New Order-Based Crossovers for the Graph Coloring Problem

Mumford, Christine L.

doi:10.1007/11844297_89

Cited by 22 publications

(20 citation statements)

References 13 publications

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“…Experiments with crossover operators have been omitted from the present study. Although successful order-based crossovers (POP and MIS) for the related graph coloring problem (Mumford 2006) have been developed by the present author, and one of them (POP) used for multiobjective timetabling in Mumford (2007), further tests failed to demonstrate their effectiveness in the present context. The first set of experiments involve the use of grouping and reordering heuristics as described in Sect.…”

Section: The Greedy Algorithms In a Multiobjective Frameworkmentioning

confidence: 65%

“…Focusing their attention on sorting and reordering whole color classes (i.e., groups of nodes assigned the same color), these techniques are capable of producing excellent results. Previous studies by the present author have used the CL heuristics as a preprocessor for new order-based crossovers (i.e., crossovers that work on orderings of exams) for an evolutionary algorithm, as well as for local search operators in their own right (Mumford 2006(Mumford , 2007. Of particular significance to this type of work is a rare property of the CL heuristics, which we shall call the 'non-deterioration' property:…”

Section: The Grouping and Reordering Heuristicsmentioning

confidence: 97%

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A multiobjective framework for heavily constrained examination timetabling problems

Mumford

2008

Ann Oper Res

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University examination timetabling is a challenging set partitioning problem that comes in many variations, and real world applications usually carry multiple constraints and require the simultaneous optimization of several (often conflicting) objectives. This paper presents a multiobjective framework capable of solving heavily constrained timetabling problems. In this prototype study, we focus on the two objectives: minimizing timetable length while simultaneously optimizing the spread of examinations for individual students. Candidate solutions are presented to a multiobjective memetic algorithm as orderings of examinations, and a greedy algorithm is used to construct violation free timetables from permutation sequences of exams. The role of the multiobjective algorithm is to iteratively improve a population of orderings, with respect to the given objectives, using various mutation and reordering heuristics.

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Section: The Greedy Algorithms In a Multiobjective Frameworkmentioning

confidence: 65%

Section: The Grouping and Reordering Heuristicsmentioning

confidence: 97%

A multiobjective framework for heavily constrained examination timetabling problems

Mumford

2008

Ann Oper Res

Self Cite

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“…These ids are assigned either based on the group cardinality or based on the lowest index in each group [40]. In [36], a similar method is proposed where again an order based crossover is utilized and some competent results are obtained on a few benchmark instances.…”

Section: Gas and Graph Coloringmentioning

confidence: 99%

Multi-objective Genetic Algorithms for grouping problems

Korkmaz

2008

Appl Intell

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Linear Linkage Encoding (LLE) is a convenient representational scheme for Genetic Algorithms (GAs). LLE can be used when a GA is applied to a grouping problem and this representation does not suffer from the redundancy problem that exists in classical encoding schemes. LLE has been mainly used in data clustering. One-point crossover has been utilized in these applications. In fact, the standard recombination operators are not suitable to be used with LLE. These operators can easily disturb the building blocks and cannot fully exploit the power of the representation. In this study, a new crossover operator is introduced for LLE. The operator which is named as group-crossover is tested on the data clustering problem and a very significant performance increase is obtained compared to classical one-point and uniform crossover operations. Graph coloring is the second domain where the proposed framework is tested. This is a challenging combinatorial optimization problem for search methods and no significant success has been obtained on the problem with pure GA. The experimental results denote that GAs powered with LLE can provide satisfactory outcomes in this domain, too.

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“…A permutation indicates an order of vertices that can be decoded into an actual coloring by greedily assigning colors one by one in this order. Since indirect encodings lie outside the scope of this chapter, we refer the reader to [52] for interesting recombination issues in this context. However, according to [16,19], both early uniform crossovers failed to make the evolutionary search reach significantly better results that local search.…”

Section: Specialized Recombination Operatorsmentioning

confidence: 99%

Recent Advances in Graph Vertex Coloring

Galinier

Hamiez

Hao

et al. 2013

Handbook of Optimization

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Graph vertex coloring is one of the most studied NP-hard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, population-based approaches and hybrid methods. The research in graph coloring heuristics is very active and improved results have been obtained recently, notably for coloring large and very large graphs. This chapter surveys and analyzes graph coloring heuristics with a focus on the most recent advances.

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New Order-Based Crossovers for the Graph Coloring Problem

Cited by 22 publications

References 13 publications

A multiobjective framework for heavily constrained examination timetabling problems

A multiobjective framework for heavily constrained examination timetabling problems

Multi-objective Genetic Algorithms for grouping problems

Recent Advances in Graph Vertex Coloring

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