12,626 research outputs found
Experimental Evaluation of Branching Schemes for the CSP
The search strategy of a CP solver is determined by the variable and value
ordering heuristics it employs and by the branching scheme it follows. Although
the effects of variable and value ordering heuristics on search effort have
been widely studied, the effects of different branching schemes have received
less attention. In this paper we study this effect through an experimental
evaluation that includes standard branching schemes such as 2-way, d-way, and
dichotomic domain splitting, as well as variations of set branching where
branching is performed on sets of values. We also propose and evaluate a
generic approach to set branching where the partition of a domain into sets is
created using the scores assigned to values by a value ordering heuristic, and
a clustering algorithm from machine learning. Experimental results demonstrate
that although exponential differences between branching schemes, as predicted
in theory between 2-way and d-way branching, are not very common, still the
choice of branching scheme can make quite a difference on certain classes of
problems. Set branching methods are very competitive with 2-way branching and
outperform it on some problem classes. A statistical analysis of the results
reveals that our generic clustering-based set branching method is the best
among the methods compared.Comment: To appear in the 3rd workshop on techniques for implementing
constraint programming systems (TRICS workshop at the 16th CP Conference),
St. Andrews, Scotland 201
Symmetry-Based Search Space Reduction For Grid Maps
In this paper we explore a symmetry-based search space reduction technique
which can speed up optimal pathfinding on undirected uniform-cost grid maps by
up to 38 times. Our technique decomposes grid maps into a set of empty
rectangles, removing from each rectangle all interior nodes and possibly some
from along the perimeter. We then add a series of macro-edges between selected
pairs of remaining perimeter nodes to facilitate provably optimal traversal
through each rectangle. We also develop a novel online pruning technique to
further speed up search. Our algorithm is fast, memory efficient and retains
the same optimality and completeness guarantees as searching on an unmodified
grid map
Models and Strategies for Variants of the Job Shop Scheduling Problem
Recently, a variety of constraint programming and Boolean satisfiability
approaches to scheduling problems have been introduced. They have in common the
use of relatively simple propagation mechanisms and an adaptive way to focus on
the most constrained part of the problem. In some cases, these methods compare
favorably to more classical constraint programming methods relying on
propagation algorithms for global unary or cumulative resource constraints and
dedicated search heuristics. In particular, we described an approach that
combines restarting, with a generic adaptive heuristic and solution guided
branching on a simple model based on a decomposition of disjunctive
constraints. In this paper, we introduce an adaptation of this technique for an
important subclass of job shop scheduling problems (JSPs), where the objective
function involves minimization of earliness/tardiness costs. We further show
that our technique can be improved by adding domain specific information for
one variant of the JSP (involving time lag constraints). In particular we
introduce a dedicated greedy heuristic, and an improved model for the case
where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia
: Italy (2011
Models for the optimization of promotion campaigns: exact and heuristic algorithms.
This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. The complexity of the problem makes it very difficult to produce optimal solutions using standard optimization methods. We propose an alternative set covering formulation and develop a branch-and-price algorithm to solve it. We also describe five heuristics to approximate an optimal solution. Two of these heuristics are algorithms based on restricted versions of the basic formulation, the third is a successive exact k-item knapsack procedure. A heuristic inspired by the Next-Product-To-Buy model and a depth-first branch-and-price heuristic are also presented. Finally, we perform extensive computational experiments for the two formulations as well as for the five heuristics.Promotion campaign; Minimum quantity commitment; Integer programming; Branch-and-price algorithm; Non-approximability; Heuristics; Business-to-business; Business-to-consumer;
Performance improvement of an optical network providing services based on multicast
Operators of networks covering large areas are confronted with demands from
some of their customers who are virtual service providers. These providers may
call for the connectivity service which fulfils the specificity of their
services, for instance a multicast transition with allocated bandwidth. On the
other hand, network operators want to make profit by trading the connectivity
service of requested quality to their customers and to limit their
infrastructure investments (or do not invest anything at all).
We focus on circuit switching optical networks and work on repetitive
multicast demands whose source and destinations are {\em \`a priori} known by
an operator. He may therefore have corresponding trees "ready to be allocated"
and adapt his network infrastructure according to these recurrent
transmissions. This adjustment consists in setting available branching routers
in the selected nodes of a predefined tree. The branching nodes are
opto-electronic nodes which are able to duplicate data and retransmit it in
several directions. These nodes are, however, more expensive and more energy
consuming than transparent ones.
In this paper we are interested in the choice of nodes of a multicast tree
where the limited number of branching routers should be located in order to
minimize the amount of required bandwidth. After formally stating the problem
we solve it by proposing a polynomial algorithm whose optimality we prove. We
perform exhaustive computations to show an operator gain obtained by using our
algorithm. These computations are made for different methods of the multicast
tree construction. We conclude by giving dimensioning guidelines and outline
our further work.Comment: 16 pages, 13 figures, extended version from Conference ISCIS 201
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