464 research outputs found
A study on exponential-size neighborhoods for the bin packing problem with conflicts
We propose an iterated local search based on several classes of local and
large neighborhoods for the bin packing problem with conflicts. This problem,
which combines the characteristics of both bin packing and vertex coloring,
arises in various application contexts such as logistics and transportation,
timetabling, and resource allocation for cloud computing. We introduce
evaluation procedures for classical local-search moves, polynomial variants of
ejection chains and assignment neighborhoods, an adaptive set covering-based
neighborhood, and finally a controlled use of 0-cost moves to further diversify
the search. The overall method produces solutions of good quality on the
classical benchmark instances and scales very well with an increase of problem
size. Extensive computational experiments are conducted to measure the
respective contribution of each proposed neighborhood. In particular, the
0-cost moves and the large neighborhood based on set covering contribute very
significantly to the search. Several research perspectives are open in relation
to possible hybridizations with other state-of-the-art mathematical programming
heuristics for this problem.Comment: 26 pages, 8 figure
Algorithms for the minimum sum coloring problem: a review
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex
coloring problem which has a number of AI related applications. Due to its
theoretical and practical relevance, MSCP attracts increasing attention. The
only existing review on the problem dates back to 2004 and mainly covers the
history of MSCP and theoretical developments on specific graphs. In recent
years, the field has witnessed significant progresses on approximation
algorithms and practical solution algorithms. The purpose of this review is to
provide a comprehensive inspection of the most recent and representative MSCP
algorithms. To be informative, we identify the general framework followed by
practical solution algorithms and the key ingredients that make them
successful. By classifying the main search strategies and putting forward the
critical elements of the reviewed methods, we wish to encourage future
development of more powerful methods and motivate new applications
Acyclic orientations with path constraints
Many well-known combinatorial optimization problems can be stated over the
set of acyclic orientations of an undirected graph. For example, acyclic
orientations with certain diameter constraints are closely related to the
optimal solutions of the vertex coloring and frequency assignment problems. In
this paper we introduce a linear programming formulation of acyclic
orientations with path constraints, and discuss its use in the solution of the
vertex coloring problem and some versions of the frequency assignment problem.
A study of the polytope associated with the formulation is presented, including
proofs of which constraints of the formulation are facet-defining and the
introduction of new classes of valid inequalities
Two genetic algorithms for the bandwidth multicoloring problem
In this paper the Bandwidth Multicoloring Problem (BMCP) and the Bandwidth Coloring Problem (BCP) are considered. The problems are solved by two genetic algorithms (GAs) which use the integer encoding and standard genetic operators adapted to the problems. In both proposed implementations, all individuals are feasible by default, so search is directed into the promising regions. The first proposed method named GA1 is a constructive metaheuristic that construct solution, while the second named GA2 is an improving metaheuristic used to improve an existing solution. Genetic algorithms are tested on the publicly-available GEOM instances from the literature. Proposed GA1 has achieved a much better solution than the calculated upper bound for a given problem, and GA2 has significantly improved the solutions obtained by GA1. The obtained results are also compared with the results of the existing methods for solving BCP and BMCP
An exact algorithm for the Partition Coloring Problem
We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation with an exponential number of variables. To solve this formulation to optimality, we design an effective Branch-and-Price algorithm. Good quality initial solutions are computed via a new metaheuristic algorithm based on adaptive large neighborhood search. Extensive computational experiments on a benchmark test of instances from the literature show that our Branch-and-Price algorithm, combined with the new metaheuristic algorithm, is able to solve for the first time to proven optimality several open instances, and compares favorably with the current state-of-the-art exact algorithm
An Efficient Coded Multicasting Scheme Preserving the Multiplicative Caching Gain
Coded multicasting has been shown to be a promis- ing approach to
significantly improve the caching performance of content delivery networks with
multiple caches downstream of a common multicast link. However, achievable
schemes proposed to date have been shown to achieve the proved order-optimal
performance only in the asymptotic regime in which the number of packets per
requested item goes to infinity. In this paper, we first extend the asymptotic
analysis of the achievable scheme in [1], [2] to the case of heterogeneous
cache sizes and demand distributions, providing the best known upper bound on
the fundamental limiting performance when the number of packets goes to
infinity. We then show that the scheme achieving this upper bound quickly loses
its multiplicative caching gain for finite content packetization. To overcome
this limitation, we design a novel polynomial-time algorithm based on random
greedy graph- coloring that, while keeping the same finite content
packetization, recovers a significant part of the multiplicative caching gain.
Our results show that the order-optimal coded multicasting schemes proposed to
date, while useful in quantifying the fundamental limiting performance, must be
properly designed for practical regimes of finite packetization.Comment: 6 pages, 7 figures, Published in Infocom CNTCV 201
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