Marques, A., Henriques, R., & Castelli, M. (2026). Gaussian mixture modeling layer and its application to end-to-end generative high-dimensional clustering. Neurocomputing, 703, Article 134773. https://doi.org/10.1016/j.neucom.2026.134773

Automatic speech recognition for low-resource languages often relies on synthetic utterances to augment limited speech data; these utterances are generated by pairing large-language-model transcripts with neural text-to-speech (TTS) audio. However, indiscriminate incorporation of synthetic audio can reduce training efficiency and introduce errors such as unnatural speech patterns. We introduce WAVe, a model that verifies word-to-audio frame correspondence by aligning text representations with audio features. To evaluate WAVe, we generated 22k Portuguese and 35k Dutch synthetic audio samples using GPT-4o-mini and a TTS system. We created four training subsets per language with varying proportions of synthetic data and fine-tuned three Whisper models of different sizes. For Portuguese, our high-quality 29k-sample subset achieved a 7.9% word error rate with Whisper-Large-v3, outperforming a recent competitive 55k-sample model trained under identical conditions. Experiments on Dutch showed similarly consistent improvements. WAVe reduces the number of training steps by 34%, substantially lowering computational cost while improving ASR quality. Cross-domain evaluation on the Multilingual LibriSpeech benchmark demonstrates that WAVe-based filtering reduces WER from 13.54% to 6.89%. These results establish WAVe as an effective quality control mechanism for synthetic data pipelines, enabling the identification and removal of poorly synthesized audio-text pairs prior to ASR fine-tuning.

Abstract Geometric Semantic Genetic Programming ( $$\mathsf {GSGP}$$ ) is a powerful variant of Genetic Programming (GP) that defines genetic operators inducing unimodal fitness landscapes. In recent years, a new mutation operator, Geometric Semantic Mutation with Local Search (GSM-LS), has been proposed to include a local search step in the mutation process. The core idea of GSM-LS is to incorporate a linear regression step during mutation, thereby accelerating convergence toward high-quality solutions. While GSM-LS helps the convergence of the evolutionary search, it is prone to overfitting. Thus, it was suggested to apply GSM-LS only for a limited number of generations and then revert to standard geometric semantic mutation. A more recently defined variant of $$\mathsf {GSGP}$$ (called $$\mathsf {GSGP}$$ -reg) also includes a local search step, but shares similar strengths and weaknesses with GSM-LS. Here, we investigate several strategies to mitigate overfitting in GSM-LS and $$\mathsf {GSGP}$$ -reg, ranging from simple regularized regression techniques to adaptive methods that estimate overfitting risk at each mutation. The latter approaches partition the training set into two subsets: one used to perform the mutation, and the other to evaluate the risk of overfitting based on the mutation’s impact on held-out data. Experimental evaluations across seven real-world regression benchmarks show that, while plain GSGP underperforms on all datasets, methods incorporating local search often achieve significantly better test performance. For example, on the Airfoil dataset, the GSM-LS variant achieves a median RMSE below 10 compared to 30 with standard GSGP. On the LD50 and Bioavailability datasets, the proposed gen and ridge-regularized variants effectively mitigate overfitting, reducing test RMSE by up to 40% relative to baseline GSGP. We conclude that local search, when used with regularization strategies, enhances GSGP’s performance and generalization capability across a diverse range of tasks.

This manuscript presents an improved version of the Inclusive Genetic Programming (IGP) algorithm. The IGP was developed to promote and maintain the population's genotypic diversity and showed superior performance compared to standard Genetic Programming (GP). In this work, two modifications to the IGP are proposed: first, the diversity promotion and maintenance mechanism is enhanced with information from the phenotype of the individuals rather than only the genotype; second, the Evolutionary Demes Despeciation Algorithm - V2 (EDDA-V2) is used to initialize the population. The phenotype is considered to differentiate the individuals also according to their behaviour rather than only their structure, while EDDA-V2 is employed to start the evolution with a simultaneously diverse and fit population, contrary to traditional initialization techniques. The algorithms incorporating these improvements are called Full Inclusive Genetic Programming (FIGP) and FIGP _E, respectively with and without the EDDA-V2 initialization. The experimental results, performed over eight benchmarks and considering six algorithms, demonstrate the superior performance of FIGP and FIGP _E in comparison to other GP formulations. Moreover, the EDDA-V2 initialization allows for a significant reduction of the computational time.

Full-reference image quality measures are a fundamental tool to approximate the human visual system in various applications for digital data management: from retrieval to compression to detection of unauthorized uses. Inspired by both the effectiveness and the simplicity of hand-crafted Structural Similarity Index Measure (SSIM), in this work, we present a framework for the formulation of SSIM-like image quality measures through genetic programming. We explore different terminal sets, defined from the building blocks of structural similarity at different levels of abstraction, and we propose a two-stage genetic optimization that exploits hoist mutation to constrain the complexity of the solutions. Our optimized measures are selected through a cross-dataset validation procedure, which results in superior performance against different versions of structural similarity, measured as correlation with human mean opinion scores. We also demonstrate how, by tuning on specific datasets, it is possible to obtain solutions that are competitive with (or even outperform) more complex image quality measures.

The growing production of digital content and its dissemination across the worldwide web require eficient and precise management. In this context, image quality assessment measures (IQAMs) play a pivotal role in guiding the development of numerous image processing systems for compression, enhancement, and restoration. The structural similarity index (SSIM) is one of the most common IQAMs for estimating the similarity between a pristine reference image and its corrupted variant. The multi-scale SSIM is one of its most popular variants that allows assessing image quality at multiple spatial scales. This paper proposes a two-stage genetic programming (GP) approach to evolve novel multi-scale IQAMs, that are simultaneously more effective and efficient. We use GP to perform feature selection in the first stage, while the second stage generates the final solutions. The experimental results show that the proposed approach outperforms the existing MS-SSIM. A comprehensive analysis of the feature selection indicates that, for extracting multi-scale similarities, spatially-varying convolutions are more effective than dilated convolutions. Moreover, we provide evidence that the IQAMs learned for one database can be successfully transferred to previously unseen databases. We conclude the paper by presenting a set of evolved multi-scale IQAMs and providing their interpretation.

We investigate the use of Genetic Programming (GP) as a convolutional predictor for missing pixels in images. The training phase is performed by sweeping a sliding window over an image, where the pixels on the border represent the inputs of a GP tree. The output of the tree is taken as the predicted value for the central pixel. We consider two topologies for the sliding window, namely the Moore and the Von Neumann neighborhood. The best GP tree scoring the lowest prediction error over the training set is then used to predict the pixels in the test set. We experimentally assess our approach through two experiments. In the first one, we train a GP tree over a subset of 1000 complete images from the MNIST dataset. The results show that GP can learn the distribution of the pixels with respect to a simple baseline predictor, with no significant differences observed between the two neighborhoods. In the second experiment, we train a GP convolutional predictor on two degraded images, removing around 20% of their pixels. In this case, we observe that the Moore neighborhood works better, although the Von Neumann neighborhood allows for a larger training set.

Tasks related to Natural Language Processing (NLP) have recently been the focus of a large research endeavor by the machine learning community. The increased interest in this area is mainly due to the success of deep learning methods. Genetic Programming (GP), however, was not under the spotlight with respect to NLP tasks. Here, we propose a first proof-of-concept that combines GP with the well established NLP tool word2vec for the next word prediction task. The main idea is that, once words have been moved into a vector space, traditional GP operators can successfully work on vectors, thus producing meaningful words as the output. To assess the suitability of this approach, we perform an experimental evaluation on a set of existing newspaper headlines. Individuals resulting from this (pre-)training phase can be employed as the initial population in other NLP tasks, like sentence generation, which will be the focus of future investigations, possibly employing adversarial co-evolutionary approaches.

The evolution of networks is a fundamental topic in network analysis and mining. One of the approaches that has been recently considered in this field is the analysis of temporal networks, where relations between elements can change over time. A relevant problem in the analysis of temporal networks is the identification of cohesive or dense subgraphs since they are related to communities. In this contribution, we present a method based on genetic algorithms and on a greedy heuristic to identify dense subgraphs in a temporal network. We present experimental results considering both synthetic and real-networks, and we analyze the performance of the proposed method when varying the size of the population and the number of generations. The experimental results show that our heuristic generally performs better in terms of quality of the solutions than the state-of-art method for this problem. On the other hand, the state-of-art method is faster, although comparable with our method, when the size of the population and the number of generations are limited to small values.

Computational Intelligence (CI) is a computer science discipline encompassing the theory, design, development and application of biologically and linguistically derived computational paradigms. Traditionally, the main elements of CI are Evolutionary Computation, Swarm Intelligence, Fuzzy Logic, and Neural Networks. CI aims at proposing new algorithms able to solve complex computational problems by taking inspiration from natural phenomena. In an intriguing turn of events, these nature-inspired methods have been widely adopted to investigate a plethora of problems related to nature itself. In this paper we present a variety of CI methods applied to three problems in life sciences, highlighting their effectiveness: we describe how protein folding can be faced by exploiting Genetic Programming, the inference of haplotypes can be tackled using Genetic Algorithms, and the estimation of biochemical kinetic parameters can be performed by means of Swarm Intelligence. We show that CI methods can generate very high quality solutions, providing a sound methodology to solve complex optimization problems in life sciences.

Grammatical evolution (GE) is one of the most widespread techniques in evolutionary computation. Genotypes in GE are bit strings while phenotypes are strings, of a language defined by a user-provided context-free grammar. In this paper, we propose a novel procedure for mapping genotypes to phenotypes that we call weighted hierarchical GE (WHGE). WHGE imposes a form of hierarchy on the genotype and encodes grammar symbols with a varying number of bits based on the relative expressive power of those symbols. WHGE does not impose any constraint on the overall GE framework, in particular, WHGE may handle recursive grammars, uses the classical genetic operators, and does not need to define any bound in advance on the size of phenotypes. We assessed experimentally our proposal in depth on a set of challenging and carefully selected benchmarks, comparing the results of the standard GE framework as well as two of the most significant enhancements proposed in the literature: 1) position-independent GE and 2) structured GE. Our results show that WHGE delivers very good results in terms of fitness as well as in terms of the properties of the genotype-phenotype mapping procedure.

Context-free grammars are useful tools for modeling the solution space of problems that can be solved by optimization algorithms. For a given solution space, there exists an infinite number of grammars defining that space, and there are clues that changing the grammar may impact the effectiveness of the optimization. In this article, we investigate theoretically and experimentally the possibility of specializing a grammar in a problem, that is, of systematically improving the quality of the grammar for the given problem. To this end, we define the quality of a grammar for a problem in terms of the average fitness of the candidate solutions generated using that grammar. Theoretically, we demonstrate the following findings: 1) that a simple mutation operator employed in a (1 + 1)-EA setting can be used to specialize a grammar in a problem without changing the solution space defined by the grammar and 2) that three grammars of equal quality for a grammar-based version of the ONEMAX problem greatly vary in how they can be specialized with that (1 + 1)-EA, as the expected time required to obtain the same improvement in quality can vary exponentially among grammars. Then, experimentally, we validate the theoretical findings and extend them to other problems, grammars, and a more general version of the mutation operator.

Bakurov, I., Castelli, M., Fontanella, F., & Vanneschi, L. (2019). A regression-like classification system for geometric semantic genetic programming. In J. J. Merelo, J. Garibaldi, A. Linares-Barranco, K. Madani, K. Warwick, & K. Warwick (Eds.), Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019) (Vol. 1, pp. 40-48). (IJCCI 2019 - Proceedings of the 11th International Joint Conference on Computational Intelligence). SciTePress.

Re, A., Vanneschi, L., & Castelli, M. (2019). Universal learning machine with genetic programming. In J. J. Merelo, J. Garibaldi, A. Linares-Barranco, K. Madani, K. Warwick, & K. Warwick (Eds.), Proceedings of the 11th International Joint Conference on Computational Intelligence (Vol. 1, pp. 115-122). (IJCCI 2019 - Proceedings of the 11th International Joint Conference on Computational Intelligence). Viena: SciTePress.

RNA inverse folding problem is a bioinformatics problem where the objective is to find an RNA sequence that folds into a given target secondary structure. In this paper, we use evolutionary computation to solve a new and innovative multiobjective definition of this problem. In this new multiobjective definition of the problem, we have considered the similarity between target and predicted structures as a constraint, and three objective functions: 1) partition function (free energy of the ensemble); 2) ensemble diversity; and 3) nucleotides composition. The multiobjective metaheuristic to design RNA sequences (m2dRNAs) proposed in this paper is compared against other RNA inverse folding methods published in the literature, such as RNAinverse, RNA secondary structure designer, inverse folding of RNA, MODENA, NUPACK, fRNAkenstein, dynamics in sequence space optimization, RNAiFOLD, antaRNA, evolutionary RNA design, and Eterna players. After a comprehensive comparative study on two well-known benchmarks (Rfam and Eterna100), we conclude that m2dRNAs is capable of obtaining very promising results in terms of both quality of RNA designs and required runtime. The source code of m2dRNAs is available at http://arco.unex.es/arl/m2dRNAs-source_code.zip.

The multiple sequence alignment is a well-known bioinformatics problem that consists in the alignment of three or more biological sequences (protein or nucleic acid). In the literature, a number of tools have been proposed for dealing with this biological sequence alignment problem, such as progressive methods, consistency-based methods, or iterative methods; among others. These aligners often use a default parameter configuration for all the input sequences to align. However, the default configuration is not always the best choice, the alignment accuracy of the tool may be highly boosted if specific parameter configurations are used, depending on the biological characteristics of the input sequences. In this paper, we propose a characteristic-based framework for multiple sequence aligners. The idea of the framework is, given an input set of unaligned sequences, extract its characteristics and run the aligner with the best parameter configuration found for another set of unaligned sequences with similar characteristics. In order to test the framework, we have used the well-known multiple sequence comparison by log-expectation (MUSCLE) v3.8 aligner with different benchmarks, such as benchmark alignments database v3.0, protein reference alignment benchmark v4.0, and sequence alignment benchmark v1.65. The results shown that the alignment accuracy and conservation of MUSCLE might be greatly improved with the proposed framework, specially in those scenarios with a low percentage of identity. The characteristic-based framework for multiple sequence aligners is freely available for downloading at http://arco.unex.es/arl/fwk-msa/cbf-msa.zip.

Genetic Programming (GP) has been around for over two decades and has been used in a wide range of practical applications producing human competitive results in several domains. In this paper we present a discussion and a proposal of a GP algorithm that could be conveniently implemented on an embedded system, as part of a broader research project that pursues the implementation of a complete GP system in a Field Programmable Gate Array (FPGA). Motivated by the significant time savings associated with such a platform, as well as low power consumption, low maintenance requirements, small size of the system and the possibility of performing several parallel processes. The proposal is focused on the Geometric Semantic Genetic Programming (GSGP) approach that has been recently introduced with promising results. GSGP induces a unimodal fitness landscape, simplifying the search process. The experimental work considers five variants of GSGP, that incorporate local search strategies, optimal mutations and alignment in error space. Best results were obtained by a simple variant that uses both the optimal mutation step and the standard geometric semantic mutation, using three difficult real-world problems to evaluate the methods, outperforming the original GSGP formulation in terms of fitness and empirical convergence.

Initializing the population is a crucial step for genetic programming, and several strategies have been proposed so far. The issue is particularly important for geometric semantic genetic programming, where initialization is known to play a very important role. In this paper, we propose an initialization technique inspired by the biological phenomenon of demes despeciation, i.e. the combination of demes of previously distinct species into a new population. In synthesis, the initial population of geometric semantic genetic programming is created using the best individuals of a set of separate subpopulations, or demes, some of which run standard genetic programming and the others geometric semantic genetic programming for few generations. Geometric semantic genetic programming with this novel initialization technique is shown to outperform geometric semantic genetic programming using the traditional ramped half-and-half algorithm on six complex symbolic regression applications. More specifically, on the studied problems, the proposed initialization technique allows us to generate solutions with comparable or even better generalization ability, and of significantly smaller size than the ramped half-and-half algorithm.

Geometric semantic genetic programming is a hot topic in evolutionary computation and recently it has been used with success on several problems from Biology and Medicine. Given the young age of geometric semantic genetic programming, in the last few years theoretical research, aimed at improving the method, and applicative research proceeded rapidly and in parallel. As a result, the current state of the art is confused and presents some “holes”. For instance, some recent improvements of geometric semantic genetic programming have never been applied to some popular biomedical applications. The objective of this paper is to fill this gap. We consider the biomedical applications that have more frequently been used by genetic programming researchers in the last few years and we systematically test, in a consistent way, using the same parameter settings and configurations, all the most popular existing variants of geometric semantic genetic programming on all those applications. Analysing all these results, we obtain a much more homogeneous and clearer picture of the state of the art, that allows us to draw stronger conclusions.

Inspired by a recent approach for genome reconstruction from incomplete data, we consider a variant of the longest common subsequence problem for the comparison of two sequences, one of which is incomplete, i.e. it has some missing elements. The new combinatorial problem, called Longest Filled Common Subsequence, given two sequences A and B, and a multiset M of symbols missing in B, asks for a sequence B* obtained by inserting the symbols of M into B so that B* induces a common subsequence with A of maximum length. First, we investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol. Then, we give a 3/5 approximation algorithm for the problem. Finally, we present a fixed-parameter algorithm, when the problem is parameterized by the number of symbols inserted in B that "match" symbols of A.

In iterative supervised learning algorithms it is common to reach a point in the search where no further induction seems to be possible with the available data. If the search is continued beyond this point, the risk of overfitting increases significantly. Following the recent developments in inductive semantic stochastic methods, this paper studies the feasibility of using information gathered from the semantic neighborhood to decide when to stop the search. Two semantic stopping criteria are proposed and experimentally assessed in Geometric Semantic Genetic Programming (GSGP) and in the Semantic Learning Machine (SLM) algorithm (the equivalent algorithm for neural networks). The experiments are performed on real-world high-dimensional regression datasets. The results show that the proposed semantic stopping criteria are able to detect stopping points that result in a competitive generalization for both GSGP and SLM. This approach also yields computationally efficient algorithms as it allows the evolution of neural networks in less than 3 seconds on average, and of GP trees in at most 10 seconds. The usage of the proposed semantic stopping criteria in conjunction with the computation of optimal mutation/learning steps also results in small trees and neural networks.

Although several computational methods have been developed for predicting interactions between miRNA and target genes, there are substantial differences in the achieved results. For this reason, machine learning approaches are widely used for integrating the predictions obtained from different tools. In this work we adopt a method, called M3GP, which relies on a genetic programming approach, to classify results from three tools: miRanda, TargetScan, and RNAhybrid. Such algorithm is highly parallelizable and its adoption provides great advantages while handling problems involving big datasets, since it is independent from the implementation and from the architecture on which it is executed. More precisely, we apply this technique for the classification of the achieved miRNA target predictions and we compare its results with those obtained with other classifiers.

Since its introduction, Geometric Semantic Genetic Programming (GSGP) has aroused the interest of numerous researchers and several studies have demonstrated that GSGP is able to effectively optimize training data by means of small variation steps, that also have the effect of limiting overfitting. In order to speed up the search process, in this paper we propose a system that integrates a local search strategy into GSGP (called GSGP-LS). Furthermore, we present a hybrid approach, that combines GSGP and GSGP-LS, aimed at exploiting both the optimization speed of GSGP-LS and the ability to limit overfitting of GSGP. The experimental results we present, performed on a set of complex real-life applications, show that GSGP-LS achieves the best training fitness while converging very quickly, but severely overfits. On the other hand, GSGP converges slowly relative to the other methods, but is basically not affected by overfitting. The best overall results were achieved with the hybrid approach, allowing the search to converge quickly, while also exhibiting a noteworthy ability to limit overfitting. These results are encouraging, and suggest that future GSGP algorithms should focus on finding the correct balance between the greedy optimization of a local search strategy and the more robust geometric semantic operators.

The paper above (ibid., vol. 44, no. 1, pp. 103-113, Jan. 2014), was printed with the incorrect author list as follows: M. Castelli, L. Vanneschi, S. Silva, A. Agapitos, and M. O'Neill. The correct author list is: M. Castelli, L. Vanneschi and S. Silva.

The concept of semantics (in the sense of input-output behavior of solutions on training data) has been the subject of a noteworthy interest in the genetic programming (GP) research community over the past few years. In this paper, we present a new GP system that uses the concept of semantics to improve search effectiveness. It maintains a distribution of different semantic behaviors and biases the search toward solutions that have similar semantics to the best solutions that have been found so far. We present experimental evidence of the fact that the new semantics-based GP system outperforms the standard GP and the well-known bacterial GP on a set of test functions, showing particularly interesting results for noncontinuous (i.e., generally harder to optimize) test functions. We also observe that the solutions generated by the proposed GP system often have a larger size than the ones returned by standard GP and bacterial GP and contain an elevated number of introns, i.e., parts of code that do not have any effect on the semantics. Nevertheless, we show that the deletion of introns during the evolution does not affect the performance of the proposed method.

Reaction systems is a formalism inspired by chemical reactions introduced by Rozenberg and Ehrenfeucht. Recently, an evolutionary algorithm based on this formalism, called Evolutionary Reaction Systems, has been presented. This new algorithm proved to have comparable performances to other well-established machine learning methods, like genetic programming, neural networks and support vector machines on both artificial and real-life problems. Even if the results are encouraging, to make Evolutionary Reaction Systems an established evolutionary algorithm, an in depth analysis of the effect of its parameters on the search process is needed, with particular focus on those parameters that are typical of Evolutionary Reaction Systems and do not have a counterpart in traditional evolutionary algorithms. Here we address this problem for the first time. The results we present show that one particular parameter, between the ones tested, has a great influence on the performances of Evolutionary Reaction Systems, and thus its setting deserves practitioners' particular attention: the number of symbols used to represent the reactions that compose the system. Furthermore, this work represents a first step towards the definition of a set of default parameter values for Evolutionary Reaction Systems, that should facilitate their use for beginners or inexpert practitioners.

Genetic programming (GP) is not a field noted for the rigor of its benchmarking. Some of its benchmark problems are popular purely through historical contingency, and they can be criticized as too easy or as providing misleading information concerning real-world performance, but they persist largely because of inertia and the lack of good alternatives. Even where the problems themselves are impeccable, comparisons between studies are made more difficult by the lack of standardization. We argue that the definition of standard benchmarks is an essential step in the maturation of the field. We make several contributions towards this goal. We motivate the development of a benchmark suite and define its goals; we survey existing practice; we enumerate many candidate benchmarks; we report progress on reference implementations; and we set out a concrete plan for gathering feedback from the GP community that would, if adopted, lead to a standard set of benchmarks.

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.

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.

Recent contributions clearly show that eliminating bloat in a genetic programming system does not necessarily eliminate overfitting and vice-versa. This fact seems to contradict a common agreement of many researchers known as the minimum description length principle, which states that the best model is the one that minimizes the amount of information needed to encode it. Another common agreement is that overfitting should be, in some sense, related to the functional complexity of the model. The goal of this paper is to define three measures to respectively quantify bloat, overfitting and functional complexity of solutions and show their suitability on a set of test problems including a simple bidimensional symbolic regression test function and two real-life multidimensional regression problems. The experimental results are encouraging and should pave the way to further investigation. Advantages and drawbacks of the proposed measures are discussed, and ways to improve them are suggested. In the future, these measures should be useful to study and better understand the relationship between bloat, overfitting and functional complexity of solutions.