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Vehicle Routing with Time Windows using Genetic Algorithms
, 1995
"... In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being ..."
Abstract

Cited by 38 (3 self)
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In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. As finding a feasible solution to the problem is NPcomplete, search methods based upon heuristics are most promising for problems of practical size. In this paper we describe GIDEON, a genetic algorithm heuristic for solving the VRPTW. GIDEON consists of a global customer clustering method and a local postoptimization method. The global customer clustering method uses an adaptive search strategy based upon population genetics, to assign vehicles to customers. The best solution obtained from the clustering method is improved by a local postoptimization method. The synergy a between global adaptive clustering method and a local route optimization method produce better results than those obtained by competing heuristic search methods. On a standard set of 56 VRPTW problems obtained from the literature the GIDEON system obtained 41 new best known solutions.
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 ..."
Abstract

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
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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.
Node Reclamation and Replacement for Longlived Sensor Networks
"... Abstract—When deployed for longterm tasks, the energy required to support sensor nodes ’ activities is far more than the energy that can be preloaded in their batteries. No matter how the battery energy is conserved, once the energy is used up, the network life terminates. Therefore, guaranteeing l ..."
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Cited by 4 (4 self)
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Abstract—When deployed for longterm tasks, the energy required to support sensor nodes ’ activities is far more than the energy that can be preloaded in their batteries. No matter how the battery energy is conserved, once the energy is used up, the network life terminates. Therefore, guaranteeing longterm energy supply has persisted as a big challenge. To address this problem, we propose a node replacement and reclamation (NRR) strategy, with which a mobile robot or human labor called mobile repairman (MR) periodically traverses the sensor network, reclaims nodes with low or no power supply, replaces them with fullycharged ones, and brings the reclaimed nodes back to an energy station for recharging. To effectively and efficiently realize the strategy, we develop an adaptive rendezvousbased twotier scheduling (ARTS) scheme to schedule the replacement/reclamation activities of the MR and the duty cycles of nodes. Extensive simulations have been conducted to verify the effectiveness and efficiency of the ARTS scheme. I.
Random access wireless networks with controlled mobility
 In Proc. IFIP MEDHOCNET’09
, 2009
"... Abstract—This paper considers wireless networks where messages arriving randomly (in time and space) are collected by a mobile receiver. The messages are transmitted to the mobile receiver according to a random access scheme and the receiver dynamically adjusts its position in order to receive these ..."
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Cited by 3 (3 self)
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Abstract—This paper considers wireless networks where messages arriving randomly (in time and space) are collected by a mobile receiver. The messages are transmitted to the mobile receiver according to a random access scheme and the receiver dynamically adjusts its position in order to receive these messages in minimum time. We investigate the use of wireless transmission and controlled mobility to improve the delay performance in such systems. In particular, we characterize the tradeoff between wireless transmission and physical movement of the mobile receiver. We derive a lower bound for the delay in the system and show how it is affected by different communication parameters. We show that the combination of mobility and wireless transmission results in a significant improvement in delay as compared to a system where wireless transmission is not used. I.
Adaptive memory programming for the vehicle routing problem with multiple trips
 Computers & Operations Research
, 2007
"... The Vehicle Routing Problem with Multiple Trips is an extension of the classical Vehicle Routing Problem in which each vehicle may perform several routes in the same planning period. In this paper, an adaptive memory algorithm to solve this problem is proposed. The algorithm was run over a set of be ..."
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Cited by 2 (0 self)
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The Vehicle Routing Problem with Multiple Trips is an extension of the classical Vehicle Routing Problem in which each vehicle may perform several routes in the same planning period. In this paper, an adaptive memory algorithm to solve this problem is proposed. The algorithm was run over a set of benchmark problem instances, consistently finding highquality solutions.
A Family Competition Genetic Algorithm for the Pickup and Delivery Problems with Time Window
"... This paper presents a new approach based on genetic algorithms to solving the singlevehicle pickup and delivery problem with time window constraints (1PDPTW). In particular, we illustrate how the Family Competition Genetic Algoritm (FCGA) is applied to the 1PDPTW, and compare its results with prev ..."
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Cited by 1 (0 self)
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This paper presents a new approach based on genetic algorithms to solving the singlevehicle pickup and delivery problem with time window constraints (1PDPTW). In particular, we illustrate how the Family Competition Genetic Algoritm (FCGA) is applied to the 1PDPTW, and compare its results with previous solutions to the problem. Genetic algorithms have been shown to find feasible or nearoptimal solutions when traditional methods would fail within a reasonble amount of time. By incorporating the concept of families to maintain diversity, FCGA further improves solution quality and increases the probability of finding the optimal solutions without much extra resource demands. Extensive experiments on FCGA with various crossover and mutation operators show that the new approach succeeds in finding the optimal solutions for 1PDPTW under 50 tasks, and can obtain nearoptimal or feasible solutions in most problems up to 100 tasks.
A PTAS for the Multiple Depot Vehicle Routing Problem ⋆
"... Abstract. We design a simple PTAS for a multi depot capacitated vehicle routing problem. In this problem a set of customers and set of depots are represented by points in the Euclidean plane. Vehicles have capacities expressed in the number of customers that can be visited on one route starting and ..."
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Abstract. We design a simple PTAS for a multi depot capacitated vehicle routing problem. In this problem a set of customers and set of depots are represented by points in the Euclidean plane. Vehicles have capacities expressed in the number of customers that can be visited on one route starting and ending in a depot. The objective is to determine a set of routes such that all customers are visited and the total length of the routes is minimized. Our results extend the results by Haimovich and Rinnooy Kan [6]. 1
Using Family Competition Genetic Algorithm in Pickup and Delivery Problem with . . .
, 2002
"... In this paper, we propose a novel research scheme to solve the single vehicle pickup and delivery problem (PDPTW) with time window constraints. The family competition genetic algorithm (FCGA) is a modern approach that has been successfully applied to solve the traveling salesman problem. We illustra ..."
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In this paper, we propose a novel research scheme to solve the single vehicle pickup and delivery problem (PDPTW) with time window constraints. The family competition genetic algorithm (FCGA) is a modern approach that has been successfully applied to solve the traveling salesman problem. We illustrate the family competition GA and give the experimental results that show the FCGA is a brilliant algorithm for solving the single vehicle PDPTW. Genetic algorithms (GA) have been successful applied to solve the combinatorial computation problems. The family competition will improve the achievements for obtaining optimal solutions and the probability to hit the feasible solutions. By comparing FCGA with traditional GA, this excellent approach does not need enormous resources. Applying FCGA to single vehicle PDPTW, it succeeded in finding feasible solutions for all problems and obtained efficient results in our experimentation.
Submitted to the book on "Applications Handbook of Genetic Algorithms:New Frontiers" Vehicle Routing with Time Windows using Genetic Algorithms
"... Abstract In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers with ..."
Abstract
 Add to MetaCart
Abstract In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. As finding a feasible solution to the problem is NPcomplete, search methods based upon heuristics are most promising for problems of practical size. In this paper we describe GIDEON, a genetic algorithm heuristic for solving the VRPTW. GIDEON consists of a global customer clustering method and a local postoptimization method. The global customer clustering method uses an adaptive search strategy based upon population genetics, to assign vehicles to customers. The best solution obtained from the clustering method is improved by a local postoptimization method. The synergy a between global adaptive clustering method and a local route optimization method produce better results than those obtained by competing heuristic search methods. On a standard set of 56 VRPTW problems obtained from the literature the GIDEON system obtained 41 new best known solutions.