The k-coloring fitness landscape

Bouziri, Hend; Mellouli, Khaled; Talbi, El‐Ghazali

doi:10.1007/s10878-009-9249-2

Cited by 17 publications

(8 citation statements)

References 4 publications

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“…In a more recent work, the landscape analysis is used to propose a new population based algorithm Qasem and Prügel-Bennett (2010). The landscape of many other problems have been studied, including the landscape of graph drawing Lehn and Kuntz (2001), graphcolouring Hertz et al (1994); Bouziri et al (2011); Tayarani and Prügel Bennett (2014), antenna design Alander et al (2002), maximum satisfiability Prügel-Bennett and Tayarani-N. (2011), flow-shop scheduling Czogalla and Fink (2011) and Bayesian network structure Wu et al (2011) problems.…”

Section: Previous Landscape Analysismentioning

confidence: 99%

An Analysis of the Fitness Landscape of Travelling Salesman Problem

Tayarani-N.

Prügel-Bennett

2016

Evolutionary Computation

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The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.

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Section: Previous Landscape Analysismentioning

confidence: 99%

An Analysis of the Fitness Landscape of Travelling Salesman Problem

Tayarani-N.

Prügel-Bennett

2016

Evolutionary Computation

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“…These have been studied elsewhere (e.g. [6]) and we include them here more for the sake of completeness, than because of their interest. We also give formulae for the cumulants, which, as far as we know, have not been given elsewhere.…”

Section: Density Of Configurationsmentioning

confidence: 99%

“…The frozen set is a particular set of vertices that in every globally optimal configuration of the problem has the same colour class. Bouziri et al [6] study the statistical properties of some benchmark graph-colouring problems. There are several properties of the fitness landscape that can be studied, such as the distribution of the fitness function, the number and distribution of local optima, the structure of the basins of attraction, the presence and structure of neutral networks, correlation between the quality of a solution and its distance to a local or global optimum and landscape ruggedness.…”

Section: Introductionmentioning

confidence: 99%

Anatomy of the fitness landscape for dense graph-colouring problem

Tayarani-N.

Prügel-Bennett

2015

Swarm and Evolutionary Computation

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“…In that work, the authors already stated that basins of attraction seem to be highly intertwined, giving a canyon-like structure to the landscape, rather than a crater-like structure. Nevertheless, this finding was ignored by those works referring to it (Stützle, 2006;Preux and Talbi, 1999;Angel and Zissimopoulos, 2002;Bouziri et al, 2009). For instance, seven years after that publication, the author in Stützle (2006) contradicted it: Intuitively, the search landscape can be imagined as a (multi-dimensional) mountainous region with hills, craters, and valleys.…”

Section: Introductionmentioning

confidence: 99%

Anatomy of the Attraction Basins: Breaking with the Intuition

Hernando

Mendiburu

Lozano

2019

Evolutionary Computation

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Solving combinatorial optimization problems efficiently requires the development of algorithms that consider the specific properties of the problems. In this sense, local search algorithms are designed over a neighborhood structure that partially accounts for these properties. Considering a neighborhood, the space is usually interpreted as a natural landscape, with valleys and mountains. Under this perception, it is commonly believed that, if maximizing, the solutions located in the slopes of the same mountain belong to the same attraction basin, with the peaks of the mountains being the local optima. Unfortunately, this is a widespread erroneous visualization of a combinatorial landscape. Thus, our aim is to clarify this aspect, providing a detailed analysis of, first, the existence of plateaus where the local optima are involved, and second, the properties that define the topology of the attraction basins, picturing a reliable visualization of the landscapes. Some of the features explored in this article have never been examined before. Hence, new findings about the structure of the attraction basins are shown. The study is focused on instances of permutation-based combinatorial optimization problems considering the 2-exchange and the insert neighborhoods. As a consequence of this work, we break away from the extended belief about the anatomy of attraction basins.

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The k-coloring fitness landscape

Cited by 17 publications

References 4 publications

An Analysis of the Fitness Landscape of Travelling Salesman Problem

An Analysis of the Fitness Landscape of Travelling Salesman Problem

Anatomy of the fitness landscape for dense graph-colouring problem

Anatomy of the Attraction Basins: Breaking with the Intuition

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