDPTW问题时，在计算时间和优化整体目标上更具优势。     

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.     

Synchronized arc routing for snow plowing operations

This paper introduces a synchronized arc routing problem for snow plowing operations. In this problem, routes must be designed in such a way that street segments with two or more lanes in the same direction are plowed simultaneously by different synchronized vehicles. A mixed integer formulation and an adaptive large neighborhood search heuristic are proposed. The performance of the proposed algorithm is evaluated over a large instance set, including artificial and real data. Computational results confirm the efficiency of the algorithm.     

An integration of mixed VND and VNS: the case of the multivehicle covering tour problem

The multivehicle covering tour problem (m‐CTP) is a transportation problem with different kinds of locations, where a set of locations must be visited while another set must be close enough to planned routes. Given two sets of vertices V and W, where V represents the set of vertices that may be visited and W is a set of vertices that must be covered by up to m vehicles, the m‐CTP problem is to minimize vehicle routes on a subset of V including T, which represents the subset of vertices that must be visited through the use of potential locations in V. The variant of m‐CTP without a route‐length constraint is treated in this paper. To tackle this problem, we propose a variable neighborhood search heuristic based on variable neighborhood descent method. Experiments were conducted using the datasets based on traveling salesman problem library instances.     

A variable neighborhood descent algorithm for a real waste collection problem with mobile depots

We consider a waste collection problem encountered in Due Carrare, a town located in Northern Italy. The original feature of the problem consists in the need for arranging appointments between vehicles along their routes so that small vehicles can dump their contents in the large ones and continue their work. This feature identifies the problem as a generalization of the well‐known Capacitated Arc Routing Problem (CARP). We propose a local search heuristic obtained from a variable neighborhood procedure suggested by Hertz and Mittaz (2001) for the CARP. In the Due Carrare instance, the proposed algorithm decreases the total route duration, apart from the required time for any feasible set of routes, of about 30% with respect to the routes so far adopted.     

Skewed general variable neighborhood search for the location routing scheduling problem

The integrated location routing scheduling problem is a variant of the well-known location routing problem. The location routing problem consists in selecting a set of depots to open and in building a set of routes from these depots, to serve a set of customers at minimum cost. In this variant, a vehicle can perform more than a single route in the planning period. As a consequence, the routes have to be scheduled within the workdays of each vehicle. The problem arises typically when routes are constrained to have a short duration. It happens for example within the boundaries of small geographic areas or in the transportation of perishable goods. In this paper, we propose a skewed general variable neighborhood search based heuristic to solve it. The algorithm is tested extensively and we show that it is efficient and provides the proven optimal solution in a significant number of cases. Moreover, it clearly outperforms a multi-start VND based heuristic that uses the same neighborhood structures.     

Variable neighborhood search for location routing

In this paper we propose various neighborhood search heuristics (VNS) for solving the location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. The objective is to find depot locations and to design least cost routes for vehicles. We integrate a variable neighborhood descent as the local search in the general variable neighborhood heuristic framework to solve this problem. We propose five neighborhood structures which are either of routing or location type and use them in both shaking and local search steps. The proposed three VNS methods are tested on benchmark instances and successfully compared with other two state-of-the-art heuristics.     

A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows

This paper presents a two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows and multiple vehicles (PDPTW). The first stage uses a simple simulated annealing algorithm to decrease the number of routes, while the second stage uses Large neighborhood search (LNS) to decrease total travel cost. Experimental results show the effectiveness of the algorithm which has produced many new best solutions on problems with 100, 200, and 600 customers. In particular, it has improved 47% and 76% of the best solutions on the 200 and 600-customer benchmarks, sometimes by as much as 3 vehicles. These results further confirm the benefits of two-stage approaches in vehicle routing. They also answer positively the open issue in the original LNS paper, which advocated the use of LNS for the PDPTW and argue for the robustness of LNS with respect to side-constraints.     

A comparison of five heuristics for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times.     

Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a relatively new version of the classical capacitated vehicle routing problem, and it is equivalent to a traveling repairman problem with capacity constraints and a homogeneous vehicle fleet, which aims to minimize the total arrival time at customers. Many real‐world applications can be modeled by this problem, such as the important application resulting from the humanitarian aid following a natural disaster. In this paper, two heuristics are proposed. The first one is a constructive heuristic to generate an initial solution and the second is the skewed variable neighborhood search (SVNS) heuristic. The SVNS algorithm starts with the initial solution. At each iteration, the perturbation phase and the local search phase are used to improve the solution of the CCVRP, and the distance function in acceptance criteria phase is used to improve the exploration of faraway valleys. This algorithm is applied to a set of benchmarks, and the comparison results show that the proposed algorithms provide better solutions than those reported in the previous literature on memetic algorithms and adaptive large neighborhood search heuristics.     

Battery swap station location-routing problem with capacitated electric vehicles

In this paper, we present an electric vehicles battery swap stations location routing problem (BSS–EV–LRP), which aims to determine the location strategy of battery swap stations (BSSs) and the routing plan of a fleet of electric vehicles (EVs) simultaneously under battery driving range limitation. The problem is formulated as an integer programming model under the basic and extended scenarios. A four-phase heuristic called SIGALNS and a two-phase Tabu Search-modified Clarke and Wright Savings heuristic (TS-MCWS) are proposed to solve the problem. In the proposed SIGALNS, the BSSs location stage and the vehicle routing stage are alternated iteratively, which considers the information from the routing plan while improving the location strategy. In the first phase, an initial routing plan is generated with a modified sweep algorithm, leading to the BSSs location subproblem, which is then solved by using an iterated greedy heuristic. In the third phase, the vehicle routes resulting from the location subproblem are determined by applying an adaptive large neighborhood search heuristic with several new neighborhood structures. At the end of SIGALNS, the solution is further improved by a split procedure. Compared with the MIP solver of CPLEX and TS-MCWS over three sets of instances, SIGALNS searches the solution space more efficiently, thus producing good solutions without excessive computation on the medium and large instances. Furthermore, we systematically conduct economic and environmental analysis including the comparison between basic and extended scenarios, sensitivity analysis on battery driving range and efficiency analysis about the vehicle emissions reduction when EVs are used in the logistics practice.     

A GRASP with adaptive large neighborhood search for pickup and delivery problems with transshipment

The pickup and delivery problem (PDP) has been studied extensively for applications ranging from courier, cargo and postal services, to public transportation. The work presented here was inspired by a daily route planning problem at a regional air carrier who was trying to determine the benefits of transshipment. Accordingly, a primary goal of this paper is identify the circumstances under which measurable cost saving can be achieved when one aircraft transports a request from its origin to an intermediate point and a second aircraft picks it up and delivers it to its final destination. In structuring the analysis, we describe a unique way to model this transshipment option on a directed graph and introduce a specialized two-route insertion heuristic that considers when to exploit this option. Based on the new representation, most existing heuristics for the PDP can be readily extended to handle transshipments.To find solutions, we developed a greedy randomized adaptive search procedure (GRASP) with several novel features. In the construction phase, shipment requests are inserted into routes until all demand is satisfied or no feasible insertion exists. In the improvement phase, an adaptive large neighborhood search algorithm is used to modify portions of the feasible routes. Specialized removal and insertion heuristics were designed for this purpose. In the absence of test cases in the literature, we also developed a procedure for randomly generating problem instances. Testing was done on 56 existing PDP instances which have 50 requests each, and on 50 new data sets with 25 requests each and one transshipment location. For the former, the performance and solution quality of the GRASP were comparable to the best known heuristics. For the latter, GRASP found the solutions within 1% of optimality on 88% of the instances.     

一种多目标置换流水车间调度问题的优化算法

针对最大完工时间最小和总流经时间最小的多目标置换流水车间调度问题(permutation flow shopscheduling problem, PFSP), 提出一种粒子群优化算法与变邻域搜索算法结合的混合粒子群优化(hybrid particleswarm optimization algorithm, HPSO)算法, 并使算法在集中搜索和分散搜索之间达到合理的平衡. 在该混合算法中,采用NEH 启发式算法进行种群初始化, 以提高初始解质量;运用随机键表示法设计基于升序排列规则(ranked-order-value, ROV), 将连续PSO 算法应用于置换流水车间调度问题;引入外部档案集存贮Pareto 解, 并采用强支配关系和聚集距离相结合的混合策略保证解集的分布性;采用Sigma 法和基于聚集距离的轮盘赌法进行全局最优解的选择;提出变邻域搜索算法, 对外部集中的Pareto 解作进一步地局部搜索. 最后, 运用提出的混合算法求解Taillard 基准测试集, 并将测试结果与SPEA2 算法进行比较, 验证该调度算法的有效性.     

A two-phase hybrid heuristic algorithm for the capacitated location-routing problem

In this paper, we propose a two-phase hybrid heuristic algorithm to solve the capacitated location-routing problem (CLRP). The CLRP combines depot location and routing decisions. We are given on input a set of identical vehicles (each having a capacity and a fixed cost), a set of depots with restricted capacities and opening costs, and a set of customers with deterministic demands. The problem consists of determining the depots to be opened, the customers and the vehicles to be assigned to each open depot, and the routes to be performed to fulfill the demand of the customers. The objective is to minimize the sum of the costs of the open depots, of the fixed cost associated with the used vehicles, and of the variable traveling costs related to the performed routes. In the proposed hybrid heuristic algorithm, after a Construction phase (first phase), a modified granular tabu search, with different diversification strategies, is applied during the Improvement phase (second phase). In addition, a random perturbation procedure is considered to avoid that the algorithm remains in a local optimum for a given number of iterations. Computational experiments on benchmark instances from the literature show that the proposed algorithm is able to produce, within short computing time, several solutions obtained by the previously published methods and new best known solutions.     

An adaptive large neighborhood search heuristic for the share-a-ride problem

The Share-a-Ride Problem (SARP) aims at maximizing the profit of serving a set of passengers and parcels using a set of homogeneous vehicles. We propose an adaptive large neighborhood search (ALNS) heuristic to address the SARP. Furthermore, we study the problem of determining the time slack in a SARP schedule. Our proposed solution approach is tested on three sets of realistic instances. The performance of our heuristic is benchmarked against a mixed integer programming (MIP) solver and the Dial-a-Ride Problem (DARP) test instances. Compared to the MIP solver, our heuristic is superior in both the solution times and the quality of the obtained solutions if the CPU time is limited. We also report new best results for two out of twenty benchmark DARP instances.     

A filter-and-fan algorithm for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.     

The synchronized arc and node routing problem: Application to road marking

This paper introduces the synchronized arc and node routing problem, inspired from a real application arising in road marking operations. In this setting, several capacitated vehicles are used to paint lines on the roads and a tank vehicle is used to replenish the painting vehicles. The aim of the problem is to determine the routes and schedules for the painting and replenishment vehicles so that the pavement marking is completed within the least possible time. This must be done in such a way that the routes of the painting and replenishment vehicles are synchronized. An adaptive large neighborhood heuristic is described and evaluated over a large set of artificial instances.     

Generalized mixed integer and VNS heuristic approach to solving the multisize containers drayage problem

This paper addresses the problem of vehicle routing in drayage operations, where vehicles can carry containers of different sizes. The multisize container drayage problem with time windows is modeled as a multiple matching problem and formulated as a mixed integer linear program (MILP) model. The proposed MILP model determines optimal pickup and delivery routes of vehicles and is applicable to any type of vehicles capable of simultaneously transporting any arbitrary number of 20‐ and 40‐ft containers. To solve larger sized problems, we proposed a variable neighborhood search (VNS) heuristic. Both MILP and VNS approaches have been tested on numerous test instances and their performances are reported.