What Makes a Problem Hard for a Genetic Algorithm? Some Anomalous Results and Their Explanation
Machine Learning - Special issue on genetic algorithms
The evolution of evolvability in genetic programming
Advances in genetic programming
The royal tree problem, a benchmark for single and multiple population genetic programming
Advances in genetic programming
Fitness landscapes and evolvability
Evolutionary Computation
Evolutionary Computation
Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms
Proceedings of the 6th International Conference on Genetic Algorithms
A Study of Fitness Distance Correlation as a Difficulty Measure in Genetic Programming
Evolutionary Computation
Strong recombination, weak selection, and mutation
Proceedings of the 8th annual conference on Genetic and evolutionary computation
An adverse interaction between crossover and restricted tree depth in genetic programming
GECCO '96 Proceedings of the 1st annual conference on Genetic and evolutionary computation
Negative slope coefficient: a measure to characterize genetic programming fitness landscapes
EuroGP'06 Proceedings of the 9th European conference on Genetic Programming
Large Barrier Trees for Studying Search
IEEE Transactions on Evolutionary Computation
Evolving team behaviours in environments of varying difficulty
Artificial Intelligence Review
NK Landscapes Difficulty and Negative Slope Coefficient: How Sampling Influences the Results
EvoWorkshops '09 Proceedings of the EvoWorkshops 2009 on Applications of Evolutionary Computing: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoGAMES, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, EvoNUM, EvoSTOC, EvoTRANSLOG
Dealings with problem hardness in genetic algorithms
WSEAS Transactions on Computers
The new negative slope coefficient measure
EC'09 Proceedings of the 10th WSEAS international conference on evolutionary computing
Limitations of the fitness-proportional negative slope coefficient as a difficulty measure
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
A study of some implications of the no free lunch theorem
Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
Negative slope coefficient and the difficulty of random 3-SAT instances
Evo'08 Proceedings of the 2008 conference on Applications of evolutionary computing
Open issues in genetic programming
Genetic Programming and Evolvable Machines
Practical performance models of algorithms in evolutionary program induction and other domains
Artificial Intelligence
A fine-grained view of GP locality with binary decision diagrams as ant phenotypes
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Predicting problem difficulty for genetic programming applied to data classification
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Estimating classifier performance with genetic programming
EuroGP'11 Proceedings of the 14th European conference on Genetic programming
Defining locality as a problem difficulty measure in genetic programming
Genetic Programming and Evolvable Machines
A study of the neutrality of Boolean function landscapes in genetic programming
Theoretical Computer Science
An empirical tool for analysing the collective behaviour of population-based algorithms
EvoApplications'12 Proceedings of the 2012t European conference on Applications of Evolutionary Computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
A survey of techniques for characterising fitness landscapes and some possible ways forward
Information Sciences: an International Journal
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The Negative Slope Coefficient (nsc) is an empirical measure of problem hardness based on the analysis of offspring-fitness vs. parent-fitness scatterplots. The nsc has been tested empirically on a large variety problems showing considerable reliability in distinguishing easy from hard problems. However, neither a theoretical justification nor a theoretical analysis of the nsc have ever been given. This paper presents a modification of nsc, the fitness-proportional negative slope coefficient (fpncs), for which it is possible to give a theoretical explanation and analysis. To illustrate the approach we compute fpnsc theoretically for the class of invertible functions of unitation, and for two mutation operators. We apply the theory to compute fpnsc for three benchmark functions: Onemax, Trap and Onemix. We then compare the predictions of fpnsc with the success probability recorded in actual runs. The results suggest that fpnsc is able to broadly discriminate between easy and hard GA problems.