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Here we report first results of applying Genetic Programming to obtain equations for constructing reduced-order models of quantum systems, with a particular interest in nuclear Density Functional Theory. We employ the reduced basis method to obtain reduced coordinates as the amplitudes of the reduced basis, and use genetic programming to avoid the need of constructing the reduced equations through, for example, a Galerkin projection. The resulting reduced-order models show excellent performance in both accuracy and speed, including for extrapolations in the control parameters, and show promise as an effective method for emulating computationally demanding calculations in Nuclear Physics

Existing genetic programming (GP) methods are typically designed based on a certain representation, such as tree-based or linear representations. These representations show various pros and cons in different domains. However, due to the complicated relationships among representation and fitness landscapes of GP, it is hard to intuitively determine which GP representation is the most suitable for solving a certain problem. Evolving programs (or models) with multiple representations simultaneously can alternatively search on different fitness landscapes since representations are highly related to the search space that essentially defines the fitness landscape. Fully using the latent synergies among different GP individual representations might be helpful for GP to search for better solutions. However, existing GP literature rarely investigates the simultaneous effective use of evolving multiple representations. To fill this gap, this paper proposes a multi-representation GP algorithm based on tree-based and linear representations, which are two commonly used GP representations. In addition, we develop a new cross-representation crossover operator to harness the interplay between tree-based and linear representations. Empirical results show that navigating the learned knowledge between basic tree-based and linear representations successfully improves the effectiveness of GP with solely tree-based or linear representation in solving symbolic regression and dynamic job shop scheduling problems.

Sharpness-Aware Minimization (SAM) was recently introduced as a regularization procedure for training deep neural networks. It simultaneously minimizes the fitness (or loss) function and the so-called fitness sharpness. The latter serves as a measure of the nonlinear behavior of a solution and does so by finding solutions that lie in neighborhoods having uniformly similar loss values across all fitness cases. In this contribution, we adapt SAM for tree Genetic Programming (TGP) by exploring the semantic neighborhoods of solutions using two simple approaches. By capitalizing upon perturbing input and output of program trees, sharpness can be estimated and used as a second optimization criterion during the evolution. To better understand the impact of this variant of SAM on TGP, we collect numerous indicators of the evolutionary process, including generalization ability, complexity, diversity, and a recently proposed genotype-phenotype mapping to study the amount of redundancy in trees. The experimental results demonstrate that using any of the two proposed SAM adaptations in TGP allows (i) a significant reduction of tree sizes in the population and (ii) a decrease in redundancy of the trees. When assessed on real-world benchmarks, the generalization ability of the elite solutions does not deteriorate., Comment: Submitted to the Genetic Programming Theory and Practice workshop 2024

In recent years, genetic programming (GP)-based evolutionary feature construction has achieved significant success. However, a primary challenge with evolutionary feature construction is its tendency to overfit the training data, resulting in poor generalization on unseen data. In this research, we draw inspiration from PAC-Bayesian theory and propose using sharpness-aware minimization in function space to discover symbolic features that exhibit robust performance within a smooth loss landscape in the semantic space. By optimizing sharpness in conjunction with cross-validation loss, as well as designing a sharpness reduction layer, the proposed method effectively mitigates the overfitting problem of GP, especially when dealing with a limited number of instances or in the presence of label noise. Experimental results on 58 real-world regression datasets show that our approach outperforms standard GP as well as six state-of-the-art complexity measurement methods for GP in controlling overfitting. Furthermore, the ensemble version of GP with sharpness-aware minimization demonstrates superior performance compared to nine fine-tuned machine learning and symbolic regression algorithms, including XGBoost and LightGBM., Comment: Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence

In this contribution, we discuss the basic concepts of genotypes and phenotypes in tree-based GP (TGP), and then analyze their behavior using five benchmark datasets. We show that TGP exhibits the same behavior that we can observe in other GP representations: At the genotypic level trees show frequently unchecked growth with seemingly ineffective code, but on the phenotypic level, much smaller trees can be observed. To generate phenotypes, we provide a unique technique for removing semantically ineffective code from GP trees. The approach extracts considerably simpler phenotypes while not being limited to local operations in the genotype. We generalize this transformation based on a problem-independent parameter that enables a further simplification of the exact phenotype by coarse-graining to produce approximate phenotypes. The concept of these phenotypes (exact and approximate) allows us to clarify what evolved solutions truly predict, making GP models considered at the phenotypic level much better interpretable.

Autonomous robots deployed in the real world will need control policies that rapidly adapt to environmental changes. To this end, we propose AutoRobotics-Zero (ARZ), a method based on AutoML-Zero that discovers zero-shot adaptable policies from scratch. In contrast to neural network adaptation policies, where only model parameters are optimized, ARZ can build control algorithms with the full expressive power of a linear register machine. We evolve modular policies that tune their model parameters and alter their inference algorithm on-the-fly to adapt to sudden environmental changes. We demonstrate our method on a realistic simulated quadruped robot, for which we evolve safe control policies that avoid falling when individual limbs suddenly break. This is a challenging task in which two popular neural network baselines fail. Finally, we conduct a detailed analysis of our method on a novel and challenging non-stationary control task dubbed Cataclysmic Cartpole. Results confirm our findings that ARZ is significantly more robust to sudden environmental changes and can build simple, interpretable control policies., Comment: Published and Best Overall Paper Finalist at International Conference on Intelligent Robots and Systems (IROS) 2023. See https://youtu.be/sEFP1Hay4nE for associated video file

This paper examines various methods of computing uncertainty and diversity for active learning in genetic programming. We found that the model population in genetic programming can be exploited to select informative training data points by using a model ensemble combined with an uncertainty metric. We explored several uncertainty metrics and found that differential entropy performed the best. We also compared two data diversity metrics and found that correlation as a diversity metric performs better than minimum Euclidean distance, although there are some drawbacks that prevent correlation from being used on all problems. Finally, we combined uncertainty and diversity using a Pareto optimization approach to allow both to be considered in a balanced way to guide the selection of informative and unique data points for training.

Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and phenotypic spaces, especially through neutral mutations, helps us to better understand the progression of evolution and its algorithmic behaviour. In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution.

Gene Regulatory Networks are networks of interactions in biological organisms responsible for determining the production levels of proteins and peptides. Proteins are workers of a cell factory, and their production defines the goal of a cell and its development. Various attempts have been made to model such networks both to understand these biological systems better and to use inspiration from understanding them to solve computational problems. In this work, a biologically more realistic model for gene regulatory networks is proposed, which incorporates Cellular Automata and Artificial Chemistry to model the interactions between regulatory proteins called the Transcription Factors and the regulatory sites of genes. The result of this work shows complex dynamics close to what can be observed in nature. Here, an analysis of the impact of the initial states of the system on the produced dynamics is performed, showing that such evolvable models can be directed towards producing desired protein dynamics., Comment: 20, pages, 12 figures

The use of correlation as a fitness function is explored in symbolic regression tasks and the performance is compared against the typical RMSE fitness function. Using correlation with an alignment step to conclude the evolution led to significant performance gains over RMSE as a fitness function. Using correlation as a fitness function led to solutions being found in fewer generations compared to RMSE, as well it was found that fewer data points were needed in the training set to discover the correct equations. The Feynman Symbolic Regression Benchmark as well as several other old and recent GP benchmark problems were used to evaluate performance., Comment: Submitted to the GPTP conference

Genetic improvement is a search technique that aims to improve a given acceptable solution to a problem. In this paper, we present the novel use of genetic improvement to find problem-specific optimized LLVM pass sequences. We develop a pass-level patch representation in the linear genetic programming framework, Shackleton, to evolve the modifications to be applied to the default optimization pass sequences. Our GI-evolved solution has a mean of 3.7% runtime improvement compared to the -O3 optimization level in the default code generation options which optimizes on runtime. The proposed GI method provides an automatic way to find a problem-specific optimization sequence that improves upon a general solution without any expert domain knowledge. In this paper, we discuss the advantages and limitations of the GI feature in the Shackleton Framework and present our results., Comment: 3 pages, 2 figures

Program synthesis aims to {\it automatically} find programs from an underlying programming language that satisfy a given specification. While this has the potential to revolutionize computing, how to search over the vast space of programs efficiently is an unsolved challenge in program synthesis. In cases where large programs are required for a solution, it is generally believed that {\it stochastic} search has advantages over other classes of search techniques. Unfortunately, existing stochastic program synthesizers do not meet this expectation very well, suffering from the scalability issue. Here we propose a new framework for stochastic program synthesis, called iterative genetic improvement to overcome this problem, a technique inspired by the practice of the software development process. The key idea of iterative genetic improvement is to apply genetic improvement to improve a current reference program, and then iteratively replace the reference program by the best program found. Compared to traditional stochastic synthesis approaches, iterative genetic improvement can build up the complexity of programs incrementally in a more robust way. We evaluate the approach on two program synthesis domains: list manipulation and string transformation. Our empirical results indicate that this method has considerable advantages over several representative stochastic program synthesizer techniques, both in terms of scalability and of solution quality., Comment: 18 pages, 10 figures, 16 tables

In this paper we introduce an active learning method for symbolic regression using StackGP. The approach begins with a small number of data points for StackGP to model. To improve the model the system incrementally adds a data point such that the new point maximizes prediction uncertainty as measured by the model ensemble. Symbolic regression is re-run with the larger data set. This cycle continues until the system satisfies a termination criterion. We use the Feynman AI benchmark set of equations to examine the ability of our method to find appropriate models using fewer data points. The approach was found to successfully rediscover 72 of the 100 Feynman equations using as few data points as possible, and without use of domain expertise or data translation., Comment: 8 page, 1 figure. Submitted to GECCO-2022

Protein engineers conventionally use tools such as Directed Evolution to find new proteins with better functionalities and traits. More recently, computational techniques and especially machine learning approaches have been recruited to assist Directed Evolution, showing promising results. In this paper, we propose POET, a computational Genetic Programming tool based on evolutionary computation methods to enhance screening and mutagenesis in Directed Evolution and help protein engineers to find proteins that have better functionality. As a proof-of-concept we use peptides that generate MRI contrast detected by the Chemical Exchange Saturation Transfer contrast mechanism. The evolutionary methods used in POET are described, and the performance of POET in different epochs of our experiments with Chemical Exchange Saturation Transfer contrast are studied. Our results indicate that a computational modelling tool like POET can help to find peptides with 400% better functionality than used before., Comment: 23 pages, 8 figures and 4 tables

In this paper we introduce Shackleton as a generalized framework enabling the application of linear genetic programming -- a technique under the umbrella of evolutionary algorithms -- to a variety of use cases. We also explore here a novel application for this class of methods: optimizing sequences of LLVM optimization passes. The algorithm underpinning Shackleton is discussed, with an emphasis on the effects of different features unique to the framework when applied to LLVM pass sequences. Combined with analysis of different hyperparameter settings, we report the results on automatically optimizing pass sequences using Shackleton for two software applications at differing complexity levels. Finally, we reflect on the advantages and limitations of our current implementation and lay out a path for further improvements. These improvements aim to surpass hand-crafted solutions with an automatic discovery method for an optimal pass sequence., Comment: 11 pages (with references), 14 figures, 8 tables

A fundamental aspect of behaviour is the ability to encode salient features of experience in memory and use these memories, in combination with current sensory information, to predict the best action for each situation such that long-term objectives are maximized. The world is highly dynamic, and behavioural agents must generalize across a variety of environments and objectives over time. This scenario can be modeled as a partially-observable multi-task reinforcement learning problem. We use genetic programming to evolve highly-generalized agents capable of operating in six unique environments from the control literature, including OpenAI's entire Classic Control suite. This requires the agent to support discrete and continuous actions simultaneously. No task-identification sensor inputs are provided, thus agents must identify tasks from the dynamics of state variables alone and define control policies for each task. We show that emergent hierarchical structure in the evolving programs leads to multi-task agents that succeed by performing a temporal decomposition and encoding of the problem environments in memory. The resulting agents are competitive with task-specific agents in all six environments. Furthermore, the hierarchical structure of programs allows for dynamic run-time complexity, which results in relatively efficient operation.

Efficient optimization of resources is paramount to success in many problems faced today. In the field of operational research the efficient scheduling of employees; packing of vans; routing of vehicles; logistics of airlines and transport of materials can be the difference between emission reduction or excess, profits or losses and feasibility or unworkable solutions. The video game Factorio, by Wube Software, has a myriad of problems which are analogous to such real-world problems, and is a useful simulator for developing solutions for these problems. In this paper we define the logistic transport belt problem and define mathematical integer programming model of it. We developed an interface to allow optimizers in any programming language to interact with Factorio, and we provide an initial benchmark of logistic transport belt problems. We present results for Simulated Annealing, quick Genetic Programming and Evolutionary Reinforcement Learning, three different meta-heuristic techniques to optimize this novel problem., Comment: Submitted to GECCO 2021

In this paper, we propose an efficient NAS algorithm for generating task-specific models that are competitive under multiple competing objectives. It comprises of two surrogates, one at the architecture level to improve sample efficiency and one at the weights level, through a supernet, to improve gradient descent training efficiency. On standard benchmark datasets (C10, C100, ImageNet), the resulting models, dubbed NSGANetV2, either match or outperform models from existing approaches with the search being orders of magnitude more sample efficient. Furthermore, we demonstrate the effectiveness and versatility of the proposed method on six diverse non-standard datasets, e.g. STL-10, Flowers102, Oxford Pets, FGVC Aircrafts etc. In all cases, NSGANetV2s improve the state-of-the-art (under mobile setting), suggesting that NAS can be a viable alternative to conventional transfer learning approaches in handling diverse scenarios such as small-scale or fine-grained datasets. Code is available at https://github.com/mikelzc1990/nsganetv2, Comment: Accepted for oral presentation at ECCV 2020

We consider a number of Artificial Chemistry models for economic activity and what consequences they have for the formation of economic inequality. We are particularly interested in what tax measures are effective in dampening economic inequality. By starting from well-known kinetic exchange models, we examine different scenarios for reducing the tendency of economic activity models to form unequal wealth distribution in equilibrium., Comment: 13 pages, 18 figures

The complexity of cooperative behavior is a crucial issue in multiagent-based social simulation. In this paper, an agent-based model is proposed to study the evolution of cooperative hunting behaviors in an artificial society. In this model, the standard hunting game of stag is modified into a new situation with social hierarchy and penalty. The agent society is divided into multiple layers with supervisors and subordinates. In each layer, the society is divided into multiple clusters. A supervisor controls all subordinates in a cluster locally. Subordinates interact with rivals through reinforcement learning, and report learning information to their corresponding supervisor. Supervisors process the reported information through repeated affiliation-based aggregation and by information exchange with other supervisors, then pass down the reprocessed information to subordinates as guidance. Subordinates, in turn, update learning information according to guidance, following the "win stay, lose shift" strategy. Experiments are carried out to test the evolution of cooperation in this closed-loop semi-supervised emergent system with different parameters. We also study the variations and phase transitions in this game setting., Comment: Conflict of interest with our previous collaborators. Thus, we retract the preprint. We retract all earlier versions of the paper as well, but due to the arXiv policy, previous versions cannot be removed. We ask that you ignore the abstract, earlier versions and do not refer to or distribute them further, and we apologize for any inconvenience caused. Thanks

Neural architecture search (NAS) has emerged as a promising avenue for automatically designing task-specific neural networks. Existing NAS approaches require one complete search for each deployment specification of hardware or objective. This is a computationally impractical endeavor given the potentially large number of application scenarios. In this paper, we propose Neural Architecture Transfer (NAT) to overcome this limitation. NAT is designed to efficiently generate task-specific custom models that are competitive under multiple conflicting objectives. To realize this goal we learn task-specific supernets from which specialized subnets can be sampled without any additional training. The key to our approach is an integrated online transfer learning and many-objective evolutionary search procedure. A pre-trained supernet is iteratively adapted while simultaneously searching for task-specific subnets. We demonstrate the efficacy of NAT on 11 benchmark image classification tasks ranging from large-scale multi-class to small-scale fine-grained datasets. In all cases, including ImageNet, NATNets improve upon the state-of-the-art under mobile settings ($\leq$ 600M Multiply-Adds). Surprisingly, small-scale fine-grained datasets benefit the most from NAT. At the same time, the architecture search and transfer is orders of magnitude more efficient than existing NAS methods. Overall, the experimental evaluation indicates that, across diverse image classification tasks and computational objectives, NAT is an appreciably more effective alternative to conventional transfer learning of fine-tuning weights of an existing network architecture learned on standard datasets. Code is available at https://github.com/human-analysis/neural-architecture-transfer, Comment: Code is available at https://github.com/human-analysis/neural-architecture-transfer

The present and future of evolutionary algorithms depends on the proper use of modern parallel and distributed computing infrastructures. Although still sequential approaches dominate the landscape, available multi-core, many-core and distributed systems will make users and researchers to more frequently deploy parallel version of the algorithms. In such a scenario, new possibilities arise regarding the time saved when parallel evaluation of individuals are performed. And this time saving is particularly relevant in Genetic Programming. This paper studies how evaluation time influences not only time to solution in parallel/distributed systems, but may also affect size evolution of individuals in the population, and eventually will reduce the bloat phenomenon GP features. This paper considers time and space as two sides of a single coin when devising a more natural method for fighting bloat. This new perspective allows us to understand that new methods for bloat control can be derived, and the first of such a method is described and tested. Experimental data confirms the strength of the approach: using computing time as a measure of individuals' complexity allows to control the growth in size of genetic programming individuals.

Early advancements in convolutional neural networks (CNNs) architectures are primarily driven by human expertise and by elaborate design processes. Recently, neural architecture search was proposed with the aim of automating the network design process and generating task-dependent architectures. While existing approaches have achieved competitive performance in image classification, they are not well suited to problems where the computational budget is limited for two reasons: (1) the obtained architectures are either solely optimized for classification performance, or only for one deployment scenario; (2) the search process requires vast computational resources in most approaches. To overcome these limitations, we propose an evolutionary algorithm for searching neural architectures under multiple objectives, such as classification performance and floating-point operations (FLOPs). The proposed method addresses the first shortcoming by populating a set of architectures to approximate the entire Pareto frontier through genetic operations that recombine and modify architectural components progressively. Our approach improves computational efficiency by carefully down-scaling the architectures during the search as well as reinforcing the patterns commonly shared among past successful architectures through Bayesian model learning. The integration of these two main contributions allows an efficient design of architectures that are competitive and in most cases outperform both manually and automatically designed architectures on benchmark image classification datasets: CIFAR, ImageNet, and human chest X-ray. The flexibility provided from simultaneously obtaining multiple architecture choices for different compute requirements further differentiates our approach from other methods in the literature. Code is available at https://github.com/mikelzc1990/nsganetv1, Comment: Published in IEEE Transactions on Evolutionary Computation, 23 pages

Lexicase selection achieves very good solution quality by introducing ordered test cases. However, the computational complexity of lexicase selection can prohibit its use in many applications. In this paper, we introduce Batch Tournament Selection (BTS), a hybrid of tournament and lexicase selection which is approximately one order of magnitude faster than lexicase selection while achieving a competitive quality of solutions. Tests on a number of regression datasets show that BTS compares well with lexicase selection in terms of mean absolute error while having a speed-up of up to 25 times. Surprisingly, BTS and lexicase selection have almost no difference in both diversity and performance. This reveals that batches and ordered test cases are completely different mechanisms which share the same general principle fostering the specialization of individuals. This work introduces an efficient algorithm that sheds light onto the main principles behind the success of lexicase, potentially opening up a new range of possibilities for algorithms to come.

This contribution argues that the notion of time used in the scientific modeling of reality deprives time of its real nature. Difficulties from logic paradoxes to mathematical incompleteness and numerical uncertainty ensue. How can the emergence of novelty in the Universe be explained? How can the creativity of the evolutionary process leading to ever more complex forms of life be captured in our models of reality? These questions are deeply related to our understanding of time. We argue here for a computational framework of modeling that seems to us the only currently known type of modeling available in Science able to capture aspects of the nature of time required to better model and understand real phenomena., Comment: 12 pages, book chapter

This paper introduces NSGA-Net -- an evolutionary approach for neural architecture search (NAS). NSGA-Net is designed with three goals in mind: (1) a procedure considering multiple and conflicting objectives, (2) an efficient procedure balancing exploration and exploitation of the space of potential neural network architectures, and (3) a procedure finding a diverse set of trade-off network architectures achieved in a single run. NSGA-Net is a population-based search algorithm that explores a space of potential neural network architectures in three steps, namely, a population initialization step that is based on prior-knowledge from hand-crafted architectures, an exploration step comprising crossover and mutation of architectures, and finally an exploitation step that utilizes the hidden useful knowledge stored in the entire history of evaluated neural architectures in the form of a Bayesian Network. Experimental results suggest that combining the dual objectives of minimizing an error metric and computational complexity, as measured by FLOPs, allows NSGA-Net to find competitive neural architectures. Moreover, NSGA-Net achieves error rate on the CIFAR-10 dataset on par with other state-of-the-art NAS methods while using orders of magnitude less computational resources. These results are encouraging and shows the promise to further use of EC methods in various deep-learning paradigms., Comment: GECCO 2019

Recent empirical studies show that the performance of GenProg is not satisfactory, particularly for Java. In this paper, we propose ARJA, a new GP based repair approach for automated repair of Java programs. To be specific, we present a novel lower-granularity patch representation that properly decouples the search subspaces of likely-buggy locations, operation types and potential fix ingredients, enabling GP to explore the search space more effectively. Based on this new representation, we formulate automated program repair as a multi-objective search problem and use NSGA-II to look for simpler repairs. To reduce the computational effort and search space, we introduce a test filtering procedure that can speed up the fitness evaluation of GP and three types of rules that can be applied to avoid unnecessary manipulations of the code. Moreover, we also propose a type matching strategy that can create new potential fix ingredients by exploiting the syntactic patterns of the existing statements. We conduct a large-scale empirical evaluation of ARJA along with its variants on both seeded bugs and real-world bugs in comparison with several state-of-the-art repair approaches. Our results verify the effectiveness and efficiency of the search mechanisms employed in ARJA and also show its superiority over the other approaches. In particular, compared to jGenProg (an implementation of GenProg for Java), an ARJA version fully following the redundancy assumption can generate a test-suite adequate patch for more than twice the number of bugs (from 27 to 59), and a correct patch for nearly four times of the number (from 5 to 18), on 224 real-world bugs considered in Defects4J. Furthermore, ARJA is able to correctly fix several real multi-location bugs that are hard to be repaired by most of the existing repair approaches., Comment: 30 pages, 26 figures