Neutral Fitness Landscape in the Cellular Automata Majority Problem

Vérel, Sebástien; Collard, Philippe; Tomassini, Marco; Vanneschi, Leonardo

doi:10.1007/11861201_31

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…The question of "what makes a fitness landscape hard" continues Forrest and Mitchell (1993); Jones and Forrest (1995), and new methods of capturing the hardness of the problems are proposed, like algebraic properties of the solutions in the landscape Grover (1992); Stadler (1995), modality (number of local optima) Horn and Goldberg (1995) and the fractal dimension of the fitness landscape Hoshino et al (1998). Some researchers try to explain when a problem becomes hard, by studying the area in the landscape called "Olympus", in which the better local optima are located Verel et al (2007); Vérel et al (2008). Fitness cloud is another method proposed to visualise the fitness landscape which tries to represent some properties of the fitness landscape Collard et al (2007); Lu et al (2011);Vanneschi et al (2007), reflecting the problem hardness.…”

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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“…Problems such as these that present an algorithm with misleading information are known as deceptive problems and many studies on problem hardness have focussed on deception as the main determining factor [5,18,19,27]. Neutrality is yet another factor that can have an influence on problem difficulty [59,60,63,55,41]. This phenomenon is illustrated in Figure 4.5d, where there is a lack of information around the candidate solution x for guiding search towards the global optimum.…”

Section: What Makes An Optimisation Problem Hard?mentioning

confidence: 94%

Fitness Landscape Analysis for Metaheuristic Performance Prediction

Malan

Engelbrecht

2014

Emergence, Complexity and Computation

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Abstract. Metaheuristics have become popular for solving complex optimisation problems where classical techniques are either infeasible or perform poorly. Despite many success stories, it is well known that metaheuristics sometimes fail and that researchers and practitioners frequently resort to trial and error to find an appropriate algorithm or setting to solve a given problem. Within the framework of the general algorithm selection problem, this chapter addresses the feasibility of predicting algorithm performance on unknown real-valued problems based on fitness landscape features. Normalized metrics are proposed for quantifying algorithm performance on known problems to generate suitable training data. Performance metrics are tested using a standard particle swarm optimisation algorithm and are investigated alongside three existing fitness landscape measures. This preliminary investigation highlights the need for a shift in focus away from predicting general problem hardness towards characterising problems where each fitness landscape technique has value as a part-predictor of algorithm performance.

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“…Algebraic properties of the solutions in the landscape [16], [25], modality (number of local optima) [26] and the fractal dimension of the fitness landscape [27] are other examples. Some researchers try to explain when a problem becomes hard, by studying the area in the landscape called "Olympus", in which the better local optima are located [28], [29]. Fitness clouds is another method proposed to visualise the fitness landscape, which tries to represent some properties of the fitness landscape [30], [31], [32], reflecting the problem hardness.…”

Section: A Previous Literaturementioning

confidence: 99%

On the Landscape of Combinatorial Optimization Problems

Tayarani-N.

Prügel-Bennett

2014

IEEE Trans. Evol. Computat.

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Abstract-This paper carries out a comparison of the fitness landscape for four classic optimisation problems: Max-Sat, Graph-Colouring, Travelling Salesman and Quadratic Assignment. We have focused on two types of properties, local average properties of the landscape and properties of the local optima. For the local optima we give a fairly comprehensive description of the properties, including the expected time to reach a local optimum, the number of local optima at different cost levels, the distance between optima, and the expected probability of reaching the optima. Principle component analysis is used to understand the correlations between the local optima. Most of the properties we examine have not be studied previously, particularly those concerned with properties of the local optima. We compare and contrast the behaviour of the four different problems. Although, the problems are very different at the low level, many of the long-range properties exhibit a remarkable degree of similarity.

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Neutral Fitness Landscape in the Cellular Automata Majority Problem

Cited by 3 publications

References 14 publications

An Analysis of the Fitness Landscape of Travelling Salesman Problem

An Analysis of the Fitness Landscape of Travelling Salesman Problem

Fitness Landscape Analysis for Metaheuristic Performance Prediction

On the Landscape of Combinatorial Optimization Problems

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