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Probabilistic Diversification And Intensification In Local Search For Vehicle Routing
 Journal of Heuristics
, 1995
"... : This paper presents a probabilistic technique to diversify, intensify and parallelize a local search adapted for solving vehicle routing problems. This technique may be applied to a very wide variety of vehicle routing problems and local searches. It is shown that efficient first level taboo sear ..."
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Cited by 108 (3 self)
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: This paper presents a probabilistic technique to diversify, intensify and parallelize a local search adapted for solving vehicle routing problems. This technique may be applied to a very wide variety of vehicle routing problems and local searches. It is shown that efficient first level taboo searches for vehicle routing problems may be significantly improved with this technique. Moreover, the solutions produced by this technique may often be improved by a postoptimization technique presented in this paper too. The solutions of nearly 40 problem instances of the literature have been improved. Key words : Vehicle routing, local searches, parallel algorithms. 1. INTRODUCTION More and more, local search methods are used to find good solutions to combinatorial optimization problems. Throughout the paper, we use the term local search as a synonym of neighbourhood search. Local searches are sometimes restricted to steepest descent algorithms but we also include taboo search and simulated...
Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problems with Time Windows. Working paper
, 1993
"... The Vehicle Routing Problem with Time Windows (VRPTW) involves servicing a set of customers, with earliest and latest time deadlines, with varying demands using capacitated vehicles with limited travel times. The objective of the problem is to service all customers while minimizing the number of veh ..."
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Cited by 32 (1 self)
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The Vehicle Routing Problem with Time Windows (VRPTW) involves servicing a set of customers, with earliest and latest time deadlines, with varying demands using capacitated vehicles with limited travel times. The objective of the problem is to service all customers while minimizing the number of vehicles and travel distance without violating the capacity and travel time of the vehicles and customer time constraints. In this paper we describe a λinterchange mechanism that moves customers between routes to generate neighborhood solutions for the VRPTW. The λinterchange neighborhood is searched using Simulated Annealing and Tabu Search strategies. The initial solutions to the VRPTW are obtained using the PushForward Insertion heuristic and a Genetic Algorithm based sectoring heuristic. The hybrid combination of the implemented heuristics, collectively known as the GenSAT system, were used to solve 60 problems from the literature with customer sizes varying from 100 to 417 customers. The computational results of GenSAT obtained new best solutions for 40 test problems. For the remaining 20 test problems, 11 solutions obtained by the GenSAT system equal previously known best solutions. The average performance of GenSAT is significantly better than known competing heuristics. For known optimal solutions to the VRPTW problems, the GenSAT system obtained the optimal number of vehicles. Keywords:
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.
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 21 (0 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.
A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows
 Combinatorial Optimization and Applications
"... Abstract This paper considers a transportation problem for moving empty or laden containers for a logistic company. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for ser ..."
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Cited by 20 (0 self)
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Abstract This paper considers a transportation problem for moving empty or laden containers for a logistic company. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multiobjective and multimodal combinatorial optimization problem, a hybrid multiobjective evolutionary algorithm (HMOEA) is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decisionmaking information from the multiobjective optimization results The computational results have shown that the HMOEA is effective for solving multiobjective combinatorial problems, such as finding useful tradeoff solutions for the TTVRP. 1
Multiobjective Genetic Algorithms for Vehicle Routing Problem with Time Windows
 APPLIED INTELLIGENCE
, 2006
"... The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NPComplete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multiobjective problem and present a genet ..."
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Cited by 18 (1 self)
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The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NPComplete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multiobjective problem and present a genetic algorithm solution using the Pareto ranking technique. We use a direct interpretation of the VRPTW as a multiobjective problem, in which the two objective dimensions are number of vehicles and total cost (distance). An advantage of this approach is that it is unnecessary to derive weights for a weighted sum scoring formula. This prevents the introduction of solution bias towards either of the problem dimensions. We argue that the VRPTW is most naturally viewed as a multimodal problem, in which both vehicles and cost are of equal value, depending on the needs of the user. A result of our research is that the multiobjective optimization genetic algorithm returns a set of solutions that fairly consider both of these dimensions. Our approach is quite effective, as it provides solutions competitive with the best known in the literature, as well as new solutions that are not biased toward the number of vehicles. A set of wellknown benchmark data are used to compare the effectiveness of the proposed method for solving the VRPTW.
Parallel simulated annealing for the vehicle routing problem with time windows
 10th Euromicro Workshop on Parallel, Distributed and Networkbased Processing, Canary Islands–Spain
, 2002
"... A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is presented. The objective is to find the best possible solutions to some wellknown instances of the problem by using parallelism. The empirical evidence indicate that parallel simulated annealing can be ..."
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Cited by 15 (0 self)
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A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is presented. The objective is to find the best possible solutions to some wellknown instances of the problem by using parallelism. The empirical evidence indicate that parallel simulated annealing can be applied with success to bicriterion optimization problems. Key words. Parallel simulated annealing, message passing model of parallel computation, vehicle routing problem with time windows, bicriterion optimization 1
A twostage hybrid algorithm for the pickup and delivery vehicle routing problem with time windows
 Comput. Oper. Res
, 2005
"... Abstract. This paper presents a twostage hybrid algorithm for pickup and delivery vehicle routing problems with time windows and multiple vehicles (PDPTW). The first stage uses a simple simulated annealing algorithm to decrease the number of routes, while the second stage uses LNS to decrease total ..."
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Cited by 13 (2 self)
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Abstract. This paper presents a twostage hybrid algorithm for pickup and delivery vehicle routing problems with time windows and multiple vehicles (PDPTW). The first stage uses a simple simulated annealing algorithm to decrease the number of routes, while the second stage uses LNS to decrease total travel cost. Experimental results show the effectiveness of the algorithm which has produced many new best solutions on problems with 100, 200, and 600 customers. In particular, it has improved 47 % and 76 % of the best solutions on the 200 and 600customer benchmarks, sometimes by as much as 3 vehicles. These results further confirm the benefits of twostage approaches in vehicle routing. They also answer positively the open issue in the original LNS paper, which advocated the use of LNS for the PDPTW and argue for the robustness of LNS with respect to sideconstraints. 1
A Heuristic for the Vehicle Routing Problem with Time Windows
 Journal of Heuristics
, 2001
"... Editor: Abstract. In this paper we propose a heuristic algorithm to solve theVehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical kopt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second ..."
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Cited by 9 (0 self)
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Editor: Abstract. In this paper we propose a heuristic algorithm to solve theVehicle Routing Problem with Time Windows. Its framework is a smart combination of three simple procedures: the classical kopt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective function drives the search out of local optima. No parameter tuning is required and no random choice is made: these are the distinguishing features with respect to the recent literature. The algorithm has been tested on benchmark problems which prove ittobe more e ective than comparable algorithms.