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A TwoStage Hybrid Local Search for the Vehicle Routing Problem with Time Windows
, 2004
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HumanGuided Simple Search
 IN PROCEED OF AAAI 2000, JULY 30–AUGUST 3
, 2000
"... Scheduling, routing, and layout tasks are examples of hard operationsresearch problems that have broad application in industry. Typical algorithms for these problems combine some form of gradient descent to find local minima with some strategy for escaping nonoptimal local minima. Our idea is to di ..."
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Cited by 48 (10 self)
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Scheduling, routing, and layout tasks are examples of hard operationsresearch problems that have broad application in industry. Typical algorithms for these problems combine some form of gradient descent to find local minima with some strategy for escaping nonoptimal local minima. Our idea is to divide these two subtasks cleanly between human and computer: in our paradigm of humanguided simple search the computer is responsible only for finding local minima using a simple hillclimbing search; using visualization and interaction techniques, the human user identifies promising regions of the search space for the computer to explore, and intervenes to help it escape nonoptimal local minima. We have applied our approach to the problem of capacitated vehicle routing with time windows, a commercially important problem with a rich research history. Despite its simplicity, our prototype system is competitive with the majority of previously reported systems on benchmark academic problems, and has the advantage of keeping a human tightly in the loop to handle the complexities of realworld applications.
Adaptive Memory Programming: A Unified View of Metaheuristics
, 1998
"... The paper analyses recent developments of a number of memorybased metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the ..."
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Cited by 44 (3 self)
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The paper analyses recent developments of a number of memorybased metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the name of Adaptive Memory Programming (AMP). A number of methods recently developed for the quadratic assignment, vehicle routing and graph colouring problems are reviewed and presented under the adaptive memory programming point of view. AMP presents a number of interesting aspects such as a high parallelization potential and the ability of dealing with real and dynamic applications.
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 39 (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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Cited by 34 (2 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 #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
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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.
A parallel hybrid evolutionary metaheuristic for the vehicle routing problem with time windows
 University of Jyväskyla
, 1999
"... The vehicle routing problem with time windows (VRPTW) is an extension of the wellknown vehicle routing problem with a central depot. The objective function of the VRPTW considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance (secondary c ..."
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The vehicle routing problem with time windows (VRPTW) is an extension of the wellknown vehicle routing problem with a central depot. The objective function of the VRPTW considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance (secondary criterion). In this paper, a twophase procedural approach for solving the VRPTW is parallelized. The aim of the first phase is the minimization of the number of vehicles by means of a (1, λ)evolution strategy, whereas in the second phase the total distance is minimized using a tabu search algorithm. The parallelization of this sequential hybrid procedure follows the concept of cooperative autonomy, i.e., several autonomous sequential solution procedures cooperate through the exchange of solutions. However, exchanges of solutions lead to the corresponding jumps in the solution space only if certain acceptance conditions are met. The good performance of both the sequential and the parallel approach is demonstrated by means of wellknown and new benchmark problems. Key words: Evolution strategy, metaheuristic, tabu search, hybridization, parallelization, vehicle routing, time windows.
Reactive search: machine learning for memorybased heuristics
 Teofilo F. Gonzalez (Ed.), Approximation Algorithms and Metaheuristics, Taylor & Francis Books (CRC Press
, 2005
"... 1 Introduction: the role of the user in heuristics Most stateoftheart heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology [5, 41, 51]. In some cases, these parameters are tuned through a ..."
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Cited by 13 (5 self)
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1 Introduction: the role of the user in heuristics Most stateoftheart heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology [5, 41, 51]. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed by the
Efficient Local Search Algorithms for the Vehicle Routing Problem with Time Windows
 EUR. J. OPER. RES
, 2001
"... this paper is to present new methods for solving the vehicle routing problem with time windows (VRPTW). VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visite ..."
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Cited by 12 (2 self)
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this paper is to present new methods for solving the vehicle routing problem with time windows (VRPTW). VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle
Reactive Search Optimization: Learning while Optimizing
"... The final purpose of Reactive Search Optimization (RSO) is to simplify the life for the final user of optimization. While researchers enjoy designing algorithms, testing alternatives, tuning parameters and choosing solution schemes — in fact this is part of their daily life — the final users ’ inter ..."
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Cited by 7 (3 self)
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The final purpose of Reactive Search Optimization (RSO) is to simplify the life for the final user of optimization. While researchers enjoy designing algorithms, testing alternatives, tuning parameters and choosing solution schemes — in fact this is part of their daily life — the final users ’ interests are different: solving a problem in the
Management
"... Abstract: The Vehicle Routing Problem with Time Windows (VRPTW) is an important problem occurring in many logistics systems. The objective of VRPTW is to serve a set of customers within their predefined time windows at minimum cost. Ant Colony System algorithm (ACS) that is capable of searching mult ..."
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Cited by 5 (0 self)
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Abstract: The Vehicle Routing Problem with Time Windows (VRPTW) is an important problem occurring in many logistics systems. The objective of VRPTW is to serve a set of customers within their predefined time windows at minimum cost. Ant Colony System algorithm (ACS) that is capable of searching multiple search areas simultaneously in the solution space is good in diversification. On the other hand, Simulated Annealing algorithm (SA) is a local search technique that has been successfully applied to many NPhard problems. A hybrid algorithm (IACSSA) that combines an improved ACS with SA is proposed in this paper. The algorithm has been tested on 56 Solomon benchmark problems. The results show that our IACSSA is competitive with other metaheuristic approaches in the literature. The results also indicate that such a hybrid algorithm outperforms the individual heuristic alone. Key Words: logistics, ant colony system, simulated annealing, hybrid algorithm 1.