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Guided Local Search
, 2010
"... Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many real-life combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast Local Sea ..."
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Cited by 64 (5 self)
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Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many real-life combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast Local Search (FLS) and surveys their applications. GLS is a penalty-based meta-heuristic algorithm that sits on top of other local search algorithms, with the aim to improve their efficiency and robustness. FLS is a way of reducing the size of the neighbourhood to improve the efficiency of local search. The chapter also provides guidance for implementing and using GLS and FLS. Four problems, representative of general application categories, are examined with detailed information provided on how to build a GLS-based method in each case.
An Evolutionary Approach with Diversity Guarantee and Well-Informed Grouping Recombination for Graph Coloring
, 2010
"... We present a diversity-oriented hybrid evolutionary approach for the graph coloring problem. This approach is based on both generally applicable strategies and specifically tailored techniques. Particular attention is paid to ensuring population diversity by carefully controlling spacing among indiv ..."
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Cited by 21 (13 self)
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We present a diversity-oriented hybrid evolutionary approach for the graph coloring problem. This approach is based on both generally applicable strategies and specifically tailored techniques. Particular attention is paid to ensuring population diversity by carefully controlling spacing among individuals. Using a distance measure between potential solutions, the general population management strategy decides whether an offspring should be accepted in the population, which individual needs to be replaced and when mutation is applied. Furthermore, we introduce a special grouping-based multi-parent crossover operator which relies on several relevant features to identify meaningful building blocks for offspring construction. The proposed approach can be generally characterized as “well-informed”, in the sense that the design of each component is based on the most pertinent information which is identified by both experimental observation and careful analysis of the given problem. The resulting algorithm proves to be highly competitive when it is applied on the whole set of the DIMACS benchmark graphs.
Hyper-rectangle-based discriminative data generalization and applications in data mining
, 2007
"... The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as human-comprehensible patterns from which end-users can gain intuitions and insights. Axis-parallel hyper-rectangles provide interpretable generalizations for multi-dimensional data points ..."
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Cited by 5 (2 self)
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The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as human-comprehensible patterns from which end-users can gain intuitions and insights. Axis-parallel hyper-rectangles provide interpretable generalizations for multi-dimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectangle-based discriminative data generalization in the context of several useful data mining applications: cluster description, rule learning, and Nearest Rectangle classification. Clustering is one of the most important data mining tasks. However, most clustering methods output sets of points as clusters and do not generalize them into interpretable patterns. We perform a systematic study of cluster description, where we propose novel description formats leading to enhanced expressive power and introduce novel description problems specifying different trade-offs between interpretability and accuracy. We also present efficient heuristic algorithms for the introduced problems in the proposed formats. If-then rules are
SAT Algorithms for Colouring Some Special Classes of Graphs: Some Theoretical and Experimental Results
"... The local search algorithm GSAT is based on the notion of Satisfiability. It has been used successfully for colouring graphs, solving instances of the 3SAT problem, planning blocks world exercises, and other applications. The runtime performance of GSAT can be considerably enhanced by the incorporat ..."
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Cited by 3 (0 self)
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The local search algorithm GSAT is based on the notion of Satisfiability. It has been used successfully for colouring graphs, solving instances of the 3SAT problem, planning blocks world exercises, and other applications. The runtime performance of GSAT can be considerably enhanced by the incorporation of a noise generating component such as tabu search or random walk. This has been verified experimentally on numerous occasions, but few attempts have been made to explain the observed phenomena analytically. This paper examines, in the context of graph colouring, some aspects of the role of the tabu list in GSAT. Two slightly different SAT formulations of graph colouring are considered. Three classes of graphs are defined that have the interesting property that, for certain initial partial colourings of the nodes, a proper colouring cannot be achieved by GSAT without the use of a tabu list. The minimum length of the tabu list that is necessary for solving the problem is determined for each class. It is found that this length varies considerably from case to case, and is sometimes quite large. We study experimentally the variation of runtime with the length of the tabu list to verify and further explore the theoretical results. We examine the general performance of other local search SAT methods like WalkSAT, Novelty, RNovelty, Novelty+ and RNovelty+ on these classes of graphs and to make a comparative assessment of all these methods.
A local search heuristic for chromatic sum
, 2011
"... A coloring of an undirected graph is a labelling of the vertices in the graph such that no two adjacent vertices receive the same label. The sum coloring problem asks to find a coloring, using natural numbers as labels, such that the total sum of the colors used is minimized. We design and test a lo ..."
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Cited by 3 (0 self)
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A coloring of an undirected graph is a labelling of the vertices in the graph such that no two adjacent vertices receive the same label. The sum coloring problem asks to find a coloring, using natural numbers as labels, such that the total sum of the colors used is minimized. We design and test a local search algorithm, based on variable neighborhood search and iterated local search, that outperforms in several instances the currently existing benchmarks on this problem.
Very Large-Scale Neighborhood Search: Overview and Case Studies on Coloring Problems
, 2008
"... Two key issues in local search algorithms are the definition of a neighborhood and the way to examine it. In this chapter we consider techniques for examining very large neighborhoods, in particular, ways for exactly searching them. We first illustrate such techniques using three paradigmatic examp ..."
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Cited by 2 (1 self)
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Two key issues in local search algorithms are the definition of a neighborhood and the way to examine it. In this chapter we consider techniques for examining very large neighborhoods, in particular, ways for exactly searching them. We first illustrate such techniques using three paradigmatic examples. In the largest part of the chapter, we focus on the development and experimental study of very largescale neighborhood search algorithms for two coloring problems. The first example concerns the well-known (vertex) graph coloring problem. Despite initial promising results on the use of very large-scale neighborhoods, our final conclusion was negative: the usage of the proposed very large-scale neighborhoods did not help to improve the performance of effective stochastic local search algorithms. The second example, the graph set T-coloring problem, yielded more positive results. In this case, a very large-scale neighborhood that was specially tailored for this problem and that can be efficiently searched, resulted to be an essential component of a new state-of-the-art algorithm for various instance classes.
Improving the Extraction and Expansion Method for Large Graph Coloring
, 2012
"... Graph coloring is one of the most studied combinatorial optimization problems. This paper presents an improved extraction and expansion method (IE 2 COL) initially introduced in [47]. IE 2 COL employs a forward independent set extraction strategy to reduce the initial graph G. From the reduced graph ..."
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Cited by 1 (0 self)
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Graph coloring is one of the most studied combinatorial optimization problems. This paper presents an improved extraction and expansion method (IE 2 COL) initially introduced in [47]. IE 2 COL employs a forward independent set extraction strategy to reduce the initial graph G. From the reduced graph, IE 2 COL triggers a backward coloring process which uses extracted independent sets as new color classes for intermediate subgraph coloring. The proposed method is assessed on 20 large benchmark graphs with 900 to 4000 vertices. Computational results show that it provides new upper bounds for 6 graphs and matches consistently the current best known results for 12 other graphs.
Reinforced Tabu Search for Graph Coloring
, 2007
"... Tabu search (TS) [21] was first applied to graph coloring by Hertz and de Werra in 1987 [23]. Even today, the original Tabucol algorithm as well as its variants are among the best reference algorithms for general graph coloring. In this paper, we describe a Reinforced TS (RTS) coloring algorithm and ..."
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Cited by 1 (1 self)
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Tabu search (TS) [21] was first applied to graph coloring by Hertz and de Werra in 1987 [23]. Even today, the original Tabucol algorithm as well as its variants are among the best reference algorithms for general graph coloring. In this paper, we describe a Reinforced TS (RTS) coloring algorithm and show improved results on the well-established Dimacs challenge graphs. The improvement is essentially achieved by employing more informative evaluation functions as well as an adaptive technique for tuning the tabu list. We show that RTS can equal the best-known results for many of the Dimacs graphs while remaining quite simple. 1
