Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Silva, Sara; Dignum, Stephen; Vanneschi, Leonardo

doi:10.1007/s10710-011-9150-5

Cited by 60 publications

(32 citation statements)

References 84 publications

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“…Therefore, selection will favor larger trees, causing an increase in the average size of trees within the population, effectively bootstrapping the bloating effect. This theory seems very promising, and experimental data supports it [32]. Moreover, powerful bloat control methods have been developed based on CBT, namely operator equalisation [32].…”

Section: Recent Advances In Bloatmentioning

confidence: 96%

“…This theory seems very promising, and experimental data supports it [32]. Moreover, powerful bloat control methods have been developed based on CBT, namely operator equalisation [32]. However, recent studies have made the matter significantly less clear.…”

Section: Recent Advances In Bloatmentioning

confidence: 96%

“…This work revisits another bloat theory, which can be called the fitness-causesbloat theory (FCBT), developed by Langdon and Poli [13,14]. The main arguments of FCBT proceed as follows [13,14,32]. For a variable length GP representation (such as a tree based GP) many genotypically different programs, of different sizes, can produce the same outputs on a given set of fitness cases.…”

Section: Recent Advances In Bloatmentioning

confidence: 99%

“…Stated more precisely, bloat is excessive code growth within the individuals of the evolving population without a proportional improvement in fitness. Over the years, many bloat theories have been developed and many bloat control methods have been proposed [31,32]. One of the most promising attempts at explaining the bloat phenomenon is the crossover bias theory [5,28], that has lead to a powerful bloat control method called operator equalisation [32].…”

Section: Introductionmentioning

confidence: 99%

“…Over the years, many bloat theories have been developed and many bloat control methods have been proposed [31,32]. One of the most promising attempts at explaining the bloat phenomenon is the crossover bias theory [5,28], that has lead to a powerful bloat control method called operator equalisation [32]. However, recent experimental results have blurred what is understood regarding the causes of bloat [29], as well as what are the best strategies that can be used to eliminate it from GP runs [7,29].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Trujillo

Naredo

Martínez

2013

EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation IV

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Abstract. Bloat is one of the most interesting theoretical problems in genetic programming (GP), and one of the most important pragmatic limitations in the development of real-world GP solutions. Over the years, many theories regarding the causes of bloat have been proposed and a variety of bloat control methods have been developed. It seems that one of the underlying causes of bloat is the search for fitness; as the fitness-causes-bloat theory states, selective bias towards fitness seems to unavoidably lead the search towards programs with a large size. Intuitively, however, abandoning fitness does not appear to be an option. This paper, studies a GP system that does not require an explicit fitness function, instead it relies on behavior-based search, where programs are described by the behavior they exhibit and selective pressure is biased towards unique behaviors using the novelty search algorithm. Initial results are encouraging, the average program size of the evolving population does not increase with novelty search; i.e., bloat is avoided by focusing on novelty instead of quality.

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Section: Recent Advances In Bloatmentioning

confidence: 96%

Section: Recent Advances In Bloatmentioning

confidence: 96%

Section: Recent Advances In Bloatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Trujillo

Naredo

Martínez

2013

EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation IV

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Time Control or Size Control? Reducing Complexity and Improving Accuracy of Genetic Programming Models

Sambo

Azad

Kovalchuk

et al. 2020

Lecture Notes in Computer Science

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Complexity of evolving models in genetic programming (GP) can impact both the quality of the models and the evolutionary search. While previous studies have proposed several notions of GP model complexity, the size of a GP model is by far the most researched measure of model complexity. However, previous studies have also shown that controlling the size does not automatically improve the accuracy of GP models, especially the accuracy on out of sample (test) data. Furthermore, size does not represent the functional composition of a model, which is often related to its accuracy on test data. In this study, we explore the evaluation time of GP models as a measure of their complexity; we define the evaluation time as the time taken to evaluate a model over some data. We demonstrate that the evaluation time reflects both a model's size and its composition; also, we show how to measure the evaluation time reliably. To validate our proposal, we leverage four well-known methods to size-control but to control evaluation times instead of the tree sizes; we thus compare size-control with time-control. The results show that time-control with a nuanced notion of complexity produces more accurate models on 17 out of 20 problem scenarios. Even when the models have slightly greater times and sizes, time-control counterbalances via superior accuracy on both training and test data. The paper also argues that time-control can differentiate functional complexity even better in an identically-sized population. To facilitate this, the paper proposes Fixed Length Initialisation (FLI) that creates an identically-sized but functionally-diverse population. The results show that while FLI particularly suits time-control, it also generally improves the performance of size-control. Overall, the paper poses evaluation-time as a viable alternative to tree sizes to measure complexity in GP.

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Learning a Formula of Interpretability to Learn Interpretable Formulas

Virgolin

Lorenzo

Medvet

et al. 2020

Parallel Problem Solving From Nature – PPSN XVI

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Many risk-sensitive applications require Machine Learning (ML) models to be interpretable. Attempts to obtain interpretable models typically rely on tuning, by trial-and-error, hyper-parameters of model complexity that are only loosely related to interpretability. We show that it is instead possible to take a meta-learning approach: an ML model of non-trivial Proxies of Human Interpretability (PHIs) can be learned from human feedback, then this model can be incorporated within an ML training process to directly optimize for interpretability. We show this for evolutionary symbolic regression. We first design and distribute a survey finalized at finding a link between features of mathematical formulas and two established PHIs, simulatability and decomposability. Next, we use the resulting dataset to learn an ML model of interpretability. Lastly, we query this model to estimate the interpretability of evolving solutions within bi-objective genetic programming. We perform experiments on five synthetic and eight real-world symbolic regression problems, comparing to the traditional use of solution size minimization. The results show that the use of our model leads to formulas that are, for a same level of accuracy-interpretability trade-off, either significantly more or equally accurate. Moreover, the formulas are also arguably more interpretable. Given the very positive results, we believe that our approach represents an important stepping stone for the design of next-generation interpretable (evolutionary) ML algorithms.

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Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Cited by 60 publications

References 84 publications

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Preliminary Study of Bloat in Genetic Programming with Behavior-Based Search

Time Control or Size Control? Reducing Complexity and Improving Accuracy of Genetic Programming Models

Learning a Formula of Interpretability to Learn Interpretable Formulas

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