Showing papers on "Vehicle routing problem published in 1994"
TL;DR: Numerical tests on a set of benchmark problems indicate that tabu search outperforms the best existing heuristics, and TABUROUTE often produces the bes known solutions.
Abstract: The purpose of this paper is to describe TABUROUTE, a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route. This is done by means of a generalized insertion procedure previously developed by the authors. During the course of the algorithm, infeasible solutions are allowed. Numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics, and TABUROUTE often produces the best known solutions.
1,100 citations
TL;DR: Two approaches to managing this operation are compared, one in which the production scheduling and vehicle routing problems are solved separately, and another in which they are coordinated within a single model.
545 citations
TL;DR: This work shows that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once.
Abstract: We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25–71 customers.
521 citations
TL;DR: This paper shows how the introduction of new primitive constraints over finite domains in the constraint logic programming system CHIP result in finding very rapidly good solutions for a large class of difficult sequencing, scheduling, geometrical placement and vehicle routing problems.
365 citations
TL;DR: It is proved that the relaxation approach in designing the subproblem of pricing out only the feasible routes for the set partition formulation of the VRPTW is justified on complexity grounds, and the first dynamic programming model presented in M. Desrochers, J. Desrosiers and M. Solomon 1992 is NP-hard in the strong sense.
Abstract: In this note we prove that the relaxation approach in designing the subproblem of pricing out only the feasible routes for the set partition formulation of the VRPTW is justified on complexity grounds. That is, the first dynamic programming model presented in M. Desrochers, J. Desrosiers and M. Solomon 1992, that is able to price out all feasible routes, is NP-hard in the strong sense.
305 citations
TL;DR: Computational results indicate that by using an appropriate combination of constraints, the gap between the lower and upper bounds at the root of the search tree can be reduced considerably.
243 citations
TL;DR: This work develops a simple heuristic consisting of pick-up and delivery along the travelling salesman tour along the Cheapest Insertion heuristic and introduces an alternative solution method which is an extension of the well known Cheapest insertion heuristic.
165 citations
TL;DR: A parallel Tabu search heuristic for the Vehicle Routing Problem with Time Windows, which is synchronous and runs on a Multiple-Instruction Multiple-Data computer architecture.
159 citations
TL;DR: In this paper, the authors considered the asymmetric capacitated vehicle routing problem CVRP, a particular case of the standard asymmetric vehicle routing problems in which only the vehicle capacity constraints are imposed.
Abstract: We consider the asymmetric capacitated vehicle routing problem CVRP, a particular case of the standard asymmetric vehicle routing problem in which only the vehicle capacity constraints are imposed. CVRP is known to be NP-hard and finds practical applications in distribution and scheduling. We describe two new bounding procedures for CVRP, based on the so-called additive approach. Each procedure computes a sequence of nondecreasing lower bounds, obtained by solving different relaxations of CVRP. Effective implementations of the procedures are also outlined which considerably reduce the computational effort. The two procedures are combined into an overall bounding algorithm. A branch-and-bound exact algorithm is then proposed, whose performance is enhanced by means of reduction procedures, dominance criteria, and feasibility checks. Extensive computational results on both real-world and random test problems are presented, showing that the proposed approach favorably compares with previous algorithms from the literature.
138 citations
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01 Jan 1994
TL;DR: The objective is to find a shortest feasible tour visiting all customers, emanating from and ending at the warehouse, and an efficient (O(N^2)) heuristic is introduced for this problem.
TL;DR: A new heuristic for the vehicle routeing problem which makes use of repeated matching is described, and the numerical results are comparable to or better than the best published for most of the 14 benchmark problems commonly used to evaluate VRP heuristics.
Abstract: A new heuristic for the vehicle routeing problem which makes use of repeated matching is described. The numerical results are comparable to or better than the best published for most of the 14 benchmark problems commonly used to evaluate VRP heuristics.
TL;DR: By using cuts defined by multistars, partial multistar and generalized subtour elimination constraints, this work is able to consistently solve 60-city problems to proven optimality and is currently attempting to solve problems involving a hundred cities.
Abstract: We present a branch-and-cut algorithm for the identical customer Vehicle Routing Problem. Transforming the problem into an equivalent Path-Partitioning Problem allows us to exploit its polyhedral structure and to generate strong cuts corresponding to facet-inducing inequalities. By using cuts defined by multistars, partial multistars and generalized subtour elimination constraints, we are able to consistently solve 60-city problems to proven optimality and are currently attempting to solve problems involving a hundred cities. We also present details of the computer implementation and our computational results.
27 Jun 1994
TL;DR: The main purpose of this paper is to show how elastic network ideas can be applied to two TSP generalizations: the multiple traveling salesmen problem (MTSP) and the vehicle routing problem (VRP).
Abstract: Using neural networks to find an approximate solution to difficult optimization problems is a very attractive prospect. The traveling salesman problem (TSP), probably the best-known problem in combinatorial optimization, has been attacked by a variety of neural network approaches. The main purpose of this paper is to show how elastic network ideas can be applied to two TSP generalizations: the multiple traveling salesmen problem (MTSP) and the vehicle routing problem (VRP). >
TL;DR: A simple heuristic is presented which is shown to converge to the lower-bound almost surely under mild probabilistic conditions, when the number of retailers is increased to infinity.
TL;DR: In this article, the Spacefilling Curve with Optimal Partitioning (SFC OP) heuristic was introduced for vehicle routing problems, which has the property that it generates good routes extremely quickly and the time required increases nearly linearly with problem size.
15 Dec 1994
TL;DR: In this paper, the authors explored the potential of GA to solve order based problems with particular emphasis on solving the traveling salesman problem (TSP) and the time constrained vehicle routing problem (VRPTC).
Abstract: This study explores the potential of genetic algorithms (GA) to solve order based problems with particular emphasis on solving the traveling salesman problem (TSP) and the time constrained vehicle routing problem (VRPTC). As a result of a thorough review of current literature, several issues related to developing GA to solve ordering problems are uncovered. An in-depth, empirically valid computational study using an a-priori statistical design is conducted to determine the best combination of parameter settings and design decisions to use when building GA to solve ordering problems. This test was conducted using the GA Testing System (GATS) developed as part of this effort. A suite of real world problems selected from literature and the TSPlib 1.2 were solved with 144 different GA designed to solve the tsp (GA-TSP), also developed as part of this study. More than 5,000 problems were solved by GA-TSP during this phase of the study.
The results of the GA-TSP test were used to develop a GA to solve the VRPTC (GA-VRPTC). To evaluate GA-VRPTC, a set of VRPTC were solved and the results were compared with the results obtained when solving the same set of problems using traditional algorithms. We find that GA-VRPTC performs well in terms of solution quality; however, the amount of CPU time required to solve these problems exceeded that used by traditional methods by several orders of magnitude. After reporting and analyzing the results of the GA-VRPTC test, suggestions for further improvement and extensions are made.
TL;DR: In this paper, the LP relaxation and the Lagrangean dual are solved in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya.
Abstract: We propose techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization and nonlinear programming problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in problems of a certain structure our techniques find not only the optimal solution value, but the solution as well. Our techniques lead to significant improvements in the theoretical running time compared with previously known methods (interior point methods, Ellipsoid algorithm, Vaidya's algorithm). We use our method to the solution of the LP relaxation and the Langrangean dual of several classical combinatorial problems, like the traveling salesman problem, the vehicle routing problem, the Steiner tree problem, thek-connected problem, multicommodity flows, network design problems, network flow problems with side constraints, facility location problems,K-polymatroid intersection, multiple item capacitated lot sizing problem, and stochastic programming. In all these problems our techniques significantly improve the theoretical running time and yield the fastest way to solve them.
Posted Content•
TL;DR: A combined branching and subproblem modification scheme is developed that generalizes existing approaches, and the use of lower bounds to reduce tailing-off effects is described.
Abstract: An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented. The family of problems that can be treated includes not only standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0 - 1 components and a right hand side vector of 1 's, but also the cutting stock problem in which the columns and right hand side are nonnegative integer vectors. We develop a combined branching and subproblem modification scheme that generalizes existing approaches, and also describe the use of lower bounds to reduce tailing-off effects.
TL;DR: Results show that continuous space models can provide substantial improvements in the initial customer partition compared to single-annulus methods, and that Daganzo's model provides accurate predictions of average distance between stops, especially on large problems with identical shipment sizes.
Abstract: This paper creates and tests a vehicle routing heuristic that combines features of continuous space modeling and discrete modeling. The goals of the paper were (1) to determine whether exploiting continuous space approximations in the formation of an initial partition of customers into districts produces significant improvements in solution quality and (2) to test the validity of Daganzo's route-length approximation in cases where shipment sizes are either identical or variable. The initial partition is created by dividing the service region into multiple annuli and then partitioning the annuli with a modified sweep algorithm. The initial solution is iteratively updated with a generalized assignment algorithm, which employs a new method for approximating the cost of inserting a stop into a tour. Computational tests have been systematically performed on over 500 sample problems with up to 170 stops and 70 districts. Unlike prior research, sample problems are sufficiently large to exhibit the multiple-annuli phenomenon studied in Daganzo's work. Results show that continuous space models can provide substantial improvements in the initial customer partition compared to single-annulus methods. However, after repeated application of a generalized assignment algorithm, the initial advantage of the continuous space solution tends to evaporate. Results also show that Daganzo's model provides accurate predictions of average distance between stops, especially on large problems with identical shipment sizes. © 1994 by John Wiley & Sons, Inc.
TL;DR: In this article, a mixed integer linear programming formulation for a vehicle routing problem with an upper limit T on every tour length and with arc lengths that satisfy the triangular inequality is given, which is more concise than in the previously mentioned paper.
01 Aug 1994
TL;DR: This paper focuses on the graphic and interactive features of Micro-ALTO and shows how the current microcomputer technology was used so as to provide a sophisticated environment to the user.
Abstract: A microcomputer vehicle routing and scheduling system aimed at supporting algorithm designers is described. The system is called Micro-ALTO and stems from the experience gained with a previous system running on specialized hardware. The paper focuses on the graphic and interactive features of Micro-ALTO and shows how we used the current microcomputer technology so as to provide a sophisticated environment to the user.
27 Jun 1994
TL;DR: A genetic algorithm is applied to the search of good parameter settings for a vehicle routing heuristic, which allows the insertion heuristic to generate solutions that are much better than the solutions previously reported on a standard set of routing problems.
Abstract: A genetic algorithm is applied to the search of good parameter settings for a vehicle routing heuristic. The parameter settings identified by the genetic search allow the insertion heuristic to generate solutions that are much better than the solutions previously reported on a standard set of routing problems. >
TL;DR: In this paper, a new decomposition strategy for the capacity-constrained vehicle routing problem (VRP) is introduced, which separates the decisions of a dispatcher from those of the individual drivers.
31 Aug 1994
TL;DR: The authors' results show that the genetic algorithms can effectively find optimum solutions to the vehicle routing problem and proposed new method that does not permit overlapping of genes.
Abstract: Genetic algorithms are proposed as a new learning paradigm for combinatorial optimization that models a natural evolution mechanism. The authors attempt to apply genetic algorithms to the vehicle routing problem. As it is easy to generate the same gene while a generation shift goes on, it is feared that a solution will fall into a local minimum. The authors propose a new method that does not permit overlapping of genes. Some experiments are performed on digital road maps. The authors' results show that the genetic algorithms can effectively find optimum solutions. >
08 May 1994
TL;DR: A mathematical model of a multiple vehicle system is exhibited, which has similarities to the Timed Traces models developed to reason about parallel processes, and a denotational semantics is derived, ascribing meaning to a simple language of service operations and concurrent path planning.
Abstract: The application of autonomous guided vehicles to well-structured industrial sites requires considerably more than a path planning algorithm onboard each vehicle. Issues such as task planning, vehicle routing and vehicle-vehicle interactions predominate in determining the overall system ability. We exhibit a mathematical model of a multiple vehicle system, which has similarities to the Timed Traces models developed to reason about parallel processes. A denotational semantics is derived from this model, ascribing meaning to a simple language of service operations and concurrent path planning. This semantics captures a complete description of vehicles' behaviour, which can provide a global planning strategy guaranteeing both satisfiability and liveness. >