5,901 research outputs found
Reinforcement learning based local search for grouping problems: A case study on graph coloring
Grouping problems aim to partition a set of items into multiple mutually
disjoint subsets according to some specific criterion and constraints. Grouping
problems cover a large class of important combinatorial optimization problems
that are generally computationally difficult. In this paper, we propose a
general solution approach for grouping problems, i.e., reinforcement learning
based local search (RLS), which combines reinforcement learning techniques with
descent-based local search. The viability of the proposed approach is verified
on a well-known representative grouping problem (graph coloring) where a very
simple descent-based coloring algorithm is applied. Experimental studies on
popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves
competitive performances compared to a number of well-known coloring
algorithms
Two novel evolutionary formulations of the graph coloring problem
We introduce two novel evolutionary formulations of the problem of coloring
the nodes of a graph. The first formulation is based on the relationship that
exists between a graph's chromatic number and its acyclic orientations. It
views such orientations as individuals and evolves them with the aid of
evolutionary operators that are very heavily based on the structure of the
graph and its acyclic orientations. The second formulation, unlike the first
one, does not tackle one graph at a time, but rather aims at evolving a
`program' to color all graphs belonging to a class whose members all have the
same number of nodes and other common attributes. The heuristics that result
from these formulations have been tested on some of the Second DIMACS
Implementation Challenge benchmark graphs, and have been found to be
competitive when compared to the several other heuristics that have also been
tested on those graphs.Comment: To appear in Journal of Combinatorial Optimizatio
Network conduciveness with application to the graph-coloring and independent-set optimization transitions
We introduce the notion of a network's conduciveness, a probabilistically
interpretable measure of how the network's structure allows it to be conducive
to roaming agents, in certain conditions, from one portion of the network to
another. We exemplify its use through an application to the two problems in
combinatorial optimization that, given an undirected graph, ask that its
so-called chromatic and independence numbers be found. Though NP-hard, when
solved on sequences of expanding random graphs there appear marked transitions
at which optimal solutions can be obtained substantially more easily than right
before them. We demonstrate that these phenomena can be understood by resorting
to the network that represents the solution space of the problems for each
graph and examining its conduciveness between the non-optimal solutions and the
optimal ones. At the said transitions, this network becomes strikingly more
conducive in the direction of the optimal solutions than it was just before
them, while at the same time becoming less conducive in the opposite direction.
We believe that, besides becoming useful also in other areas in which network
theory has a role to play, network conduciveness may become instrumental in
helping clarify further issues related to NP-hardness that remain poorly
understood
A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring
The Artificial Bee Colony (ABC) is the name of an optimization algorithm that
was inspired by the intelligent behavior of a honey bee swarm. It is widely
recognized as a quick, reliable, and efficient methods for solving optimization
problems. This paper proposes a hybrid ABC (HABC) algorithm for graph
3-coloring, which is a well-known discrete optimization problem. The results of
HABC are compared with results of the well-known graph coloring algorithms of
today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of
the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive
experimentations has shown that the HABC matched the competitive results of the
best graph coloring algorithms, and did better than the traditional heuristics
EA-SAW when solving equi-partite, flat, and random generated medium-sized
graphs
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
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