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Routing and Wavelength Assignment of Scheduled Lightpath Demands
 in Procs. of ICOCN 2002, (Singapore
, 2003
"... In this paper, we present algorithms that compute the routing and wavelength assignment (RWA) for scheduled lightpath demands in a wavelengthswitching mesh network without wavelength conversion functionality. Scheduled lightpath demands are connection demands for which the setup and teardown times ..."
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Cited by 47 (5 self)
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In this paper, we present algorithms that compute the routing and wavelength assignment (RWA) for scheduled lightpath demands in a wavelengthswitching mesh network without wavelength conversion functionality. Scheduled lightpath demands are connection demands for which the setup and teardown times are known in advance. We formulate separately the routing problem and the wavelength assignment problem as spatiotemporal combinatorial optimization problems. For the former, we propose a branch and bound algorithm for exact resolution and an alternative tabu search algorithm for approximate resolution. A generalized graph coloring approach is used to solve the wavelength assignment problem. We compared the proposed algorithms to an RWA algorithm that sequentially computes the route and wavelength assignment for the scheduled lightpath demands.
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 38 (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
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 #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.
Branch and Bound Algorithms  Principles And Examples
, 1999
"... A large number of realworld planning problems called combinatorial optimization problems share the following properties: They are optimization problems, are easy to state, and have a finite but usually very large number of feasible solutions. While some of these as e.g. the Shortest Path proble ..."
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Cited by 20 (0 self)
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A large number of realworld planning problems called combinatorial optimization problems share the following properties: They are optimization problems, are easy to state, and have a finite but usually very large number of feasible solutions. While some of these as e.g. the Shortest Path problem and the Minimum Spanning Tree problem have polynomial algoritms, the majority of the problems in addition share the property that no polynomial method for their solution is known. Examples here are vehicle
Solving largescale QAP problems in parallel with the search library ZRAM.
 J. Parallel and Distributed Com.
, 1998
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Tree Elaboration Strategies In Branch and Bound Algorithms For Solving the Quadratic Assignment Problem
, 1999
"... This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst searc ..."
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Cited by 12 (3 self)
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This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst search of Mautor and Roucairol which extends a node by all assignments of an unassigned facility to unassigned locations based upon the counting of 'forbidden' locations. A forbidden location is one where the addition of the corresponding leader (linear cost) element would increase the lower bound beyond the upper bound. We learned that this fortuitous situation never occurs near the root on Nugent problems larger than 15. One has to make better estimates of the bound if the strategy is to work. We have, therefore, designed and implemented an increasingly improved set of bound calculations. The better of these bound calculations to be utilized near the root and the less accurate (poorer bounds) utilized further into the tree. The result is an effective and powerful technique for shortening the run times of problem instances in the range of size 16 to 25. Run times were decreased generally by five or sixtoone and the number of nodes evaluated was decreased as much as 10toone. Later improvements in our strategy produced a better than 3to1 reduction in runtime so that overall improvement in run time was as high as 20to1 as compared to our earlier results. At the end of our paper, we compare the performance of the four most successful algorithms for exact solution of the QAP.
Synthesizing minimal tile sets for patterned DNA selfassembly
 In DNA
, 2010
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Search Heuristics for Box Decomposition Methods
 Journal of Global Optimization
, 2001
"... In this paper we study search heuristics for box decomposition methods that solve problems such as global optimization, minimax optimization, or quantified constraint solving. For this we unify these methods as nested branchandbound algorithms, and develop a model that is more convenient for study ..."
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Cited by 8 (6 self)
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In this paper we study search heuristics for box decomposition methods that solve problems such as global optimization, minimax optimization, or quantified constraint solving. For this we unify these methods as nested branchandbound algorithms, and develop a model that is more convenient for studying heuristics for these algorithms than the traditional models from Artificial Intelligence. We use the result to prove various theorems about heuristics and apply the outcome to the box decomposition methods under consideration. We support the findings with timings for the method of quantified constraint solving developed by the author.
Joining Forces in Solving LargeScale Quadratic Assignment Problems in Parallel
 In Proc. of the 11th International Parallel Processing Symposium
, 1996
"... Program libraries are one way to make the cooperation between specialists from various fields successful: the separation of applicationspecific knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and flexibility. The current paper demonstrates the success ..."
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Cited by 8 (1 self)
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Program libraries are one way to make the cooperation between specialists from various fields successful: the separation of applicationspecific knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and flexibility. The current paper demonstrates the success in combining problemspecific knowledge for the quadratic assignment problem (QAP) with the raw computing power offered by contemporary parallel hardware by using the library of parallel search algorithms ZRAM. Solutions of previously unsolved large standard testinstances of the QAP are presented. 1 Introduction Since the early days of the computer age computers have been used as number crunchers to solve problemswhether they are practical problems or research problems. The people interested in solving a specific problem supplied the data and solution method and did the necessary programming to implement the solution method themselves. Today's world of problem solving looks differ...
A Skeleton for Distributed Work Pools in Eden
 in 10th International Symposium on Functional and Logic Programming, ser. LNCS 6009
, 2010
"... Abstract. We present a flexible skeleton for implementing distributed work pools in our parallel functional language Eden. The skeleton manages a pool of tasks (work pool) in a distributed manner using a demanddriven work stealing approach for load balancing. All coordination is done locally within ..."
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Cited by 3 (1 self)
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Abstract. We present a flexible skeleton for implementing distributed work pools in our parallel functional language Eden. The skeleton manages a pool of tasks (work pool) in a distributed manner using a demanddriven work stealing approach for load balancing. All coordination is done locally within the worker processes. The latter are arranged in a ring topology and exchange additional channels to shortcut communication paths. The skeleton is suited for different types of algorithms, namely simple data parallel ones and standard tree search algorithms like backtracking, and using a global state as needed for branchandbound. Runtime experiments reveal a stable runtime behaviour for the different algorithm classes as illustrated by activity profiles (timeline diagrams). Acceptable speedups can be achieved with low effort. 1