Since John Koza pioneered the paradigm of programming by means of natural selection, many applications for SR in scientific discovery have emerged [1]. Unlike other applications of machine learning techniques, scientific research demands explanation and verification, both of which are made more feasible by the generation of human-interpretable mathematical models (as opposed to fitting a model with thousands of parameters) [2-4]. Furthermore, SR can be effective even with very small datasets ( 10 items) such as those produced by difficult or expensive experiments which are not easily repeated. The mathematical expressions produced by SR can easily be extrapolated to untested or otherwise unreachable domains within a dataset (such as extreme pressures or temperatures). For decades, SR has discovered interesting models from data in many applications including inferring process models at the Dow Chemical Company [5], rainfall-runoff modeling [6], and rediscovering equations for double-pendulum motion [7]. Symbolic regression has been applied across all scales of scientific investigation, including the atomistic (interatomic potentials [8]), macroscopic (computational fluid dynamics [9]), and cosmological (dark matter overdensity [10]) scales. Some techniques facilitate search through billions of candidate expressions, such as the space of nonlinear descriptors of material properties [11]. While most applications of SR in science focus on identifying empirical patterns in data, such "data-only" approaches do not account for potential insights from background theory. In fact, some SR works emphasize their capabilities of discovery "without any prior knowledge about physics, kinematics, or geometry" [7].

In this work, we propose a novel evolutionary algorithm for neural architecture search, applicable to global search spaces. The algorithm's architectural representation organizes the topology in multiple hierarchical modules, while the design process exploits this representation, in order to explore the search space. We also employ a curation system, which promotes the utilization of well performing sub-structures to subsequent generations. We apply our method to Fashion-MNIST and NAS-Bench101, achieving accuracies of $93.2\%$ and $94.8\%$ respectively in a relatively small number of generations.

Metaheuristics are widely recognized gradient-free solvers to hard problems that do not meet the rigorous mathematical assumptions of conventional solvers. The automated design of metaheuristic algorithms provides an attractive path to relieve manual design effort and gain enhanced performance beyond human-made algorithms. However, the specific algorithm prototype and linear algorithm representation in the current automated design pipeline restrict the design within a fixed algorithm structure, which hinders discovering novelties and diversity across the metaheuristic family. To address this challenge, this paper proposes a general framework, AutoOpt, for automatically designing metaheuristic algorithms with diverse structures. AutoOpt contains three innovations: (i) A general algorithm prototype dedicated to covering the metaheuristic family as widely as possible. It promotes high-quality automated design on different problems by fully discovering potentials and novelties across the family. (ii) A directed acyclic graph algorithm representation to fit the proposed prototype. Its flexibility and evolvability enable discovering various algorithm structures in a single run of design, thus boosting the possibility of finding high-performance algorithms. (iii) A graph representation embedding method offering an alternative compact form of the graph to be manipulated, which ensures AutoOpt's generality. Experiments on numeral functions and real applications validate AutoOpt's efficiency and practicability.

Symbolic Regression (SR) is a rapidly growing subfield within machine learning (ML) to infer symbolic mathematical expressions from data [1, 2]. Interest in SR is being driven by the observation that it is not sufficient to only have accurate predictive models; however, it is often necessary that the learned models be interpretable [3]. A model is interpretable if the relationship between the input and output of the model can be logically or mathematically traced in a succinct manner. In other words, learnable models are interpretable if expressed as mathematical equations. As "disciplines" become increasingly data-rich and adopt ML techniques, the demand for interpretable models is likely to grow. For example, in the natural sciences (e.g., physics), mathematical models derived from first principles make it possible to reason about the underlying phenomenon in a way that is not possible with predictive models like deep neural networks. In critical disciplines like healthcare, non-interpretable models may never be allowed to be deployed - however accurate they maybe [4].

We develop a flexible Gaussian Process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming algorithm to search for the most expressive kernel for a given population. Our compositional search builds off the Age-Period-Cohort (APC) paradigm to construct a covariance prior best matching the spatio-temporal dynamics of a mortality dataset. We apply the resulting genetic algorithm (GA) on synthetic case studies to validate the ability of the GA to recover APC structure, and on real-life national-level datasets from the Human Mortality Database. Our machine-learning based analysis provides novel insight into the presence/absence of Cohort effects in different populations, and into the relative smoothness of mortality surfaces along the Age and Year dimensions. Our modelling work is done with the PyTorch libraries in Python and provides an in-depth investigation of employing GA to aid in compositional kernel search for GP surrogates.

We propose a new method based on discrete Fourier analysis to analyze the time evolutionary algorithms spend on plateaus. This immediately gives a concise proof of the classic estimate of the expected runtime of the $(1+1)$ evolutionary algorithm on the Needle problem due to Garnier, Kallel, and Schoenauer (1999). We also use this method to analyze the runtime of the $(1+1)$ evolutionary algorithm on a new benchmark consisting of $n/\ell$ plateaus of effective size $2^\ell-1$ which have to be optimized sequentially in a LeadingOnes fashion. Using our new method, we determine the precise expected runtime both for static and fitness-dependent mutation rates. We also determine the asymptotically optimal static and fitness-dependent mutation rates. For $\ell = o(n)$, the optimal static mutation rate is approximately $1.59/n$. The optimal fitness dependent mutation rate, when the first $k$ fitness-relevant bits have been found, is asymptotically $1/(k+1)$. These results, so far only proven for the single-instance problem LeadingOnes, thus hold for a much broader class of problems. We expect similar extensions to be true for other important results on LeadingOnes. We are also optimistic that our Fourier analysis approach can be applied to other plateau problems as well.

Prototyping robotic systems is a time consuming process. Computer aided design, however, might speed up the process significantly. Quality-diversity evolutionary approaches optimise for novelty as well as performance, and can be used to generate a repertoire of diverse designs. This design repertoire could be used as a tool to guide a designer and kick-start the rapid prototyping process. This paper explores this idea in the context of mechanical linkage based robots. These robots can be a good test-bed for rapid prototyping, as they can be modified quickly for swift iterations in design. We compare three evolutionary algorithms for optimising 2D mechanical linkages: 1) a standard evolutionary algorithm, 2) the multi-objective algorithm NSGA-II, and 3) the quality-diversity algorithm MAP-Elites. Some of the found linkages are then realized on a physical hexapod robot through a prototyping process, and tested on two different floors. We find that all the tested approaches, except the standard evolutionary algorithm, are capable of finding mechanical linkages that creates a path similar to a specified desired path. However, the quality-diversity approaches that had the length of the linkage as a behaviour descriptor were the most useful when prototyping. This was due to the quality-diversity approaches having a larger variety of similar designs to choose from, and because the search could be constrained by the behaviour descriptors to make linkages that were viable for construction on our hexapod platform.

Genome data are crucial in modern medicine, offering significant potential for diagnosis and treatment. Thanks to technological advancements, many millions of healthy and diseased genomes have already been sequenced; however, obtaining the most suitable data for a specific study, and specifically for validation studies, remains challenging with respect to scale and access. Therefore, in silico genomics sequence generators have been proposed as a possible solution. However, the current generators produce inferior data using mostly shallow (stochastic) connections, detected with limited computational complexity in the training data. This means they do not take the appropriate biological relations and constraints, that originally caused the observed connections, into consideration. To address this issue, we propose cancer-inspired genomics mapper model (CGMM), that combines genetic algorithm (GA) and deep learning (DL) methods to tackle this challenge. CGMM mimics processes that generate genetic variations and mutations to transform readily available control genomes into genomes with the desired phenotypes. We demonstrate that CGMM can generate synthetic genomes of selected phenotypes such as ancestry and cancer that are indistinguishable from real genomes of such phenotypes, based on unsupervised clustering. Our results show that CGMM outperforms four current state-of-the-art genomics generators on two different tasks, suggesting that CGMM will be suitable for a wide range of purposes in genomic medicine, especially for much-needed validation studies.

Designing protein sequences with desired biological function is crucial in biology and chemistry. Recent machine learning methods use a surrogate sequence-function model to replace the expensive wet-lab validation. How can we efficiently generate diverse and novel protein sequences with high fitness? In this paper, we propose IsEM-Pro, an approach to generate protein sequences towards a given fitness criterion. At its core, IsEM-Pro is a latent generative model, augmented by combinatorial structure features from a separately learned Markov random fields (MRFs). We develop an Monte Carlo Expectation-Maximization method (MCEM) to learn the model. During inference, sampling from its latent space enhances diversity while its MRFs features guide the exploration in high fitness regions. Experiments on eight protein sequence design tasks show that our IsEM-Pro outperforms the previous best methods by at least 55% on average fitness score and generates more diverse and novel protein sequences.

Genetic Algorithm (GA) is a popular meta-heuristic evolutionary algorithm that uses stochastic operators to find optimal solution and has proved its effectiveness in solving many complex optimization problems (such as classification, optimization, and scheduling). However, despite its performance, popularity and simplicity, not much attention has been paid towards reproducibility and reusability of GA. In this paper, we have extended Findable, Accessible, Interoperable and Reusable (FAIR) data principles to enable the reproducibility and reusability of algorithms. We have chosen GA as a usecase to the demonstrate the applicability of the proposed principles. Also we have presented an overview of methodological developments and variants of GA that makes it challenging to reproduce or even find the right source. Additionally, to enable FAIR algorithms, we propose a vocabulary (i.e. $evo$) using light weight RDF format, facilitating the reproducibility. Given the stochastic nature of GAs, this work can be extended to numerous Optimization and machine learning algorithms/methods.