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The general pickup and delivery problem
 TRANSPORTATION SCIENCE
, 1995
"... In pickup and delivery problems vehicles have to transport loads from origins to destinations without transshipment atintermediate locations. In this paper, we discuss several characteristics that distinguish them from standard vehicle routing problems and present a survey of the problem types and s ..."
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Cited by 90 (3 self)
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In pickup and delivery problems vehicles have to transport loads from origins to destinations without transshipment atintermediate locations. In this paper, we discuss several characteristics that distinguish them from standard vehicle routing problems and present a survey of the problem types and solution methods found in the literature.
HASSOP: Hybrid Ant System For The Sequential Ordering Problem
, 1997
"... We present HASSOP, a new approach to solving sequential ordering problems. HASSOP combines the ant colony algorithm, a populationbased metaheuristic, with a new local optimizer, an extension of a TSP heuristic which directly handles multiple constraints without increasing computational complexity ..."
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Cited by 45 (6 self)
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We present HASSOP, a new approach to solving sequential ordering problems. HASSOP combines the ant colony algorithm, a populationbased metaheuristic, with a new local optimizer, an extension of a TSP heuristic which directly handles multiple constraints without increasing computational complexity. We compare different implementations of HASSOP and present a new data structure that improves system performance. Experimental results on a set of twentythree test problems taken from the TSPLIB show that HASSOP outperforms existing methods both in terms of solution quality and computation time. Moreover, HASSOP improves most of the best known results for the considered problems.
An Ant Colony System Hybridized With A New Local Search For The Sequential Ordering Problem
, 2000
"... We present a new local optimizer called SOP3exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP3exchange with an Ant Col ..."
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Cited by 43 (12 self)
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We present a new local optimizer called SOP3exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP3exchange with an Ant Colony Optimization algorithm is described and we present experimental evidence that the resulting algorithm is more effective than existing methods for the problem. The bestknown results for many of a standard test set of 22 problems are improved using the SOP3exchange with our Ant Colony Optimization algorithm or in combination with the MPO/AI algorithm (Chen and Smith 1996).
Parallelization of the Vehicle Routing Problem with Time Windows
, 2001
"... Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitat ..."
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Cited by 24 (1 self)
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Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitated routing problem
(VRP or CVRP). In the VRP a
eet of vehicles must visit (service) a number
of customers. All vehicles start and end at the depot. For each pair of customers
or customer and depot there is a cost. The cost denotes how much is costs a
vehicle to drive from one customer to another. Every customer must be visited
exactly ones. Additionally each customer demands a certain quantity of goods
delivered (know as the customer demand). For the vehicles we have an upper
limit on the amount of goods that can be carried (known as the capacity). In
the most basic case all vehicles are of the same type and hence have the same
capacity. The problem is now for a given scenario to plan routes for the vehicles
in accordance with the mentioned constraints such that the cost accumulated
on the routes, the xed costs (how much does it cost to maintain a vehicle) or
a combination hereof is minimized.
In the more general VRPTW each customer has a time window, and between
all pairs of customers or a customer and the depot we have a travel time. The
vehicles now have to comply with the additional constraint that servicing of the
customers can only be started within the time windows of the customers. It
is legal to arrive before a time window \opens" but the vehicle must wait and
service will not start until the time window of the customer actually opens.
For solving the problem exactly 4 general types of solution methods have
evolved in the literature: dynamic programming, DantzigWolfe (column generation),
Lagrange decomposition and solving the classical model formulation
directly.
Presently the algorithms that uses DantzigWolfe given the best results
(Desrochers, Desrosiers and Solomon, and Kohl), but the Ph.D. thesis of Kontoravdis
shows promising results for using the classical model formulation directly.
In this Ph.D. project we have used the DantzigWolfe method. In the
DantzigWolfe method the problem is split into two problems: a \master problem"
and a \subproblem". The master problem is a relaxed set partitioning
v
vi
problem that guarantees that each customer is visited exactly ones, while the
subproblem is a shortest path problem with additional constraints (capacity and
time window). Using the master problem the reduced costs are computed for
each arc, and these costs are then used in the subproblem in order to generate
routes from the depot and back to the depot again. The best (improving) routes
are then returned to the master problem and entered into the relaxed set partitioning
problem. As the set partitioning problem is relaxed by removing the
integer constraints the solution is seldomly integral therefore the DantzigWolfe
method is embedded in a separationbased solutiontechnique.
In this Ph.D. project we have been trying to exploit structural properties in
order to speed up execution times, and we have been using parallel computers
to be able to solve problems faster or solve larger problems.
The thesis starts with a review of previous work within the eld of VRPTW
both with respect to heuristic solution methods and exact (optimal) methods.
Through a series of experimental tests we seek to dene and examine a number
of structural characteristics.
The rst series of tests examine the use of dividing time windows as the
branching principle in the separationbased solutiontechnique. Instead of using
the methods previously described in the literature for dividing a problem into
smaller problems we use a methods developed for a variant of the VRPTW. The
results are unfortunately not positive.
Instead of dividing a problem into two smaller problems and try to solve
these we can try to get an integer solution without having to branch. A cut is an
inequality that separates the (nonintegral) optimal solution from all the integer
solutions. By nding and inserting cuts we can try to avoid branching. For the
VRPTW Kohl has developed the 2path cuts. In the separationalgorithm for
detecting 2path cuts a number of test are made. By structuring the order in
which we try to generate cuts we achieved very positive results.
In the DantzigWolfe process a large number of columns may be generated,
but a signicant fraction of the columns introduced will not be interesting with
respect to the master problem. It is a priori not possible to determine which
columns are attractive and which are not, but if a column does not become part
of the basis of the relaxed set partitioning problem we consider it to be of no
benet for the solution process. These columns are subsequently removed from
the master problem. Experiments demonstrate a signicant cut of the running
time.
Positive results were also achieved by stopping the routegeneration process
prematurely in the case of timeconsuming shortest path computations. Often
this leads to stopping the shortest path subroutine in cases where the information
(from the dual variables) leads to \bad" routes. The premature exit
from the shortest path subroutine restricts the generation of \bad" routes signi
cantly. This produces very good results and has made it possible to solve
problem instances not solved to optimality before.
The parallel algorithm is based upon the sequential DantzigWolfe based
algorithm developed earlier in the project. In an initial (sequential) phase unsolved
problems are generated and when there are unsolved problems enough
vii
to start work on every processor the parallel solution phase is initiated. In the
parallel phase each processor runs the sequential algorithm. To get a good workload
a strategy based on balancing the load between neighbouring processors is
implemented. The resulting algorithm is eÆcient and capable of attaining good
speedup values. The loadbalancing strategy shows an even distribution of work
among the processors. Due to the large demand for using the IBM SP2 parallel
computer at UNIC it has unfortunately not be possible to run as many tests
as we would have liked. We have although managed to solve one problem not
solved before using our parallel algorithm.
Static Pickup and Delivery Problems: A Classification Scheme and Survey
, 2007
"... Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a threefield classification schem ..."
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Cited by 14 (2 self)
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Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a threefield classification scheme for these problems. It surveys the methods used for solving them.
Transportation on demand
 In Transportation
"... Département d’informatique et de recherche opérationnelle and Centre de recherche sur les transports, Université de Montréal ..."
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Cited by 13 (6 self)
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Département d’informatique et de recherche opérationnelle and Centre de recherche sur les transports, Université de Montréal
The Simulated Trading Heuristic for Solving Vehicle Routing Problems
 DISCRETE APPLIED MATHEMATICS
, 1996
"... We present an improvement heuristic for vehicle routing problems. The heuristic finds complex customer interchanges to improve an initial solution. Our approach is modular, thus it is easily adjusted to different side constraints such as time windows, backhauls and a heterogeneous vehicle fleet. The ..."
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Cited by 9 (0 self)
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We present an improvement heuristic for vehicle routing problems. The heuristic finds complex customer interchanges to improve an initial solution. Our approach is modular, thus it is easily adjusted to different side constraints such as time windows, backhauls and a heterogeneous vehicle fleet. The algorithm is well suited for parallelization. We report on a parallel implementation of the Simulated Trading heuristic on a cluster of workstations using PVM. The computational results were obtained using two sets of vehicle routing problems which differ in the presence of time windows. Our results show that Simulated Trading is better suited for problems with time windows.
Ant Colony Optimization
 Optimization Techniques in Engineering. SpringerVerlag
, 2004
"... Introduction Ant Colony Optimization (ACO) is a paradigm for designing metaheuristic algorithms for combinatorial optimization problems. The first algorithm which can be classified within this framework was presented in 1991 [21 , 13] and, since then, many diverse variants of the basic principle ha ..."
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Cited by 6 (0 self)
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Introduction Ant Colony Optimization (ACO) is a paradigm for designing metaheuristic algorithms for combinatorial optimization problems. The first algorithm which can be classified within this framework was presented in 1991 [21 , 13] and, since then, many diverse variants of the basic principle have been reported in the literature. The essential trait of ACO algorithms is the combination of a priori information about the structure of a promising solution with a posteriori information about the structure of previously obtained good solutions. Metaheuristic algorithms are algorithms which, in order to escape from local optima, drive some basic heuristic: either a constructive heuristic starting from a null solution and adding elements to build a good complete one, or a local search heuristic starting from a complete solution and iteratively modifying some of its elements in order to achieve a better one. The metaheuristic part permits the lowlevel heuristic to obtain solutions better
Metaheuristics in Constraint programming Experiments with Tabu Search . . .
, 1997
"... this article basic principles for implementing local search techniques and metaheuristics in Constraint Programming are presented. These principles have been applied to Tabu Search, with experimental results on various symmetric TSPs and various VRPs (with capacities, time windows, deadlines). This ..."
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Cited by 5 (2 self)
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this article basic principles for implementing local search techniques and metaheuristics in Constraint Programming are presented. These principles have been applied to Tabu Search, with experimental results on various symmetric TSPs and various VRPs (with capacities, time windows, deadlines). This article is organized as follows: After describing the types of VRP considered here, a general Constraint Programming model for the VRP is given in section 3 that allows the description of various routing problems, ranging from TSPs to PDPs. In particular, this model allows to take into account various side constraints expressed as standard Constraint Programming constraints. The solving method is then described in section 4, which consists in an adaptation of the standard twophase approach. A feasible solution is first computed using a basic construction heuristic. It is subsquently improved using local search. A way to implement local search in Constraint Programming is thus given, along with some algorithmic improvements specific to the case of the VRP. Section 5 and 6 are devoted to the main choices that were made with respect to the Tabu Search metaheuristic. Finally, experimental results are given in Section 7 that show that performance of the proposed approach. SophiaAntipolis, France, July 2124, 1997 INRIA & PRiSMVersailles 2 2ND INTERNATIONAL CONFERENCE ON METAHEURISTICS  MIC97 2 Vehicle Routing Problems
Local Search in Constraint Programming: Application to the Vehicle Routing Problem
"... . Constraint programming is an appealing technology to use for vehicle routing problems. Traditional linear programming models do not have the flexibility or generality required by businesses wishing to model complex side constraints. This paper describes how a constraint programming framework for v ..."
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Cited by 5 (0 self)
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. Constraint programming is an appealing technology to use for vehicle routing problems. Traditional linear programming models do not have the flexibility or generality required by businesses wishing to model complex side constraints. This paper describes how a constraint programming framework for vehicle routing problems was implemented using ILOG Solver. A method for incorporating local search into a monotonic constraint programming toolkit is then described. Techniques for accelerating the method via filtering processes are also presented. Computational tests using the constraint programming framework and a greedy search method were performed. Results indicate that moderately sized VRPs (100200 nodes) can be solved to within 10% of the best known solution in seconds. Keywords: Constraint Programming, Combinatorial problems, Iterative Improvement Techniques, Vehicle Routing Problem. 1 Introduction Problems such as the Traveling Salesman Problem (TSP) or the Vehicle Routing Proble...