Skeleton sequences are lightweight and compact and thus are ideal candidates for action recognition on edge devices. Recent skeleton-based action recognition methods extract features from 3-D joint coordinates as spatial-temporal cues, using these representations in a graph neural network for feature fusion to boost recognition performance. The use of first- and second-order features, that is, joint and bone representations, has led to high accuracy. Nonetheless, many models are still confused by actions that have similar motion trajectories. To address these issues, we propose fusing higher-order features in the form of angular encoding (AGE) into modern architectures to robustly capture the relationships between joints and body parts. This simple fusion with popular spatial-temporal graph neural networks achieves new state-of-the-art accuracy in two large benchmarks, including NTU60 and NTU120, while employing fewer parameters and reduced run time. Our source code is publicly available at: https://github.com/ZhenyueQin/Angular-Skeleton-Encoding.

Discrete gene regulatory networks (GRNs) play a vital role in the study of robustness and modularity. A common method of evaluating the robustness of GRNs is to measure their ability to regulate a set of perturbed gene activation patterns back to their unperturbed forms. Usually, perturbations are obtained by collecting random samples produced by a predefined distribution of gene activation patterns. This sampling method introduces stochasticity, in turn inducing dynamicity. This dynamicity is imposed on top of an already complex fitness landscape. So where sampling is used, it is important to understand which effects arise from the structure of the fitness landscape, and which arise from the dynamicity imposed on it. Stochasticity of the fitness function also causes difficulties in reproducibility and in post-experimental analyses. We develop a deterministic distributional fitness evaluation by considering the complete distribution of gene activity patterns, so as to avoid stochasticity in fitness assessment. This fitness evaluation facilitates repeatability. Its determinism permits us to ascertain theoretical bounds on the fitness, and thus to identify whether the algorithm has reached a global optimum. It enables us to differentiate the effects of the problem domain from those of the noisy fitness evaluation, and thus to resolve two remaining anomalies in the behaviour of the problem domain of Espinosa-Soto and A. Wagner (2010). We also reveal some properties of solution GRNs that lead them to be robust and modular, leading to a deeper understanding of the nature of the problem domain. We conclude by discussing potential directions toward simulating and understanding the emergence of modularity in larger, more complex domains, which is key both to generating more useful modular solutions, and to understanding the ubiquity of modularity in biological systems.

Modeling real-world phenomena is a focus of many science and engineering efforts, from ecological modeling to financial forecasting. Building an accurate model for complex and dynamic systems improves understanding of underlying processes and leads to resource efficiency. Knowledge-driven modeling builds a model based on human expertise, yet is often suboptimal. At the opposite extreme, data-driven modeling learns a model directly from data, requiring extensive data and potentially generating overfitting. We focus on an intermediate approach, model revision, in which prior knowledge and data are combined to achieve the best of both worlds. We propose a genetic model revision framework based on tree-adjoining grammar (TAG) guided genetic programming (GP), using the TAG formalism and GP operators in an effective mechanism making data-driven revisions while incorporating prior knowledge. Our framework is designed to address the high computational cost of evolutionary modeling of complex systems. Via a case study on the challenging problem of river water quality modeling, we show that the framework efficiently learns an interpretable model, with higher modeling accuracy than existing methods.

The estimation of distribution algorithms (EDAs) applied to genetic programming (GP) have been studied by a number of authors. Like all EDAs, they suffer from biases induced by the model building and sampling process. However, the biases are amplified in the algorithms for GP. In particular, many systems use stochastic grammars as their model representation, but biases arise due to grammar recursion. We define and estimate the bias due to recursion in grammar-based EDAs in GP, using methods derived from computational linguistics. We confirm the extent of bias in some simple experimental examples. We then propose some methods to repair this bias. We apply the estimation of bias, and its repair, to some more practical applications. We experimentally demonstrate the extent of bias arising from recursion, and the performance improvements that can result from correcting it.

We explore the problem space of maximum nonlinearity problems for balanced Boolean functions, examining the symmetry structure and fitness landscapes in the most common (bit string) representation. We present theoretical analyses of well understood aspects, together with detailed enumeration of the 4-bit problem, sampling of the 6-bit problem based on known optima, and sampling of the 8-bit problem based on its fittest known solutions.

We predict the progression of Immunoglobulin A Nephropathy using three classification methods: Classification and Regression Trees, Logistic Regression, and Feed-Forward Artificial Neural Networks. We treat it as a classification problem, of predicting progression to end-stage renal disease in the ten years following initial diagnosis. We compared classifier performance using ROC analysis. All three methods yielded good classifiers, with AUC between 0.85 and 0.95. The results were generally in-line with expectations, with poor kidney performance on presentation, and evident macroscopic and microscopic damage, all associated with poorer prognosis.

We propose an efficient low-overhead methodology for screening key layouts for ultimate typing speed. It is fast and complementary to existing protocols in other ways. For equal overhead, it allows testing over a wider range of users. It is subject to potential biases, but they can be quantified and adjusted. It assumes an existing standard layout which is used as a comparator. It eliminates bias from differing familiarity and finger memory by appropriately mapping both layouts. We illustrate it with two mobile phone keypad layouts: Samsung's variant of the common ABC layout, and a new user-specific layout (PM). We repeat a comparison previously undertaken by a training-based method, which used ten participants, and estimated a $54\%$ speedup for PM (SD = $35\%$). The new method used 116 participants and estimated a $19.5\%$ speedup (SD = $7.5\%$). Differences in speedup estimates can be explained by the wide confidence interval of the training-based methods, differences in test corpuses, and the inherent conservatism of the new method. Effects of user characteristics could be meaningfully tested due to the larger test group. Gender had no detectable effect on any of the measures, but age and keypad experience were significantly related to ABC and PM performance. However, the relative speedup was unaffected by age or keypad experience: the method can remove comparison biases arising from differing experience levels.

Genetic programming is very computationally intensive, particularly in CPU time. A number of approaches to evaluation cost reduction have been proposed, among them early termination of evaluation (applicable in problem domains where estimates of the final fitness value are available during evaluation). Like all cost reduction techniques, early termination balances overall computation cost against the risk of finding worse solutions. We evaluate the influence of various properties of the problem domain - problem class, reliability of fitness estimates, trajectory of fitness estimates, and evolutionary trajectory - to determine whether any is able to predict the effects of early termination. There is little correlation with any of these, with one exception. Boolean problems see little change in running time, and hence only small changes in performance, are distinguished by both problem class, and each of the other metrics.

Symmetry has hitherto been studied piecemeal in a variety of evolutionary computation domains, with little consistency between the definitions. Here we provide formal definitions of symmetry that are consistent across the field of evolutionary computation. We propose a number of evolutionary and estimation of distribution algorithms suitable for variable symmetries in Cartesian power domains, and compare their utility, integration of the symmetry knowledge with the probabilistic model of an EDA yielding the best outcomes. We test the robustness of the algorithm to inexact symmetry, finding adequate performance up to about 1% noise. Finally, we present evidence that such symmetries, if not known a priori, may be learnt during evolution.

In estimation of distribution algorithms (EDAs), probability models hold accumulating evidence on the location of an optimum. Stochastic sampling drift has been heavily researched in EDA optimization but not in EDAs applied to genetic programming (EDA-GP). We show that, for EDA-GPs using probabilistic prototype tree models, stochastic drift in sampling and selection is a serious problem, inhibiting scaling to complex problems. Problems requiring deep dependence in their probability structure see such rapid stochastic drift that the usual methods for controlling drift are unable to compensate. We propose a new alternative, analogous to likelihood weighting of evidence. We demonstrate in a small-scale experiment that it does counteract the drift, sufficiently to leave EDA-GP systems subject to similar levels of stochastic drift to other EDAs.

We introduce replicator-mutator mechanisms from evolutionary dynamics into a two-dimensional daisyworld model, thereby coupling evolutionary changes with daisyworld’s bidirectional feedback between biota and environment. Daisyworld continues to self-regulate in the presence of these evolutionary forces. The most interesting behaviours, exhibiting a complex and dynamic dance through space and time in species’ abundance, emerges through the introduction of additive spatio-temporal random perturbations in the form of thermal noise. The balance between ecosystem feedback and fluctuations in the ecosystem determines the spatial coexistence of domains of dominance between daisy species and their mutants or adaptants.

Much recent research in Estimation of Distribution Algorithms (EDA) applied to Genetic Programming has adopted a Stochastic Context Free Grammar(SCFG)-based model formalism. However these methods generate biases which may be indistinguishable from selection bias, resulting in sub-optimal performance. The primary factor generating this bias is the combined effect of recursion in the grammars and depth limitation removing some sample trees from the distribution. Here, we demonstrate the bias and provide exact estimates of its scale (assuming infinite populations and simple recursions). We define a quantity h which determines both whether bias occurs (h >; 1) and its scale. We apply this analysis to a number of simple illustrative grammars, and to a range of practically-used GP grammars, showing that this bias is both real and important.

The Gaussian Q-function is of great importance in the field of communications, where the noise is often characterized by the Gaussian distribution. However, no simple exact closed form of the Q-function is known. Consequently, a number of approximations have been proposed over the past several decades. In this paper, we use Genetic Programming with semantic based crossover to approximate the Q-function in two forms: the free and the exponential forms. Using this form, we found approximations in both forms that are more accurate than all previous approximations designed by human experts.

The Gaussian Q-function is the integral of the tail of the Gaussian distribution; as such, it is important across a vast range of fields requiring stochastic analysis. No elementary closed form is possible, so a number of approximations have been proposed. We use a Genetic Programming (GP) system, Tree Adjoining Grammar Guided GP (TAG3P) with local search operators to evolve approximations of the Q-function in the form given by Benitez [1]. We found more accurate approximations than any previously published. This confirms the practical importance of local search in TAG3P.

We present a rapid screening method for keyboard layouts. The method relies on user familiarity with a pre-existing layout, and can provide rapid, low-cost estimates of the eventual user speed on the new layout. It provides an effective pre-screening for the expensive training curve estimates of previous methods, and provides valuable supplementary information not available from them. We provide preliminary validation of the method on a mobile phone layout problem.

In this paper, we investigate the impact of a layered learning approach with incremental sampling on Genetic Programming (GP). The new system, called GPLL, is tested and compared with standard GP on twelve symbolic regression problems. While GPLL does not differ from standard GP on univariate target functions, it has better training efficiency on problems with bivariate targets. This indicates the potential usefulness of layered learning with incremental sampling in improving the efficiency of GP evolutionary learning.

Chemical methods such as directed evolution and some forms of the SELEX procedure implement evolutionary algorithms directly in vitro. They have a wide range of applications in detecting and targeting diseases and potential applications in other areas as well [1]. However it is relatively difficult and expensive to carry out these processes (by comparison with evolutionary computation), so that the underlying theory has seen limited development. For more complex problems, where multiple and dynamic objectives are involved, there is potential for substantial improvement in the search protocols. Simulation through the methods of evolutionary computation is one potential way to gain the necessary insights. The complex fitness functions and huge populations involved in combinatorial chemistry render detailed simulation infeasible. However detailed simulation is not needed, so long as simulations are sufficiently similar to yield qualitative insights. In this paper, we investigate whether one class of problems those involving short-chain evolution, where stereochemical effects do not dominate are likely to have sufficiently similar fitness landscapes to a simple problem, string matching, for useful inferences to be made. In the outcome, it appears that the differences between more detailed simulations and string matching are not sufficient to significantly alter the behaviour of evolutionary algorithms, so that string matching could be used as a realistic surrogate. This is valuable, because string matching can be implemented in GPUs, offering speed-ups to the level where populations of 107, or even 108, might be feasible, thus reducing the population gap between chemical and computer evolution.

Estimation of Distribution Algorithms were introduced into Genetic Programming over 15 years ago, and have demonstrated good performance on a range of problems, but there has been little research into their limitations. We apply two such algorithms - scalar and vectorial Stochastic Grammar GP - to Daida's well-known Lid problem, to better understand their ability to learn specific structures. The scalar algorithm performs poorly, but the vectorial version shows good overall performance. We then extended Daida's problem to explore the vectorial algorithm's ability to find even more specific structures, finding that the performance fell off rapidly as the specificity of the required structure increased. Thus although this particular system has less severe structural difficulty issues than standard GP, it is by no means free of them. Track: Genetic Programming

All evolutionary algorithms trade off exploration and exploitation in optimisation problems; dynamic problems are no exception. We investigate this trade-off, over a range of algorithm settings, on dynamic variants of three well-known optimisation problems (One Max, Royal Road and knapsack), using Yang's XOR method to vary the scale and rate of change. Extremely exploitative algorithm settings performed best for a surprisingly wide range of problems; even where they were not the most effective, they still performed competitively, and even in those cases, the best performers were still far more exploitative than most would anticipate.

We investigate interactions between evolution, development and lifelong layered learning in a combination we call evolutionary developmental evaluation (EDE), using a specific implementation, developmental tree-adjoining grammar guided genetic programming (GP). The approach is consistent with the process of biological evolution and development in higher animals and plants, and is justifiable from the perspective of learning theory. In experiments, the combination is synergistic, outperforming algorithms using only some of these mechanisms. It is able to solve GP problems that lie well beyond the scaling capabilities of standard GP. The solutions it finds are simple, succinct, and highly structured. We conclude this paper with a number of proposals for further extension of EDE systems.

Water quality is an important global issue, requiring effective management, which needs good predictive tools. While good methods for lake water quality prediction have previously been developed, accurate prediction of river water quality has hitherto been difficult. This project combines process-model and data mining approaches through evolutionary methods, resulting in tools for more effective water management. Although the work is still in its preliminary stages, error rates of the predictive models are already around half those resulting from representative applications of either pure process-based or pure data mining approaches.

This paper presents two methods for self-adapting the semantic sensitivities in a recently proposed semantics-based crossover: Semantic Similarity based Crossover (SSC). The first self-adaptation method is inspired by a self-adaptive method for controlling mutation step size in Evolutionary Strategies (1/5 rule). The design of the second takes into account more of our previous experimental observations, that SSC works well only when a certain portion of events successfully exchange semantically similar subtrees. These two proposed methods are then tested on a number of real-valued symbolic regression problems, their performance being compared with SSC using predetermined sensitivities and with standard crossover. The results confirm the benefits of the second self-adaption method.

The main focus of this paper is to propose integration of dynamic and multiobjective algorithms for graph clustering in dynamic environments under multiple objectives. The primary application is to multiobjective clustering in social networks which change over time. Social networks, typically represented by graphs, contain information about the relations (or interactions) among online materials (or people). A typical social network tends to expand over time, with newly added nodes and edges being incorporated into the existing graph. We reflect these characteristics of social networks based on real-world data, and propose a suitable dynamic multiobjective evolutionary algorithm. Several variants of the algorithm are proposed and compared. Since social networks change continuously, the immigrant schemes effectively used in previous dynamic optimisation give useful ideas for new algorithms. An adaptive integration of multiobjective evolutionary algorithms outperformed other algorithms in dynamic social networks.

This paper investigates the role of semantic diversity and locality of crossover operators in. Genetic Programming (GP) for Boolean problems. We propose methods for measuring and storing semantics of subtrees in Boolean domains using Trace Semantics, and design several new crossovers on this basis. They can be categorised into two classes depending on their purposes: promoting semantic diversity or improving semantic locality. We test the operators on several well-known Boolean problems, comparing them with Standard GP Crossovers and with the Semantic Driven Crossover of Beadle and Johnson. The experimental results show the positive effects both of promoting semantic diversity, and of improving semantic locality, in crossover operators. They also show that the latter has a greater positive effect on GP performance than the former.

In this paper, we propose a new heuristic, called Center-Based Recursive Clustering - CBRC, for solving the bounded diameter minimum spanning tree (BDMST) problem. Our proposed hybrid genetic algorithm [12] is also extended to include the new heuristic and a multi-parent crossover operator. We test the new heuristic and genetic algorithm on two sets of benchmark problem instances for the Euclidean and Non-Euclidean cases. Experimental results show the effectiveness of the proposed heuristic and genetic algorithm.

In this paper, we investigate the value of a new selection mechanism that is inspired from biochemistry, namely, vesicular selection. We test its effectiveness when used in evolutionary algorithms on a number of benchmark problems in both static and dynamic environments. The results suggest beneficial attributes for the new selection mechanism.

Shin et al [19] and McKay et al [15] previously applied tree compression and semantics-based simplification to study the distribution of building blocks in evolving Genetic Programming populations. However their method could only give static estimates of the degree of repetition of building blocks in one generation at a time, supplying no information about the flow of building blocks between generations. Here, we use a state-of-the-art tree compression algorithm, xmlppm, to estimate the extent to which frequent building blocks from one generation are still in use in a later generation. While they compared the behaviour of different GP algorithms on one specific problem -- a simple symbolic regression problem -- we extend the analysis to a more complex problem, a symbolic regression problem to find a Fourier approximation to a sawtooth wave, and to a Boolean domain, odd parity.

Ant-based clustering methods have received significant attention as robust methods for clustering. Most ant-based algorithms use local density as a metric for determining the ants' propensities to pick up or deposit a data item; however, a number of authors in classical clustering methods have pointed out the advantages of entropy-based metrics for clustering. We introduced an entropy metric into an ant-based clustering algorithm and compared it with other closely related algorithms using local density. The results strongly support the value of entropy metrics, obtaining faster and more accurate results. Entropy governs the pickup and drop behaviors, while movement is guided by the density gradient. Entropy measures also require fewer training parameters than density-based clustering. The remaining parameters are subjected to robustness studies, and a detailed analysis is performed. In the second phase of the study, we further investigated Ramos and Abraham's (In: Proc 2003 IEEE Congr Evol Comput, Hoboken, NJ: IEEE Press; 2003. pp 1370–1375) contention that ant-based methods are particularly suited to incremental clustering. Contrary to expectations, we did not find substantial differences between the efficiencies of incremental and nonincremental approaches to data clustering. © 2009 Wiley Periodicals, Inc.

In this paper, a new hybrid genetic algorithm - known as HGA - is proposed for solving the Bounded Diameter Minimum Spanning Tree (BDMST) problem. We experiment with HGA on two sets of benchmark problem instances, both Euclidean and Non-Euclidean. On the Euclidean problem instances, HGA is shown to outperform the previous best two Genetic Algorithms (GAs) reported in the BDMST literature, while on the Non-Euclidean problem instance, HGA performs comparably with these two GAs.

In most real-world problems, we either know little about the problems or the problems are too complex to have a clear vision on how to decompose them by hand. Thus, it is usually desirable to have a method to automatically decompose a complex problem into a set of subproblems and assign one or more specialists to each subproblem. Thecooperative coevolutionary mixture of experts(CCME) model was designed to automatically decompose problems by combining the global optimization power of cooperative coevolution with the divide-and-conquer ability of mixture of experts. This paper analyzes how CCME decomposes complex classification problems through a principal-component-analysis-based visualization tool. The visualization shows that CCME decomposes the problem by driving different experts toward different regions of the input space. The paper also investigates the effect of regularization, usinglearning by forgetting(LF), on CCME. LF significantly reduces the structural complexity of CCME while maintaining the classification accuracy.

Compression algorithms generate a predictive model of data, using the model to reduce the number of bits required to transmit the data (in effect, transmitting only the differences from the model). As a consequence, the degree of compression achieved provides an estimate of the level of regularity in the data. Previous work has investigated the use of these estimates to understand the replication of building blocks within genetic programming (GP) individuals, and hence to understand how different GP algorithms promote the evolution of repeated common structure within individuals. Here, we extend this work to the population level, and use it to understand the extent of similarity between sub-structures within individuals in GP populations.

In this paper, we investigate the use of some wel-known randomised low-discrepancy sequences (Halton, Sobol, and Faure sequences) for initialising particle swarms. We experimented with the standard global-best particle swarm algorithm for function optimization on some benchmark problems, using randomised low-discrepancy sequences for initialisation, and the results were compared with the same particle swarm algorithm using uniform initialisation with a pseudo-random generator. The results show that, the former initialisation method could help the particle swarm algorithm improve its performance over the latter on the problems tried. Furthermore the comparisons also indicate that the use of different randomised low-discrepancy sequences in the initialisation phase could bring different effects on the performance of PSO.

We initialize a global-best particle swarm with a Halton sequence, comparing it with uniform initialization on a range of benchmark function optimization problems. We see substantial improvements in performance, particularly with high complexity problems /small populations. Halton initialization yields equivalent performance to uniform initialization with substantially smaller populations.

In this paper, we show some experimental results using Incremental Evaluation with Tree Adjoining Grammar Guided Genetic Programming (DEVTAG) on two symbolic regression problems, a benchmark polynomial fitting problem in genetic programming, and a Fourier series problem (sawtooth problem). In our pilot study, we compare results with standard Genetic Programming (GP) and the original Tree Adjoining Grammar Guided Genetic Programming (TAG3P). Our results on the two problems are good, outperforming both standard GP and the original TAG3P.

In this paper, we describe a new test problem for genetic programming (GP), ORDERTREE. We argue that it is a natural analogue of ONEMAX, a popular GA test problem, and that it also avoids some of the known weaknesses of other benchmark problems for Genetic Programming. Through experiments, we show that the difficulty of the problem can be tuned not only by increasing the size of the problem, but also by increasing the non-linearity in the fitness structure.

Standard tree-based genetic programming suffers from a structural difficulty problem in that it is unable to search effectively for solutions requiring very full or very narrow trees. This deficiency has been variously explained as a consequence of restrictions imposed by the tree structure or as a result of the numerical distribution of tree shapes. We show that by using a different tree-based representation and local (insertion and deletion) structural modification operators, that this problem can be almost eliminated even with trivial (stochastic hill-climbing) search methods, thus eliminating the above explanations. We argue, instead, that structural difficulty is a consequence of the large step size of the operators in standard genetic programming, which is itself a consequence of the fixed-arity property embodied in its representation.

Dynamic optimisation problems are becoming increasingly important; meanwhile, progress in optimisation techniques and in computational resources are permitting the development of effective systems for dynamic optimisation, resulting in a need for objective methods to evaluate and compare different techniques. The search for effective techniques may be seen as a multi-objective problem, trading off time complexity against effectiveness; hence benchmarks must be able to compare techniques across the Pareto front, not merely at a single point. We propose benchmarks for the dynamic travelling salesman problem, adapted from the CHN-144 benchmark of 144 Chinese cities for the static travelling salesman problem. We provide an example of the use of the benchmark, and illustrate the information that can be gleaned from analysis of the algorithm performance on the benchmarks.

In evolutionary computation, genetic operators, such as mutation and crossover, are employed to perturb individuals to generate the next population. However these fixed, problem independent genetic operators may destroy the sub-solution, usually called building blocks, instead of discovering and preserving them. One way to overcome this problem is to build a model based on the good individuals, and sample this model to obtain the next population. There is a wide range of such work in genetic algorithms; but because of the complexity of the genetic programming (GP) tree representation, little work of this kind has been done in GP. In this paper, we propose a new method, grammar model-based program evolution (GMPE) to evolved GP program. We replace common GP genetic operators with a probabilistic context-free grammar (SCFG). In each generation, an SCFG is learnt, and a new population is generated by sampling this SCFG model. On two benchmark problems we have studied, GMPE significantly outperforms conventional GP, learning faster and more reliably.

We present a boosting genetic algorithm for classification rule discovery. The method is based on the iterative rule learning approach to genetic classifiers. The boosting mechanism increases the weight of those training instances that are not classified correctly by the new rules, so that in the next iteration the algorithm focuses the search on those rules that capture the misclassified or uncovered instances. We show that the boosted genetic classifier has higher accuracy for prediction, or from an alternative and perhaps more important perspective, uses less computational resources for similar accuracy, than the original genetic classifier.

In genetic programming (GP) and most other evolutionary computing approaches, the knowledge learned during the evolutionary processing is implicitly encoded in the population. A small family of approaches, known as estimation of distribution algorithms, learn this knowledge directly in the form of probability distributions. In this research, we proposed a new approach for program synthesis - program evolution with explicit learning (PEEL), belonging to this family. PEEL learns probability distributions from previous generations and stochastically generates new populations according to this distribution. PEEL is intrinsically different from GP systems because it abandons conventional GP genetic operators and does not maintain population. On the benchmark problems we have studied, this approach shows at least comparable performance to GP.

The computer defense immune system (GDIS) is an artificial immune system for detecting computer viruses and network intrusions. We present a simple chromosome-based evaluation model for GDIS. In this model, the genotype space is a linear number sequence, and a digital pattern sequence is produced as the phenotype space using a number of mechanisms, including pattern mining and genetic algorithms. We present a range of experiment analyses to show the higher efficiency and stronger immunity of this model, improving the rate of successful prediction in intrusion detection in GDIS. The detectors generated may have higher coverage, hence would impose lower communications and computational loads on systems in which they were incorporated.

Genetic programming (GP) plays the primary role in the discovery of programs through evolving the program's set of parse trees. We present a new technique for constructing programs through ant colony optimization (ACO) using the tree adjunct grammar (TAG) formalism. We call the method AntTAG and we show that the results are very promising.

In this paper, we show some experimental results of tree-adjunct grammar-guided genetic programming (TAG3P) on the symbolic regression problem, a benchmark problem in genetic programming. We compare the results with genetic programming (GP) and grammar-guided genetic programming (GGGP). The results show that TAG3P significantly outperforms GP and GGGP on the target functions attempted in terms of the probability of success. Moreover, TAG3P still performed well when the structural complexity of the target function was scaled up.

The paper investigates the use of partial functions in genetic programming. Previous work (R.I. McKay, 2000), has shown that the convergent behaviour of populations of partial functions is very similar to that of populations of total functions. However the convergence rates of populations of partial functions have been slower. The results presented demonstrate a significant improvement in the rate of convergence of populations of partial functions, and indicate that partial functions represent a realistic alternative to total functions for a range of problems.