396 research outputs found
The Vehicle Routing Problem with Service Level Constraints
We consider a vehicle routing problem which seeks to minimize cost subject to
service level constraints on several groups of deliveries. This problem
captures some essential challenges faced by a logistics provider which operates
transportation services for a limited number of partners and should respect
contractual obligations on service levels. The problem also generalizes several
important classes of vehicle routing problems with profits. To solve it, we
propose a compact mathematical formulation, a branch-and-price algorithm, and a
hybrid genetic algorithm with population management, which relies on
problem-tailored solution representation, crossover and local search operators,
as well as an adaptive penalization mechanism establishing a good balance
between service levels and costs. Our computational experiments show that the
proposed heuristic returns very high-quality solutions for this difficult
problem, matches all optimal solutions found for small and medium-scale
benchmark instances, and improves upon existing algorithms for two important
special cases: the vehicle routing problem with private fleet and common
carrier, and the capacitated profitable tour problem. The branch-and-price
algorithm also produces new optimal solutions for all three problems
Covering tour problem with varying coverage: Application to marine environmental monitoring
In this paper, we present a novel variant of the Covering Tour Problem (CTP), called the Covering Tour Problem with Varying Coverage (CTP-VC). We consider a simple graph = ( ,), with a measure of importance assigned to each node in . A vehicle with limited battery capacity visits the nodes of the graph and has the ability to stay in each node for a certain period of time, which determines the coverage radius at the node. We refer to this feature as stay-dependent varying coverage or, in short, varying coverage. The objective is to maximize a scalarization of the weighted coverage of the nodes and the negation of the cost of moving and staying at the nodes. This problem arises in the monitoring of marine environments, where pollutants can be measured at locations far from the source due to ocean currents. To solve the CTP-VC, we propose a mathematical formulation and a heuristic approach, given that the problem is NP-hard. Depending on the availability of solutions yielded by an exact solver, we evaluate our heuristic approach against the exact solver or a constructive heuristic on various instance sets and show how varying coverage improves performance. Additionally, we use an offshore CO2 storage site in the Gulf of Mexico as a case study to demonstrate the problemâs applicability. Our results demonstrate that the proposed heuristic approach is an efficient and practical solution to the problem of stay-dependent varying coverage. We conduct numerous experiments and provide managerial insights.publishedVersio
Kiertovaihtoalgoritmi ja muunnoksia yleistetylle ajoneuvoreititysongelmalle
Vehicle routing problems have numerous applications in ïŹelds such as transportation, supply logistics and network design. The optimal design of these routes fall in the category of NP-hard optimization problems, meaning that the computational complexity increases extremely fast with increasing problem size.
The Generalized Vehicle Routing Problem (GVRP) is a general problem type that includes a broad variety of other problems as special cases. The main special feature of the GVRP is that the customers are grouped in clusters. For each cluster, only one customer is visited.
In this thesis, we implement a heuristic algorithm to solve GVRP instances in reasonable time. Especially, we include a cyclic exchange method that considers a very large search neighborhood.
In addition, we study the related Capacitated m-Ring-Star Problem (CmRSP). We present the Distance-Constrained Capacitated m-Ring-Star Problem (DCmRSP) and show that it contains the Multivehicle Covering Tour Problem (MCTP) as a special case. We show that DCmRSP instances can be transformed to (distance-constrained) GVRP with minor adaptations and solved with the same heuristic algorithm.
Our algorithm is able to ïŹnd best known solutions to all GVRP test instances; for two of them, our method shows strict improvement. The transformed CmRSP and MCTP instances are solved successfully by the same algorithm with adequate performance.Ajoneuvoreititysongelmilla on lukuisia sovelluksia muun muassa logistiikan ja verkostosuunnittelun aloilla. TĂ€llaisten reittien optimaalinen ratkaiseminen kuuluu NP-vaikeiden optimointiongelmien kategoriaan, eli ratkaisuun vaadittava laskentateho kasvaa erittĂ€in nopeasti ongelman koon suhteen.
Yleistetty ajoneuvoreititysongelma (Generalized Vehicle Routing Problem, GVRP) on ongelmatyyppi, joka kattaa joukon muita reititysongelmia erikoistapauksina. GVRP:n selkein erityispiirre on asiakkaiden jako ryppÀisiin: kussakin ryppÀÀssÀ on kÀytÀvÀ tasan yhden asiakkaan luona.
TÀssÀ diplomityössÀ esitellÀÀn ja toteutetaan heuristinen algoritmi, joka etsii kohtalaisessa ajassa ratkaisuja GVRP-ongelmiin. MenetelmÀ sisÀltÀÀ kiertovaihtoalgoritmin, joka kykenee etsimÀÀn ratkaisuja hyvin laajasta ympÀristöstÀ.
Tutkimuksen kohteena on lisÀksi m-rengastÀhtiongelma (Capacitated m-Ring-Star Problem, CmRSP). Esittelemme ongelman etÀisyysrajoitetun version (DCmRSP), ja nÀytÀmme, ettÀ kyseiseen ongelmaan sisÀltyy usean ajoneuvon peittÀvÀn reitin ongelma (Multivehicle Covering Tour Problem). NÀytÀmme, ettÀ DCmRSP-ongelman pystyy pienin muutoksin muuntamaan GVRP-ongelmaksi ja ratkaisemaan samalla heuristisella algoritmilla.
Algoritmi löytÀÀ parhaat tunnetut ratkaisut kaikkiin GVRP-testitehtÀviin. Kahdessa tapauksessa ratkaisu on parempi aiemmin löydettyihin nÀhden. Algoritmi kykenee ratkaisemaan muunnetut CmRSP- ja MCTP-testitehtÀvÀt kohtalaisella ratkaisulaadulla
The In-Transit Vigilant Covering Tour Problem of Routing Unmanned Ground Vehicles
The routing of unmanned ground vehicles for the surveillance and protection of key installations is modeled as a new variant of the Covering Tour Problem (CTP). The CTP structure provides both the routing and target sensing components of the installation protection problem. Our variant is called the in-transit Vigilant Covering Tour Problem (VCTP) and considers not only the vertex cover but also the additional edge coverage capability of the unmanned ground vehicle while sensing in-transit between vertices. The VCTP is formulated as a Traveling Salesman Problem (TSP) with a dual set covering structure involving vertices and edges. An empirical study compares the performance of the VCTP against the CTP on test problems modified from standard benchmark TSP problems to apply to the VCTP. The VCTP performed generally better with shorter tour lengths but at higher computational cost
Modélisation et résolution de problÚmes généralisés de tournées de véhicules
Le problĂšme de tournĂ©es de vĂ©hicules est un des problĂšmes d optimisation combinatoire les plus connus et les plus difficiles. Il s agit de dĂ©terminer les tournĂ©es optimales pour une flotte de vĂ©hicules afin de servir un ensemble donnĂ© de clients. Dans les problĂšmes classiques de transport, chaque client est normalement servi Ă partir d un seul nĆud (ou arc). Pour cela, on dĂ©finit toujours un ensemble donnĂ© de nĆuds (ou arcs) obligatoires Ă visiter ou traverser, et on recherche la solution Ă partir de cet ensemble de nĆuds (ou arcs). Mais dans plusieurs applications rĂ©elles oĂč un client peut ĂȘtre servi Ă partir de plus d un nĆud, (ou arc), les problĂšmes gĂ©nĂ©ralisĂ©s qui en rĂ©sultent sont plus complexes. Le but principal de cette thĂšse est d Ă©tudier trois problĂšmes gĂ©nĂ©ralisĂ©s de tournĂ©es de vĂ©hicules. Le premier problĂšme de la tournĂ©e sur arcs suffisamment proche (CEARP), comporte une application rĂ©elle intĂ©ressante en routage pour le relevĂ© des compteurs Ă distance ; les deux autres problĂšmes, problĂšme de tournĂ©es couvrantes multi-vĂ©hicules (mCTP) et problĂšme gĂ©nĂ©ralisĂ© de tournĂ©es sur nĆuds (GVRP), permettent de modĂ©liser des problĂšmes de conception des rĂ©seaux de transport Ă deux niveaux. Pour rĂ©soudre ces problĂšmes, nous proposons une approche exacte ainsi que des mĂ©taheuristiques. Pour dĂ©velopper la mĂ©thode exacte, nous formulons chaque problĂšme comme un programme mathĂ©matique, puis nous construisons des algorithmes de type branchement et coupes. Les mĂ©taheuristiques sont basĂ©es sur le ELS (ou Evolutionary Local Search) et sur le GRASP (ou Greedy Randomized Adaptive Search Procedure). De nombreuses expĂ©rimentations montrent la performance de nos mĂ©thodes.The Routing Problem is one of the most popular and challenging combinatorial optimization problems. It involves finding the optimal set of routes for fleet of vehicles in order to serve a given set of customers. In the classic transportation problems, each customer is normally served by only one node (or arc). Therefore, there is always a given set of required nodes (or arcs) that have to be visited or traversed, and we just need to find the solution from this set of nodes (or arcs). But in many real applications where a customer can be served by from more than one node (or arc), the generalized resulting problems are more complex. The primary goal of this thesis is to study three generalized routing problems. The first one, the Close-Enough Arc Routing Problem(CEARP), has an interesting real-life application to routing for meter reading while the others two, the multi-vehicle Covering Tour Problem (mCTP) and the Generalized Vehicle Routing Problem(GVRP), can model problems concerned with the design of bilevel transportation networks. The problems are solved by exact methods as well as metaheuristics. To develop exact methods, we formulate each problem as a mathematical program, and then develop branch-and-cut algorithms. The metaheuristics are based on the evolutionary local search (ELS) method et on the greedy randomized adaptive search procedure (GRASP) method. The extensive computational experiments show the performance of our methods.NANTES-ENS Mines (441092314) / SudocSudocFranceF
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Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the
ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing
problem into a travelling salesman problem and uses the assignment problem as a lower
bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational
experiments show that we are able to exactly solve large test instances with up to 1000
customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of
vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups
of instances. We wanted to determine how far the difference is between the best feasible
solution obtained by VNS and the value of optimal solution in order to use the output
of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and
bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions
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An investigation of multilevel refinement in routing and location problems
Multilevel refinement is a collaborative hierarchical solution technique. The multilevel technique aims to enhance the solution process of optimisation problems by improving the asymptotic convergence in the quality of solutions produced by its underlying local search heuristics and/or improving the convergence rate of these heuristics. To these aims, the central methodologies of the multilevel technique are filtering solutions from the search space (via coarsening), reducing the amount of problem detail considered at each level of the solution process and providing a mechanism to the underlying local search heuristics for efficiently making large moves around the search space. The neighbourhoods accessible by these moves are typically inaccessible if the local search heuristics are applied to the un-coarsened problems. The methodologies combine to meet the multilevel technique's aims, because, as the multilevel technique iteratively coarsens, extends and refines a given problem, it reduces the possibility of the local search heuristic becoming trapped in local optima of poor quality.
The research presented in this thesis investigates the application of multilevel refinement to classes of location and routing problems and develops numerous multilevel algorithms. Some of these algorithms are collaborative techniques for metaheuristics and others are collaborative techniques for local search heuristics. Additionally, new methods of coarsening for location and routing problems and enhancements for the multilevel technique are developed. It is demonstrated that the multilevel technique is suited to a wide array of problems. By extending the investigations of the multilevel technique across routing and location problems, the research was able to present generalisations regarding the multilevel technique's suitability, for these and similar types of problems.
Finally, results on a number of well known benchmarking suites for location and routing problem are presented, comparing equivalent single-level and multilevel algorithms. These results demonstrate that the multilevel technique provides significant gains over its single-level counterparts. In all cases, the multilevel algorithm was able to improve the asymptotic convergence in the quality of solutions produced by the standard (single-level) local search heuristics or metaheuristics. The multilevel technique did not improve the convergence rate of the single-level's local search heuristics in all cases. However, for large-scale problems the multilevel variants scaled in a manner superior to the single-level techniques. The research also demonstrated that for sufficiently large problems, the multilevel technique was able to improve the asymptotic convergence in the quality of solutions at a sufficiently fast rate, such that the multilevel algorithms were able to produce superior results compared to the single-level versions, without refining the solution down to the most detailed level
Spatial coverage in routing and path planning problems
Routing and path planning problems that involve spatial coverage have received increasing attention in recent years in different application areas. Spatial coverage refers to the possibility of considering nodes that are not directly served by a vehicle as visited for the purpose of the objective function or constraints. Despite similarities between the underlying problems, solution approaches have been developed in different disciplines independently, leading to different terminologies and solution techniques. This paper proposes a unified view of the approaches: Based on a formal introduction of the concept of spatial coverage in vehicle routing, it presents a classification scheme for core problem features and summarizes problem variants and solution concepts developed in the domains of operations research and robotics. The connections between these related problem classes offer insights into common underlying structures and open possibilities for developing new applications and algorithms
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