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Being able to predict the human oral bioavailability for a potential new drug is extremely important for the drug discovery process. This problem has been addressed by several prediction tools, with Genetic Programming providing some of the best results ever achieved. In this paper we use the newest developments of Genetic Programming, in particular the latest bloat control method, Operator Equalisation, to find out how much improvement we can achieve on this problem. We show examples of some actual solutions and discuss their quality, comparing them with previously published results. We identify some unexpected behaviours related to overfitting, and discuss the way for further improving the practical usage of the Genetic Programming approach. Copyright © 2012 Inderscience Enterprises Ltd.

In the first part of the chapter, evolutionary algorithms are briefly described, especially genetic algorithms and genetic programming, with sufficient detail so as to prepare the ground for the second part. The latter presents in more detail two specific applications. The first is about an important financial problem: the portfolio allocation problem. The second one deals with a biochemical problem related to drug design and efficacy. © 2008, IGI Global.

This work introduces a new technique for features construction in classification problems by means of multi objective genetic programming (MOGP). The final goal is to improve the generalization ability of the final classifier. MOGP can help in finding solutions with a better generalization ability with respect to standard genetic programming as stated in [1]. The main issue is the choice of the criteria that must be optimized by MOGP. In this work the construction of new features is guided by two criteria: the first one is the entropy of the target classes as in [7] while the second is inspired by the concept of margin used in support vector machines. © Springer-Verlag Berlin Heidelberg 2011

We present a new reverse-engineering framework for gene regulatory network reconstruction. It works on temporal series of gene activation data and, using genetic programming, it extracts the activation functions of the different genes from those data. Successively, the gene regulatory network is reconstructed exploiting the automatic feature selection performed by genetic programming and its dynamics can be simulated using the previously extracted activation functions. The framework was tested on the well-known IRMA gene regulatory network, a simple network composed by five genes in the yeast Saccharomyces cerevisiae, defined in 2009 as a simplified biological model to benchmark reverse-engineering approaches. We show that the performances of the proposed framework on this benchmark network are encouraging.

Background The ability to accurately classify cancer patients into risk classes, i.e. to predict the outcome of the pathology on an individual basis, is a key ingredient in making therapeutic decisions. In recent years gene expression data have been successfully used to complement the clinical and histological criteria traditionally used in such prediction. Many "gene expression signatures" have been developed, i.e. sets of genes whose expression values in a tumor can be used to predict the outcome of the pathology. Here we investigate the use of several machine learning techniques to classify breast cancer patients using one of such signatures, the well established 70-gene signature. Results We show that Genetic Programming performs significantly better than Support Vector Machines, Multilayered Perceptrons and Random Forests in classifying patients from the NKI breast cancer dataset, and comparably to the scoring-based method originally proposed by the authors of the 70-gene signature. Furthermore, Genetic Programming is able to perform an automatic feature selection. Conclusions Since the performance of Genetic Programming is likely to be improvable compared to the out-of-the-box approach used here, and given the biological insight potentially provided by the Genetic Programming solutions, we conclude that Genetic Programming methods are worth further investigation as a tool for cancer patient classification based on gene expression data.

In this paper a method to increase the optimization ability of genetic algorithms (GAs) is proposed. To promote population diversity, a fraction of the worst individuals of the current population is replaced by individuals from an older population. To experimentally validate the approach we have used a set of well-known benchmark problems of tunable difficulty for GAs. Standard GA with and without elitism and steady state GA have been augmented with the proposed method. The obtained results show that the algorithms augmented with the proposed method perform better than the not-augmented algorithms or have the same performances. Furthermore, the proposed method depends on two parameters: one of them regulates the size of the fraction of the population replaced and the other one decides the "age" of the population used for the replacement. Experimental results indicate that better performances have been achieved with high values of the former parameter and low values of the latter one. © 2011 Springer-Verlag

The NK landscapes are a well known benchmark for genetic algorithms (GAs) in which it is possible to tune the ruggedness of the fitness landscape by simply modifying the value of a parameter K. They have successfully been used in many theoretical studies, allowing researchers to discover interesting properties of the GAs dynamics in presence of rugged landscapes. A similar benchmark does not exist for genetic programming (GP) yet. Nevertheless, during the EuroGP conference debates of the last few years, the necessity of defining new benchmark problems for GP has repeatedly been expressed by a large part of the attendees. This paper is intended to fill this gap, by introducing an extension of the NK landscapes to tree based GP, that we call K landscapes. In this benchmark, epistasis are expressed as growing mutual interactions between the substructures of a tree as the parameter K increases. The fact that the problem becomes more and more difficult as the value of K increases is experimentally demonstrated. Interestingly, we also show that GP "bloats" more and more as K increases. Copyright 2011 ACM

The relationship between generalization and solutions functional complexity in genetic programming (GP) has been recently investigated. Three main contributions are contained in this paper: (1) a new measure of functional complexity for GP solutions, called Graph Based Complexity (GBC) is defined and we show that it has a higher correlation with GP performance on out-of-sample data than another complexity measure introduced in a recent publication. (2) A new measure is presented, called Graph Based Learning Ability (GBLA). It is inspired by the GBC and its goal is to quantify the ability of GP to learn "difficult" training points; we show that GBLA is negatively correlated with the performance of GP on out-of-sample data. (3) Finally, we use the ideas that have inspired the definition of GBC and GBLA to define a new fitness function, whose suitability is empirically demonstrated. The experimental results reported in this paper have been obtained using three real-life multidimensional regression problems.

In this paper a method to increase the optimization ability of genetic algorithms (GAs) is proposed. To promote population diversity, a fraction of the worst individuals of the current population is replaced by individuals from an older population. To experimentally validate the approach we have used a set of well-known benchmark problems of tunable difficulty for GAs, including trap functions and NK landscapes. The obtained results show that the proposed method performs better than standard GAs without elitism for all the studied test problems and better than GAs with elitism for the majority of them.

It is approximately 50 years since the first computational experiments were conducted in what has become known today as the field of Genetic Programming (GP), twenty years since John Koza named and popularised the method, and ten years since the first issue appeared of the Genetic Programming & Evolvable Machines journal. In particular, during the past two decades there has been a significant range and volume of development in the theory and application of GP, and in recent years the field has become increasingly applied. There remain a number of significant open issues despite the successful application of GP to a number of challenging real-world problem domains and progress in the develop- ment of a theory explaining the behavior and dynamics of GP. These issues must be addressed for GP to realise its full potential and to become a trusted mainstream member of the computational problem solving toolkit. In this paper we outline some of the challenges and open issues that face researchers and practitioners of GP. We hope this overview will stimulate debate, focus the direction of future research to deepen our understanding of GP, and further the development of more powerful problem solving algorithms. Science Foundation Ireland Embargo until April 2011 - AV April 2011 ke - AS 04/11/2010 ab - TS 18.11.10

The Sharpened No Free Lunch theorem states that all optimization algorithms have the same performance on sets of functions that are closed under permutation, independently of the considered performance measure. However, not all performance measures are informative on how fast or how accurately an algorithm can solve a given problem. In this paper we focus on a particular performance measure, called optimization speed, that quanti fies how fast a search algorithm is able to find an optimal solution, and we try to characterize the set of functions on which all possible search algorithms have the same optimization speed. We call fair these sets, and we prove some results about their structure, the number of such sets and the computational complexity of checking fairness.

The classification of cancer patients into risk classes is a very active field of research, with direct clinical applications. We have recently compared several machine learning methods on the well known 70-genes signature dataset. In that study, genetic programming showed promising results, given that it outperformed all the other techniques. Nevertheless, the study was preliminary, mainly because the validation dataset was preprocessed and all its features binarized in order to use logical operators for the genetic programming functional nodes. If this choice allowed simple interpretation of the solutions from the biological viewpoint, on the other hand the binarization of data was limiting, since it amounts to a sizable loss of information. The goal of this paper is to overcome this limitation, using the 70-genes signature dataset with real-valued expression data. The results we present show that genetic programming using the number of incorrectly classified instances as fitness function is not able to outperform the other machine learning methods. However, when a weighted average between false positives and false negatives is used to calculate fitness values, genetic programming obtains performances that are comparable with the other methods in the minimization of incorrectly classified instances and outperforms all the other methods in the minimization of false negatives, which is one of the main goals in breast cancer clinical applications. Also in this case, the solutions returned by genetic programming are simple, easy to understand, and they use a rather limited subset of the available features.

The goal of this paper is to present four new parallel and distributed particle swarm optimization methods and to experimentally compare their performances on a wide set of benchmark functions. These methods include a genetic algorithm whose individuals are co-evolving swarms, an "island model"-based multi-swarm system, where swarms are independent and they interact by means of particle migrations at regular time steps, and their respective variants enriched by adding a repulsive component to the particles. The benchmark functions used in our experimental study are two new sets of test functions (whose difficulty can be tuned by simply modifying the values of few real-valued parameters), the well known Rastrigin test functions, and the test functions proposed in the CEC 2005 numerical optimization competition. We show that the proposed repulsive multi-swarm system outperforms all the other presented methods. Copyright 2010 ACM.

We present a framework based on genetic algorithms to automatically generate cellular automata rules under four different asynchronous update models (fixed random sweep, random new sweep, clock and independent random ordering). We consider four different rules (18, 56, 110 and 180) with well known dynamics under synchronous update scheme. We try to reconstruct the same dynamics by means of a genetic algorithm using asynchronous update schemes. We show that in many cases it is impossible, by means of an asynchronous update scheme, to perfectly reconstruct these dynamics. Nevertheless, we show that the genetic algorithm finds the rules that more closely approximate the target behavior and the dynamics of the rules found by the genetic algorithm are rather similar to the target ones. In particular, we can always recognize a similar patter and we can also identify some differences in small details, which can be minimal (as for rule 18) or rather visible (as for rule 110). This paves the way to a deeper investigation on this track: does using asynchronous updates allow us to find more stable rules, i.e. rules that are less affected by noise, and thus do not overfit training data? This question remains open and answering it is one of the main goals of our current research.

We consider the theoretical results in GP so far and prospective areas for the future. We begin by reviewing the state of the art in genetic programming (GP) theory including: schema theories, Markov chain models, the distribution of functionality in program search spaces, the problem of bloat, the applicability of the no-free-lunch theory to GP, and how we can estimate the difficulty of problems before actually running the system. We then look at how each of these areas might develop in the next decade, considering also new possible avenues for theory, the challenges ahead and the open issues. © Springer Science+Business Media, LLC 2010.

Generalization is an important issue in machine learning. In fact, in several applications good results over training data are not as important as good results over unseen data. While this problem was deeply studied in other machine learning techniques, it has become an important issue for genetic programming only in the last few years. In this paper we compare the generalization ability of several different genetic programming frameworks, including some variants of multi-objective genetic programming and operator equalization, a recently defined bloat free genetic programming system. The test problem used is a hard regression real-life application in the field of drug discovery and development, characterized by a high number of features and where the generalization ability of the proposed solutions is a crucial issue. The results we obtained show that, at least for the considered problem, multi-optimization is effective in improving genetic programming generalization ability, outperforming all the other methods on test data. © 2010 IEEE.

Generalization is an important issue in colorimetric characterization of devices. We propose a framework based on Genetic Algorithms to select training samples from large datasets. Even though the framework is general, and can be used in principle for any dataset, we use two well known datasets as case studies: training samples are selected from the Macbeth ColorCheckerDC dataset and the trained models are tested on the Kodak Q60 photographic standard dataset. The presented experimental results show that the proposed framework has better, or at least comparable, performances than a set of other computational methods defined so far for the same goal (Hardeberg, Cheung, CIC and Schettini). Even more importantly, the proposed framework has the ability to optimize the training samples and the characterizing polynomial's coefficients at the same time. © 2010 Springer-Verlag Berlin Heidelberg.

A new variant of the Particle Swarm Optimization (PSO) algorithm is presented in this paper. It uses a well-known measure of problem hardness, the Fitness-Distance Correlation, to modify the position of the attractors for each particle, both the global one and the one which is local to it. The goal of the algorithm is to make the fitness landscape between each particle’s positions and their attractors as smooth as possible. Experimental results, obtained on 15 out of the 25 test functions belonging to the test suite used in CEC-2005 numerical optimization competition, show that this new PSO version is generally competitive, and in some cases better, than standard PSO.

Operator equalisation was recently proposed as a new bloat control technique for genetic programming. By controlling the distribution of program lengths inside the population, it can bias the search towards smaller or larger programs. In this paper we propose a new implementation of operator equalisation and compare it to a previous version, using a hard real-world regression problem where bloat and overfitting are major issues. The results show that both implementations of operator equalisation are completely bloat-free, producing smaller individuals than standard genetic programming, without compromising the generalization ability. We also show that the new implementation of operator equalisation is more efficient and exhibits a more predictable and reliable behavior than the previous version. We advance some arguable ideas regarding the relationship between bloat and overfitting, and support them with our results. Copyright 2009 ACM.

A new model of Genetic Programming with variable size population is presented in this paper and applied to the reconstruction of target functions in dynamic environments (i.e. problems where target functions change with time). The suitability of this model is tested on a set of benchmarks based on some well known symbolic regression problems. Experimental results confirm that our variable size population model finds solutions of the same quality as the ones found by standard Genetic Programming, but with a smaller amount of computational effort.

Fitness-Proportional Negative Slope Coefficient is a fitness landscapes measure that has recently been introduced as a potential indicator of problem hardness for optimisation. It is inspired to an older measure, the Negative Slope Coefficient, and it has been theoretically modelled. Preliminary experiments have suggested that it may be a good predictor of problem hardness. However, this measure has not undergone any convincing and comprehensive empirical testing. Our objective is to fill this gap. So, we perform empirical tests using a large set of invertible functions of unitation. We find that while this measure may correctly predict the degree of evolvability of a landscape, this does not necessarily correlate with the difficulty of problems. Some landscapes may show, for example, limited evolvability and yet be easy to solve because either solutions are already present in the initial population or the computational resources provided exceed evolvability obstacles. Or it may be impossible to solve them irrespective of their evolvability simply because they are far too vast for the computational resources provided. These situations are hardly captured by the Fitness-Proportional Negative Slope Coefficient.

Negative Slope Coefficient is an indicator of problem hardness that has been introduced in 2004 and that has returned promising results on a large set of problems. It is based on the concept of fitness cloud and works by partitioning the cloud into a number of bins representing as many different regions of the fitness landscape. The measure is calculated by joining the bins centroids by segments and summing all their negative slopes. In this paper, for the first time, we point out a potential problem of the Negative Slope Coefficient: we study its value for different instances of the well known NK-landscapes and we show how this indicator is dramatically influenced by the minimum number of points contained in a bin. Successively, we formally justify this behavior of the Negative Slope Coefficient and we discuss pros and cons of this measure. ©Springer-Verlag Berlin Heidelberg 2009.

The role of crossover and mutation in Genetic Programming (GP) has been the subject of much debate since the emergence of the field. In this paper, we contribute new empirical evidence to this argument using a rigorous and principled experimental method applied to six problems common in the GP literature. The approach tunes the algorithm parameters to enable a fair and objective comparison of two different GP algorithms, the first using a combination of crossover and reproduction, and secondly using a combination of mutation and reproduction. We find that crossover does not significantly outperform mutation on most of the problems examined. In addition, we demonstrate that the use of a straightforward Design of Experiments methodology is effective at tuning GP algorithm parameters.

Predicting the toxicity of new potential drugs is a fundamental step in the drug design process. Recent contributions have shown that, even though Genetic Programming is a promising method for this task, the problem of predicting the toxicity of molecular compounds is complex and difficult to solve. In particular, when executed for predicting drug toxicity, Genetic Programming undergoes the well-known phenomenon of bloat, i.e. the growth in code size during the evolutionary process without a corresponding improvement in fitness. We hypothesize that this might cause overfitting and thus prevent the method from discovering simpler and potentially more general solutions. For this reason, in this paper we investigate two recently defined variants of the operator equalization bloat control method for Genetic Programming. We show that these two methods are bloat free also when executed on this complex problem. Nevertheless, overfitting still remains an issue. Thus, contradicting the generalized idea that bloat and overfitting are strongly related, we argue that the two phenomena are independent from each other and that eliminating bloat does not necessarily eliminate overfitting. © 2009 Springer Berlin Heidelberg.

Generalization is a very important issue in Machine Learning. In this paper, we present a new idea for improving Genetic Programming generalization ability. The idea is based on a dynamic two-layered selection algorithm and it is tested on a real-life drug discovery regression application. The algorithm begins using root mean squared error as fitness and the usual tournament selection. A list of individuals called "repulsors" is also kept in memory and initialized as empty. As an individual is found to overfit the training set, it is inserted into the list of repulsors. When the list of repulsors is not empty, selection becomes a two-layer algorithm: individuals participating to the tournament are not randomly chosen from the population but are themselves selected, using the average dissimilarity to the repulsors as a criterion to be maximized. Two kinds of similarity/dissimilarity measures are tested for this aim: the well known structural (or edit) distance and the recently defined subtree crossover based similarity measure. Although simple, this idea seems to improve Genetic Programming generalization ability and the presented experimental results show that Genetic Programming generalizes better when subtree crossover based similarity measure is used, at least for the test problems studied in this paper. Copyright 2009 ACM.

The modelling of biochemical systems requires the knowledge of several quantitative parameters (e.g. reaction rates) which are often hard to measure in laboratory experiments. Furthermore, when the system involves small numbers of molecules, the modelling approach should also take into account the effects of randomness on the system dynamics. In this paper, we tackle the problem of estimating the unknown parameters of stochastic biochemical systems by means of two optimization heuristics, genetic algorithms and particle swarm optimization. Their performances are tested and compared on two basic kinetics schemes: the Michaelis-Menten equation and the Brussellator. The experimental results suggest that particle swarm optimization is a suitable method for this problem. The set of parameters estimated by particle swarm optimization allows us to reliably reconstruct the dynamics of the Michaelis-Menten system and of the Brussellator in the oscillating regime. © Springer-Verlag Berlin Heidelberg 2009.

This paper presents a research in the context of pedestrian dynamics according to Situated Cellular Agent (SCA), a Multi-Agent Systems approach whose roots are on Cellular Automata (CA). The aim of this work is to apply Genetic Programming (GP) approach, a well known Machine Learning method belonging to the family of Evolutionary Algorithms, to generate suitable behavioral rules for pedestrians in an evacuation scenario. The main contribution of this work is in the design of a testset of GP generated behaviors to represent basic behavioral models of evacuees populating a only locally known environment, a typical scenario for CA-based models. © 2008 Springer-Verlag Berlin Heidelberg.

The crossover bias theory for bloat [18] is a recent result which predicts that bloat is caused by the sampling of short, unfit programs. This theory is clear and simple, but it has some weaknesses: (1) it implicitly assumes that the population is large enough to allow sampling of all relevant program sizes (although it does explain what to expect in the many practical cases where this is not true, e.g., because the population is small); (2) it does not explain what is meant by its assumption that short programs are unfit. In this paper we discuss these weaknesses and propose a refined version of the crossover bias theory that clarifies the relationship between bloat and finite populations, and explains what features of the fitness landscape cause bloat to occur. The theory, in particular, predicts that smaller populations will bloat more slowly than larger ones. Additionally, the theory predicts that bloat will only be observed in problems where short programs are less fit than longer ones when looking at samples created by fitness-based importance sampling, i.e. samplings of the search space in which fitter programs have a higher probability of being sampled (e.g., the Metropolis-Hastings method). Experiments with two classical GP benchmarks fully corroborate the theory. Copyright 2008 ACM.

In this work we present an evolutionary framework for colorimetric characterization of scanners. The problem consists in finding a mapping from the RGB space (where points indicate how a color stimulus is produced by a given device) to their corresponding values in the CIELAB space (where points indicate how the color is perceived in standard, i.e. device independent, viewing conditions). The proposed framework is composed by two phases: in the first one we use genetic programming for assessing a characterizing polynomial; in the second one we use genetic algorithms to assess suitable coefficients of that polynomial. Experimental results are reported to confirm the effectiveness of our framework with respect to a set of methods in the state of the art. © 2008 Springer-Verlag Berlin Heidelberg.

We present different computational strategies for colorimetric characterization of scanners using multidimensional polynomials. The designed strategies allow us to determine the coefficients of an a priori fixed polynomial, taking into account different color error statistics. Moreover, since there is no clear relationship between the polynomial chosen for the characterization and the intrinsic characteristics of the scanner, we show how genetic programming could be used to generate the best polynomial. Experimental results on different devices are reported to confirm the effectiveness of our methods with respect to others in the state of the art.

We introduce the concept of "minimal" search algorithm for a set of functions to optimize. We investigate the structure of closed under permutation (c.u.p.) sets and we calculate the performance of an algorithm applied to them. We prove that each set of functions based on the distance to a given optimal solution, among which trap functions, onemax or the recently introduced onemix functions, and the NK-landscapes are not c.u.p. and thus the thesis of the sharpened No Free Lunch Theorem does not hold for them. Thus, it makes sense to look for a specific algorithm for those sets. Finally, we propose a method to build a "good" (although not necessarily minimal) search algorithm for a specific given set of problems. The algorithms produced with this technique show better average performance than a genetic algorithm executed on the same set of problems, which was expected given that those algorithms are problem-specific. Nevertheless, in general they cannot be applied for real-life problems, given their high computational complexity that we have been able to estimate. © 2008 Springer-Verlag Berlin Heidelberg.

A Genetic Programming (GP) framework for classification is presented in this paper and applied to a publicly available biomedical microarray dataset representing a collection of expression measurements from colon biopsy experiments [3]. We report experimental results obtained using two different well known fitness criteria: the area under the receiving operating curve (ROC) and the percentage of correctly classified instances (CCI). These results, and their comparison with the ones obtained by three non-evolutionary Machine Learning methods (Support Vector Machines, Voted Perceptron and Random Forests) on the same data, seem to hint that GP is a promising technique for this kind of classification both from the viewpoint of the accuracy of the proposed solutions and of the generalization ability. These results are encouraging and should pave the way to a deeper study of GP for classification applied to biomedical microarray datasets.

In evolutionary algorithms, distance metrics between solutions are often useful for many aspects of guiding and understanding the search process. A good distance measure should reflect the capability of the search: if two solutions are found to be close in distance, or similarity, they should also be close in the search algorithm sense, i.e., the variation operator used to traverse the search space should easily transform one of them into the other. This paper explores such a distance for genetic programming syntax trees. Distance measures are discussed, defined and empirically investigated. The value of such measures is then validated in the context of analysis (fitness-distance correlation is analyzed during population evolution) as well as guiding search (results are improved using our measure in a fitness sharing algorithm) and diversity (new insights are obtained as compared with standard measures). © 2008 IEEE.

Elitism, a technique which consists of copying, unchanged, one or more of the most fit individuals from one generation to the next, is widely used in generational evolutionary algorithms, including Genetic Programming (GP). Elitism ensures that the best individuals discovered in a generation (and hence in the whole run) are not lost, and, perhaps even more importantly, are made available to new generations for possible further improvements. In a recent study on the evolution of robustness in GP the average size of best of run individuals was reported to grow more slowly in the presence of elitism. This is an important finding, but no explanation was provided for why this happened nor whether this was a general effect. In this paper we model elitism mathematically and explain how, in general, elitism modulates the dynamics of the mean program size of the population, including both its positive and negative effects oil bloat. Experimental results with two GP systems and four different problems corroborate the theory

In this paper we present an empirical study of the Negative Slope Coefficient (NSC) hardness statistic to characterize the difficulty of 3-SAT fitness landscapes for randomly generated problem instances. NSC correctly classifies problem instances with a low ratio of clauses to variables as easy, while instances with a ratio close to the critical point are classified as hard, as expected. Together with previous results on many different problems and fitness landscapes, the present results confirm that NSC is a useful and reliable indicator of problem difficulty. © 2008 Springer-Verlag Berlin Heidelberg.

The success of a drug treatment is strongly correlated with the ability of a molecule to reach its target in the patient's organism without inducing toxic effects. Moreover the reduction of cost and time associated with drug discovery and development is becoming a crucial requirement for pharmaceutical industry. Therefore computational methods allowing reliable predictions of newly synthesized compounds properties are of outmost relevance. In this paper we discuss the role of genetic programming in predictive pharmacokinetics, considering the estimation of adsorption, distribution, metabolism, excretion and toxicity processes (ADMET) that a drug undergoes into the patient's organism. We compare genetic programming with other well known machine learning techniques according to their ability to predict oral bioavailability (%F), median oral lethal dose (LD50) and plasma-protein binding levels (%PPB). Since these parameters respectively characterize the percentage of initial drug dose that effectively reaches the systemic blood circulation, the harmful effects and the distribution into the organism of a drug, they are essential for the selection of potentially good molecules. Our results suggest that genetic programming is a valuable technique for predicting pharmacokinetics parameters, both from the point of view of the accuracy and of the generalization ability.

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. Copyright 2007 ACM.

Model checking is a way of analysing programs and program-like structures to decide whether they satisfy a list of temporal logic statements describing desired behaviour. In this paper we apply this to the fitness checking stage in an evolution strategy for learning finite state machines. We give experimental results consisting of learning the control program for a vending machine.

Computational methods allowing reliable pharmacokinetics predictions for newly synthesized compounds are critically relevant for drug discovery and development. Here we present an empirical study focusing on various versions of Genetic Programming and other well known Machine Learning techniques to predict Median Oral Lethal Dose (LD50) and Plasma Protein Binding (%PPB) levels. Since these two parameters respectively characterize the harmful effects and the distribution into human body of a drug, their accurate prediction is essential for the selection of effective molecules. The obtained results confirm that Genetic Programming is a promising technique for predicting pharmacokinetics parameters, both from the point of view of the accurateness and of the generalization ability.

This chapter represents a first attempt to characterize the fitness landscapes of real-life Genetic Programming applications by means of a predictive algebraic difficulty indicator. The indicator used is the Negative Slope Coefficient, whose efficacy has been recently empirically demonstrated on a large set of hand-tailored theoretical test functions and well known GP benchmarks. The real-life problems studied belong to the field of Biomedical applications and consist of automatically assessing a mathematical relationship between a set of molecular descriptors from a given dataset of drugs and some important pharmacokinetic parameters. The parameters considered here are Human Oral Bioavailability, Median Oral Lethal Dose, and Plasma Protein Binding levels. The availability of good prediction tools for pharmacokinetics parameters like these is critical for optimizing the efficiency of therapies, maximizing medical success rate and minimizing toxic effects. The experimental results presented in this chapter show that the Negative Slope Coefficient seems to be a reasonable tool to characterize the difficulty of these problems, and can be used to choose the most effective Genetic Programming configuration (fitness function, representation, parameters' values) from a set of given ones.

International audience; We study in detail the fitness landscape of a difficult cellular automata computational task: the majority problem. Our results show why this problem landscape is so hard to search, and we quantify the large degree of neutrality found in various ways. We show that a particular subspace of the solution space, called the "Olympus", is where good solutions concentrate, and give measures to quantitatively characterize this subspace.

Negative slope coefficient has been recently introduced and empirically proven a suitable hardness indicator for some well known genetic programming benchmarks, such as the even parity problem, the binomial-3 and the artificial ant on the Santa Fe trail. Nevertheless, the original definition of this measure contains several limitations. This paper points out some of those limitations, presents a new and more relevant definition of the negative slope coefficient and empirically shows the suitability of this new definition as a hardness measure for some genetic programming benchmarks, including the multiplexer, the intertwined spirals problem and the royal trees. © Springer-Verlag Berlin Heidelberg 2006.

International audience; Neutrality of some boolean parity fitness landscapes is investigated in this paper. Compared with some well known contributions on the same issue, we define some new measures that help characterizing neutral landscapes, we use a new sampling methodology, which captures some features that are disregarded by uniform random sampling, and we introduce new genetic operators to define the neighborhood of tree structures. We compare the fitness landscape induced by two different sets of functional operators (SNand and SXorNot). The different characteristics of the neutral networks seem to justify the different difficulties of these landscapes for genetic programming.

To analyse various properties of the search process of genetic programming it is useful to quantify the distance between two individuals. Using operator-based distance measures can make this analysis more accurate and reliable than using distance measures which have no relationship with the genetic operators. This paper extends a recent definition of a distance measure based on subtree crossover for genetic programming. Empirical studies are presented that show the suitability of this measure to dynamically calculate the fitness distance correlation coefficient during the evolution, to construct a fitness sharing system for genetic programming and to measure genotypic diversity in the population. These experiments confirm the accuracy of the new measure and its consistency with the subtree crossover genetic operator.