Frequency Fitness Assignment

Metaheuristic optimization procedures such as evolutionary algorithms are usually driven by an objective function that rates the quality of a candidate solution. However, it is not clear in practice whether an objective function adequately rewards intermediate solutions on the path to the global optimum and it may exhibit deceptiveness, epistasis, neutrality, ruggedness, and a lack of causality. In this paper, we introduce the frequency fitness H, subject to minimization, which rates how often solutions with the same objective value have been discovered so far. The ideas behind this method are that good solutions are difficult to find and that if an algorithm gets stuck at a local optimum, the frequency of the objective values of the surrounding solutions will increase over time, which will eventually allow it to leave that region again. We substitute a frequency fitness assignment process (FFA) for the objective function into several different optimization algorithms. We conduct a comprehensive set of experiments: the synthesis of algorithms with genetic programming (GP), the solution of MAX-3SAT problems with genetic algorithms, classification with Memetic Genetic Programming, and numerical optimization with a (1+1) Evolution Strategy, to verify the utility of FFA. Given that they have no access to the original objective function at all, it is surprising that for some problems (e.g., the algorithm synthesis task) the FFA-based algorithm variants perform significantly better. However, this cannot be guaranteed for all tested problems. Thus, we also analyze scenarios where algorithms using FFA do not perform better or perform even worse than with the original objective functions.

[1]  Thomas Weise,et al.  Global Optimization Algorithms -- Theory and Application , 2009 .

[2]  Shengxiang Yang,et al.  Evolutionary Computation in Dynamic and Uncertain Environments (Studies in Computational Intelligence) , 2007 .

[3]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[4]  L. Darrell Whitley,et al.  Genetic Algorithm Behavior in the MAXSAT Domain , 1998, PPSN.

[5]  Anne Auger,et al.  Benchmarking the (1+1) evolution strategy with one-fifth success rule on the BBOB-2009 function testbed , 2009, GECCO '09.

[6]  Xin Yao,et al.  A Memetic Genetic Programming with decision tree-based local search for classification problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[7]  Shengxiang Yang,et al.  Evolutionary Computation in Dynamic and Uncertain Environments , 2007, Studies in Computational Intelligence.

[8]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[9]  Zbigniew Michalewicz,et al.  Benchmarking Optimization Algorithms: An Open Source Framework for the Traveling Salesman Problem , 2014, IEEE Computational Intelligence Magazine.

[10]  Raymond Chiong,et al.  A Framework for Multi-model EDAs with Model Recombination , 2011, EvoApplications.

[11]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[12]  Faustino J. Gomez,et al.  Novelty-based restarts for evolution strategies , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[13]  Alain Hertz,et al.  A TUTORIAL ON TABU SEARCH , 1992 .

[14]  Alain Pétrowski,et al.  A clearing procedure as a niching method for genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[15]  Shane Legg,et al.  Fitness uniform deletion: a simple way to preserve diversity , 2005, GECCO '05.

[16]  Guido D. Salvucci,et al.  Ieee standard for binary floating-point arithmetic , 1985 .

[17]  Ludmila I. Kuncheva,et al.  Measures of Diversity in Classifier Ensembles and Their Relationship with the Ensemble Accuracy , 2003, Machine Learning.

[18]  Kenneth O. Stanley,et al.  Exploiting Open-Endedness to Solve Problems Through the Search for Novelty , 2008, ALIFE.

[19]  Shane Legg,et al.  Fitness uniform optimization , 2006, IEEE Transactions on Evolutionary Computation.

[20]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[21]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[22]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[23]  Ke Tang,et al.  Novel Loop Structures and the Evolution of Mathematical Algorithms , 2011, EuroGP.

[24]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

[25]  Raymond Chiong,et al.  Evolutionary Optimization: Pitfalls and Booby Traps , 2012, Journal of Computer Science and Technology.

[26]  Kurt Geihs,et al.  Rule-based Genetic Programming , 2007, 2007 2nd Bio-Inspired Models of Network, Information and Computing Systems.

[27]  Kenneth O. Stanley,et al.  Evolving a diversity of virtual creatures through novelty search and local competition , 2011, GECCO '11.

[28]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[29]  Kenneth O. Stanley,et al.  Abandoning Objectives: Evolution Through the Search for Novelty Alone , 2011, Evolutionary Computation.

[30]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[31]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[32]  Jean-Baptiste Mouret Novelty-Based Multiobjectivization , 2011 .

[33]  Shane Legg,et al.  Tournament versus fitness uniform selection , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[34]  Thomas Weise,et al.  Evolving Distributed Algorithms With Genetic Programming , 2012, IEEE Transactions on Evolutionary Computation.

[35]  Thomas Stützle,et al.  SATLIB: An Online Resource for Research on SAT , 2000 .

[36]  Marcus Hutter,et al.  Fitness uniform selection to preserve genetic diversity , 2001, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[37]  Zbigniew Michalewicz,et al.  Evolutionary Optimization , 2012, Variants of Evolutionary Algorithms for Real-World Applications.

[38]  Xin Yao,et al.  Evolving exact integer algorithms with Genetic Programming , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[39]  Fred W. Glover,et al.  A user's guide to tabu search , 1993, Ann. Oper. Res..

[40]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.