Enabled by the emerging industrial agent (IA) technology, swarm intelligence (SI) is envisaged to play an important role in future industrial Internet of Things (IIoT) that is shaped by Sixth Generation (6G) mobile communications and digital twin (DT). However, its fragility against data injection attack may halt it from practical deployment. In this paper we propose an efficient trust approach to address this security concern for SI.

Conventionally, federated learning aims to optimize a single objective, typically the utility. However, for a federated learning system to be trustworthy, it needs to simultaneously satisfy multiple/many objectives, such as maximizing model performance, minimizing privacy leakage and training cost, and being robust to malicious attacks. Multi-Objective Optimization (MOO) aiming to optimize multiple conflicting objectives at the same time is quite suitable for solving the optimization problem of Trustworthy Federated Learning (TFL). In this paper, we unify MOO and TFL by formulating the problem of constrained multi-objective federated learning (CMOFL). Under this formulation, existing MOO algorithms can be adapted to TFL straightforwardly. Different from existing CMOFL works focusing on utility, efficiency, fairness, and robustness, we consider optimizing privacy leakage along with utility loss and training cost, the three primary objectives of a TFL system. We develop two improved CMOFL algorithms based on NSGA-II and PSL, respectively, for effectively and efficiently finding Pareto optimal solutions, and we provide theoretical analysis on their convergence. We design specific measurements of privacy leakage, utility loss, and training cost for three privacy protection mechanisms: Randomization, BatchCrypt (An efficient version of homomorphic encryption), and Sparsification. Empirical experiments conducted under each of the three protection mechanisms demonstrate the effectiveness of our proposed algorithms.

Evolutionary algorithms are known to be robust to noise in the evaluation of the fitness. In particular, larger offspring population sizes often lead to strong robustness. We analyze to what extent the $(1+(\lambda,\lambda))$ genetic algorithm is robust to noise. This algorithm also works with larger offspring population sizes, but an intermediate selection step and a non-standard use of crossover as repair mechanism could render this algorithm less robust than, e.g., the simple $(1+\lambda)$ evolutionary algorithm. Our experimental analysis on several classic benchmark problems shows that this difficulty does not arise. Surprisingly, in many situations this algorithm is even more robust to noise than the $(1+\lambda)$~EA.

Stable or metastable crystal structures of assembled atoms can be predicted by finding the global or local minima of the energy surface with respect to the atomic configurations. Generally, this requires repeated first-principles energy calculations that are impractical for large systems, such as those containing more than 30 atoms in the unit cell. Here, we have made significant progress in solving the crystal structure prediction problem with a simple but powerful machine-learning workflow; using a machine-learning surrogate for first-principles energy calculations, we performed non-iterative, single-shot screening using a large library of virtually created crystal structures. The present method relies on two key technical components: transfer learning, which enables a highly accurate energy prediction of pre-relaxed crystalline states given only a small set of training samples from first-principles calculations, and generative models to create promising and diverse crystal structures for screening. Here, first-principles calculations were performed only to generate the training samples, and for the optimization of a dozen or fewer finally narrowed-down crystal structures. Our shotgun method was more than 5--10 times less computationally demanding and achieved an outstanding prediction accuracy that was 2--6 times higher than that of the conventional methods that rely heavily on iterative first-principles calculations.

PySR is an open-source library for practical symbolic regression, a type of machine learning which aims to discover human-interpretable symbolic models. PySR was developed to democratize and popularize symbolic regression for the sciences, and is built on a high-performance distributed back-end, a flexible search algorithm, and interfaces with several deep learning packages. PySR's internal search algorithm is a multi-population evolutionary algorithm, which consists of a unique evolve-simplify-optimize loop, designed for optimization of unknown scalar constants in newly-discovered empirical expressions. PySR's backend is the extremely optimized Julia library SymbolicRegression.jl, which can be used directly from Julia. It is capable of fusing user-defined operators into SIMD kernels at runtime, performing automatic differentiation, and distributing populations of expressions to thousands of cores across a cluster. In describing this software, we also introduce a new benchmark, "EmpiricalBench," to quantify the applicability of symbolic regression algorithms in science. This benchmark measures recovery of historical empirical equations from original and synthetic datasets.

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.