21,297 research outputs found
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
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Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
Proposed shunt rounding technique for large-scale security constrained loss minimization
The official published version can be obtained from the link below - Copyright @ 2010 IEEE.Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.This work was supported in part by the National Grid and in part by the EPSRC. Paper no. TPWRS-00653-2009
A Hybrid Monte Carlo Ant Colony Optimization Approach for Protein Structure Prediction in the HP Model
The hydrophobic-polar (HP) model has been widely studied in the field of
protein structure prediction (PSP) both for theoretical purposes and as a
benchmark for new optimization strategies. In this work we introduce a new
heuristics based on Ant Colony Optimization (ACO) and Markov Chain Monte Carlo
(MCMC) that we called Hybrid Monte Carlo Ant Colony Optimization (HMCACO). We
describe this method and compare results obtained on well known HP instances in
the 3 dimensional cubic lattice to those obtained with standard ACO and
Simulated Annealing (SA). All methods were implemented using an unconstrained
neighborhood and a modified objective function to prevent the creation of
overlapping walks. Results show that our methods perform better than the other
heuristics in all benchmark instances.Comment: In Proceedings Wivace 2013, arXiv:1309.712
Syntactic Topic Models
The syntactic topic model (STM) is a Bayesian nonparametric model of language
that discovers latent distributions of words (topics) that are both
semantically and syntactically coherent. The STM models dependency parsed
corpora where sentences are grouped into documents. It assumes that each word
is drawn from a latent topic chosen by combining document-level features and
the local syntactic context. Each document has a distribution over latent
topics, as in topic models, which provides the semantic consistency. Each
element in the dependency parse tree also has a distribution over the topics of
its children, as in latent-state syntax models, which provides the syntactic
consistency. These distributions are convolved so that the topic of each word
is likely under both its document and syntactic context. We derive a fast
posterior inference algorithm based on variational methods. We report
qualitative and quantitative studies on both synthetic data and hand-parsed
documents. We show that the STM is a more predictive model of language than
current models based only on syntax or only on topics
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