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19
A general heuristic for vehicle routing problems
 Computers & Operations Research
, 2007
"... We present a unified heuristic, which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multidepot vehicle routing problem (MDVRP), the site dependent vehicle routing pr ..."
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We present a unified heuristic, which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multidepot vehicle routing problem (MDVRP), the site dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP). All problem variants are transformed to a rich pickup and delivery model and solved using the Adaptive Large Neighborhood Search (ALNS) framework presented in Ropke and Pisinger (2004). The ALNS framework is an extension of the Large Neighborhood Search framework by Shaw (1998) with an adaptive layer. This layer adaptively chooses among a number of insertion and removal heuristics, to intensify and diversify the search. The presented approach has a number of advantages: ALNS provides solutions of very high quality, the algorithm is robust, and to some extent selfcalibrating. Moreover, the unified model allows the dispatcher to mix various variants of VRP problems for individual customers or vehicles. As we believe that the ALNS framework can be applied to a large number of tightly constrained optimization problems, a general description of the framework is given, and it is discussed how the various components can be designed in a particular setting. The paper is concluded with a computational study, in which the five different variants of the vehicle routing problem are considered on standard benchmark tests from the literature. The outcome of the tests is promising as the algorithm is able to improve 183 best known solutions out of 486 benchmark tests. The heuristic has also shown promising results for a large class of vehicle routing problems with backhauls, as demonstrated in Ropke and Pisinger (2005).
A reactive variable neighborhood search for the vehicle routing problem with time windows
 INFORMS Journal on Computing
, 2003
"... The purpose of this paper is to present a new deterministic metaheuristic based on a modification of Variable Neighborhood Search of Mladenovic and Hansen (1997) for solving the vehicle routing problem with time windows. Results are reported for the standard 100, 200 and 400 customer data sets by So ..."
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Cited by 38 (1 self)
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The purpose of this paper is to present a new deterministic metaheuristic based on a modification of Variable Neighborhood Search of Mladenovic and Hansen (1997) for solving the vehicle routing problem with time windows. Results are reported for the standard 100, 200 and 400 customer data sets by Solomon (1987) and Gehring and Homberger (1999) and two reallife problems by Russell (1995). The findings indicate that the proposed procedure outperforms other recent local searches and metaheuristics. In addition four new bestknown solutions were obtained. The proposed procedure is based on a new fourphase approach. In this approach an initial solution is first created using new route construction heuristics followed by route elimination procedure to improve the solutions regarding the number of vehicles. In the third phase the solutions are improved in terms of total traveled distance using four new local search procedures proposed in this paper. Finally in phase four the best solution obtained is improved by modifying the objective function to escape from a local minimum. (Metaheuristics; Vehicle Routing; Time Windows) 1.
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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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 #12;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
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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 #12;eld of VRPTW
both with respect to heuristic solution methods and exact (optimal) methods.
Through a series of experimental tests we seek to de#12;ne and examine a number
of structural characteristics.
The #12;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 #12;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 signi#12;cant 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
bene#12;t for the solution process. These columns are subsequently removed from
the master problem. Experiments demonstrate a signi#12;cant 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
#12;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 UNI#15;C 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.
New refinements for the solution of vehicle routing problems with branch and price
, 2005
"... Column generation is a wellknown mathematical programming technique based on two components: a master problem, which selects optimal columns (variables) in a restricted pool of columns, and a subproblem that feeds this pool with potentially good columns until an optimality criterion is met. Embedd ..."
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Cited by 3 (0 self)
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Column generation is a wellknown mathematical programming technique based on two components: a master problem, which selects optimal columns (variables) in a restricted pool of columns, and a subproblem that feeds this pool with potentially good columns until an optimality criterion is met. Embedded in Branch and Price algorithms, this solution approach proved to be very efficient in the context of numerous vehicle routing problems, where columns represent feasible vehicle routes. The subproblem is then usually expressed as a shortest path problem with resource constraints, which can be solved using dynamic programming methods that are generally very effective in practice. In this paper, we propose some new refinements to improve the capabilities of column generation approaches in this context, with a focus on the subproblem phase. For the sake of simplicity, we restrict our study to the case of the Vehicle Routing Problem with Time Windows. We first introduce the notion of Limited Discrepancy Search, which is well known in the field of Constraint Programming, and we show how LDS can be applied to dynamic programming. We also discuss how the state graph of dynamic programming can be manipulated in order to simulate local search during label extension. Finally, we present some lower bounds that allow removing a substantial number of labels during the search. Computational results demonstrate the considerable impact of these refinements in terms of computing time.
Tabu Search, Generalized kPath Inequalities, and Partial Elementarity for the Vehicle Routing Problem with Time Windows
, 2006
"... ..."
Parallelization of a mathematical model to evaluate a CCA application for VANETs
 In: 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH), The Netherlands
, 2011
"... Vehicular Adhoc Networks (VANET) are currently becoming not only an extremely important factor for vehicles engineering development but also a key issue for improving road safety. Cooperative/Chain Collision Avoidance (CCA) application comes up as a solution for decreasing accidents on the road, th ..."
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Vehicular Adhoc Networks (VANET) are currently becoming not only an extremely important factor for vehicles engineering development but also a key issue for improving road safety. Cooperative/Chain Collision Avoidance (CCA) application comes up as a solution for decreasing accidents on the road, therefore it is highly convenient to study how the system of vehicles in a platoon will behave at different stages of technology deployment until full penetration in the market. We have developed an analytical model to compute the average number of accidents in a platoon of vehicles. However, due to the model structure, when the CCA technology penetration rate is taken into account, the increase in the number of operations of the analytical model is such that the sequential computation of a numerical solution is no longer feasible. In this paper, with the goal in mind of reducing computation time, we show how we have implemented and parallelized our analytical model so as a solution can be achieved, what is conducted using the OpenMP parallelization techniques under a supercomputing shared memory environment. 1
Near Optimal Solution for Continuous Move Transportation with Time Windows and Dock Service Constraints
"... Abstract. We consider a pickup and delivery vehicle routing problem (PDP) commonly found in the realworld logistics operations. The problem includes a set of practical complications that have received little attention in the vehicle routing literature. There are multiple vehicle types available to ..."
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Abstract. We consider a pickup and delivery vehicle routing problem (PDP) commonly found in the realworld logistics operations. The problem includes a set of practical complications that have received little attention in the vehicle routing literature. There are multiple vehicle types available to cover a set of transportation orders with different pickup and delivery time windows. Transportation orders and vehicle types must satisfy a set of compatibility constraints. In addition, we include some dock service capacity constraints as required in realworld operations when there are a large number of vehicles to schedule. This problem requires to be attended on large scale instances: transportation orders ≥ 500, singlehaul vehicles ≥ 100. Exact algorithms are not suitable for large scale instances. We propose a model to solve the problem in three stages. The first stage constructs initial solutions at the aggregated level relaxing time windows and dock service constraints of the original problem. The other two stages impose time windows and dock service constraints within a cut generation scheme. Our results are favorable in finding good quality solutions in relatively short computational time.