Atif Rafiq
ABSTRACT
Symbolic Regression is sometimes treated as a multi-objective optimization problem where two objectives (Accuracy and Complexity) are optimized simultaneously. In this paper, we propose a novel approach, Hierarchical Multi-objective Symbolic Regression (HMS), where we investigate the effect of imposing a hierarchy on multiple objectives in Symbolic Regression. HMS works in two levels. In the first level, an initial random population is evolved using a single objective (Accuracy), then, when a simple trigger occurs (the current best fitness is five times better than best fitness of the initial, random population) half of the population is promoted to the next level where another objective (complexity) is incorporated. This new, smaller, population subsequently evolves using a multi-objective fitness function. Various complexity measures are tested and as such are explicitly defined as one of the objectives in addition to performance (accuracy). The validation of HMS is performed on four benchmark Symbolic Regression problems with varying difficulty. The evolved Symbolic Regression models are either competitive with or better than models produced with standard approaches in terms of performance where performance is the accuracy measured as Root Mean Square Error. The solutions are better in terms of size, effectively scaling down the computational cost.
- Bogdan Burlacu, Gabriel Kronberger, Michael Kommenda, and Michael Affenzeller. 2019. Parsimony measures in multi-objective genetic programming for symbolic regression. In Proceedings of the Genetic and Evolutionary Computation Conference Companion. 338--339.Google Scholar
Digital Library
- Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and TAMT Meyarivan. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation 6, 2 (2002), 182--197.Google Scholar
- Stephen Dignum and Riccardo Poli. 2008. Operator equalisation and bloat free GP. In European Conference on Genetic Programming. Springer, 110--121.Google ScholarCross Ref
- Michael Kommenda, Andreas Beham, Michael Affenzeller, and Gabriel Kronberger. 2015. Complexity measures for multi-objective symbolic regression. In International Conference on Computer Aided Systems Theory. Springer, 409--416.Google ScholarCross Ref
- Michael Kommenda, Gabriel Kronberger, Michael Affenzeller, Stephan M Winkler, and Bogdan Burlacu. 2016. Evolving simple symbolic regression models by multi-objective genetic programming. In Genetic Programming Theory and Practice XIII. Springer, 1--19.Google Scholar
- John R Koza and John R Koza. 1992. Genetic programming: on the programming of computers by means of natural selection. Vol. 1. MIT press.Google ScholarDigital Library
- Sean Luke. 2000. Issues in scaling genetic programming: breeding strategies, tree generation, and code bloat. Ph.D. Dissertation. University of Maryland, College Park.Google Scholar
- Sean Luke and Liviu Panait. 2002. Lexicographic parsimony pressure. In Proceedings of the 4th Annual Conference on Genetic and Evolutionary Computation. 829--836.Google ScholarDigital Library
- James McDermott, David R White, Sean Luke, Luca Manzoni, Mauro Castelli, Leonardo Vanneschi, Wojciech Jaskowski, Krzysztof Krawiec, Robin Harper, Kenneth De Jong, et al. 2012. Genetic programming needs better benchmarks. In Proceedings of the 14th annual conference on Genetic and evolutionary computation. 791--798.Google ScholarDigital Library
- Riccardo Poli. 2011. Covariant tarpeian method for bloat control in genetic programming. In Genetic Programming Theory and Practice VIII. Springer, 71--89.Google Scholar
- Atif Rafiq, Meghana Kshirsagar, Enrique Naredo, and Conor Ryan. 2021. Pyramid-Z: Evolving Hierarchical Specialists in Genetic Algorithms. In 13th International Conference on Evolutionary Computation and Applications (ECTA). IEEE.Google Scholar
- Conor Ryan, Atif Rafiq, and Enrique Naredo. 2020. Pyramid: A Hierarchical Approach to Scaling Down Population Size in Genetic Algorithms. In 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, 1--8.Google ScholarDigital Library
- Sara Silva and Ernesto Costa. 2009. Dynamic limits for bloat control in genetic programming and a review of past and current bloat theories. Genetic Programming and Evolvable Machines 10, 2 (2009), 141--179.Google ScholarDigital Library
- Guido F Smits and Mark Kotanchek. 2005. Pareto-front exploitation in symbolic regression. In Genetic programming theory and practice II. Springer, 283--299.Google Scholar
- David R White, James McDermott, Mauro Castelli, Luca Manzoni, Brian W Goldman, Gabriel Kronberger, Wojciech Jaśkowski, Una-May O'Reilly, and Sean Luke. 2013. Better GP benchmarks: community survey results and proposals. Genetic Programming and Evolvable Machines 14, 1 (2013), 3--29.Google ScholarDigital Library
Index Terms
- On the effect of embedding hierarchy within multi-objective optimization for evolving symbolic regression models
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