Particle Swarm Optimization in Solving Capacitated Vehicle Routing Problem

The Capacitated Vehicle Routing Problem (CVRP) is an NP-Hard problem, which means it is impossible to find a polynomial time solution for it. So researchers try to reach a near optimum solution by using meta-heuristic algorithms. The aim of CVRP is to find optimum route for every vehicle and a sequence of customers, that vehicle serve. This paper proposes a method on how PSO is adjusted for a discrete space problem like CVRP. The process of tweaking solutions is described in detail. At last for evaluation of proposed approach and show the effectiveness of it, the result of running proposed approach over benchmarking data set of capacitated vehicle routing problem is illustrated

Particle Swarm Optimization in Solving Capacitated Vehicle Routing Problem

The Capacitated Vehicle Routing Problem (CVRP) is an NP-Hard problem, which means it is impossible to find a polynomial time solution for it. So researchers try to reach a near optimum solution by using meta-heuristic algorithms. The aim of CVRP is to find optimum route for every vehicle and a sequence of customers, that vehicle serve. This paper proposes a method on how PSO is adjusted for a discrete space problem like CVRP. The process of tweaking solutions is described in detail. At last for evaluation of proposed approach and show the effectiveness of it, the result of running proposed approach over benchmarking data set of capacitated vehicle routing problem is illustrated

HEURISTIC FOR ASYMMETRIC CAPACITATED VEHICLE ROUTING PROBLEM

The vehicle routing problem (VRP) is commonly defined as the problem of designing optimal delivery or collection routes from one or several depots to a set of geographically scattered customers, under a variety of side conditions. This problem is generally described through a graph, whose arcs represent the road sections and vertices correspond to the depot and customer locations. The arcs (and consequently the corresponding graph) can be directed or undirected, depending on whether they can be traversed in only one direction or in both directions. Since each arc is associated with a cost then if the graph is directed, the cost matrix is asymmetric and the corresponding problem is called asymmetric vehicle routing problem (AVRP). Although the symmetric problems are special cases of the asymmetric ones, the latter were much less studied in the literature. In this paper, a type of problem, called the Asymmetric Capacitated Vehicle Routing Problem (ACVRP) is discussed and a heuristic algorithm is proposed to solve the problem. Keywords: Vehicle Routing, Asymmetric, Capacitated, Heuristi

Reachability cuts for the vehicle routing problem with time windows

This paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts for the VRPTW. In particular, any reachability cut dominates one or more k-path cuts. The paper presents separation procedures for reachability cuts and reports computational experiments on well-known VRPTW instances. The computational results suggest that reachability cuts can be highly useful as cutting planes for certain VRPTW instances.Routing; time windows; precedence constraints

A Branch-Cut-and-Price Algorithm for the Location-Routing Problem

International audienc

A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.Vehicle routing; branch-and-cut; separation

The Pyramidal Capacitated Vehicle Routing Problem

This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is de ned as a route on which the vehicle rst visits customers in increasing order of customer index, and on the remaining part of the route visits customers in decreasing order of customer index. Provided that customers are indexed in nondecreasing order of distance from the depot, the shape of a pyramidal route is such that its traversal can be divided in two parts, where on the rst part of the route, customers are visited in nondecreasing distance from the depot, and on the remaining part of the route, customers are visited in nonincreasing distance from the depot. Such a route shape is indeed found in many optimal solutions to CVRP instances. An optimal solution to the PCVRP may therefore be useful in itself as a heuristic solution to the CVRP. Further, an attempt can be made to nd an even better CVRP solution by solving a TSP, possibly leading to a non-pyramidal route, for each of the routes in the PCVRP solution. This paper develops an exact branch-and-cut-and-price (BCP) algorithm for the PCVRP. At the pricing stage, elementary routes can be computed in pseudo-polynomial time in the PCVRP, unlike in the CVRP. We have therefore implemented pricing algorithms that generate only elementary routes. Computational results suggest that PCVRP solutions are highly useful for obtaining near-optimal solutions to the CVRP. Moreover, pricing of pyramidal routes may due to its eciency prove to be very useful in column generation for the CVRP.vehicle routing; pyramidal traveling salesman; branch-and-cut-and-price

PENGOPTIMUMAN BIAYA DISTRIBUSI MENGGUNAKAN INTEGER PROGRAMMING DALAM MENYIKAPI KEBIJAKAN GANJIL-GENAP DI JAKARTA

Kebijakan Ganjil-Genap merupakan salah satu aturan yang diterapkan di Jakarta untuk mengurangi kemacetan. Kebijakan ini mengakibatkan kendaraan bermotor tidak bisa melalui ruas jalan tertentu, jika ganjil/genapnya nomor-polisi kendaraan tidak sesuai dengan ganjil/genapnya tanggal kendaraan tersebut ketika melintasi ruas jalan yang terkena kebijakan. Ada beberapa jenis kendaraan yang terkena dampak kebijakan ini, di antaranya ialah kendaraan distribusi perusahaan ekspedisi. Kebijakan ini membuat biaya distribusi perusahaan ekspedisi meningkat karena jarak perjalanan menuju konsumen menjadi lebih jauh untuk menghindari ruas jalan Ganjil-Genap ketika plat nomor polisi kendaraan yang digunakan untuk distribusi tidak sesuai dengan jenis tanggal distribusi. Proses distribusi yang meminimumkan biaya pengeluaran memerlukan penentuan rute yang optimal. Masalah penentuan rute optimal ini diformulasikan ke dalam Vehicle Routing Problem menggunakan Integer Linear Programming. Masalah ini diselesaikan menggunakan perangkat lunak LINGO 18.0 dan solusi optimal yang diperoleh berupa rute pendistribusian barang menggunakan kendaraan tertentu serta meminimumkan biaya distribusi