Black-box optimisation is one of the important areas in optimisation. The original No Free Lunch (NFL) theorems highlight the limitations of traditional black-box optimisation and learning algorithms, serving as a theoretical foundation for traditional optimisation. No Free Lunch Analysis in adversarial (also called maximin) optimisation is a long-standing problem [45, 46]. This paper first rigorously proves a (NFL) Theorem for general black-box adversarial optimisation when considering Pure Strategy Nash Equilibrium (NE) as the solution concept.

Black-box optimisation is one of the important areas in optimisation.

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation trajectory as a function of the iterations, the proposed approach devises a surrogate version of the entire optimisation pipeline. First, the method predicts a quasi-optimal topology for a given problem configuration as a surrogate model of high-fidelity topologies optimised with the homogenisation method. This is achieved by means of a feed-forward net learning the mapping between the input parameters characterising the system setup and a latent space determined by encoder/decoder blocks reducing the dimensionality of the parametric topology optimisation problem and reconstructing a high-dimensional representation of the topology. Then, the predicted topology is used as an educated initial guess for a computationally efficient algorithm penalising the intermediate values of the design variable, while enforcing the governing equations of the system. This step allows the method to correct potential errors introduced by the surrogate model, eliminate artifacts, and refine the design in order to produce topologies consistent with the underlying physics. Different architectures are proposed and the approximation and generalisation capabilities of the resulting models are numerically evaluated. The quasi-optimal topologies allow to outperform the high-fidelity optimiser by reducing the average number of optimisation iterations by $53\%$ while achieving discrepancies below $4\%$ in the optimal value of the objective functional, even in the challenging scenario of testing the model to extrapolate beyond the training and validation domain.

Black-box optimisation is one of the important areas in optimisation. The original No Free Lunch (NFL) theorems highlight the limitations of traditional black-box optimisation and learning algorithms, serving as a theoretical foundation for traditional optimisation. No Free Lunch Analysis in adversarial (also called maximin) optimisation is a long-standing problem [45, 46]. This paper first rigorously proves a (NFL) Theorem for general black-box adversarial optimisation when considering Pure Strategy Nash Equilibrium (NE) as the solution concept. In particular, if Nash Equilibrium is considered as the solution concept and the cost of the algorithm is measured in terms of the number of columns and rows queried in the payoff matrix, then the average performance of all black-box adversarial optimisation algorithms is the same. Moreover, we first introduce black-box complexity to analyse the black-box adversarial optimisation algorithm.

In recent years, the field of machine learning has witnessed significant advancements, particularly in the development of optimisation algorithms that enhance the efficiency and effectiveness of training deep neural networks. Among these algorithms, the Adam optimiser has gained widespread popularity due to its adaptive learning rate capabilities, which enable more efficient convergence compared to traditional methods such as stochastic gradient descent. However, despite its advantages, Adam is not without its limitations, particularly when it comes to handling issues such as overshooting and stagnation during the training process. To address these challenges, we introduce AdamZ as an advanced variant of the Adam optimiser. AdamZ is specifically designed to dynamically adjust the learning rate responsive to the characteristics of the loss function, thereby improving both convergence stability and model accuracy. This novel optimiser integrates mechanisms to detect and mitigate overshooting, at the point where the optimiser has stepped too far into the parameter space, and stagnation at points, where progress has started to stall despite ongoing training. By introducing hyperparameters such as overshoot and stagnation factors, thresholds, and patience levels, AdamZ provides a more responsive approach to learning rate adaptation than obtained through Adam.

Heuristic optimisation algorithms explore the search space by sampling solutions, evaluating their fitness, and biasing the search in the direction of promising solutions. However, in many cases, this fitness function involves executing expensive computational calculations, drastically reducing the reasonable number of evaluations. In this context, surrogate models have emerged as an excellent alternative to alleviate these computational problems. This paper addresses the formulation of surrogate problems as both regression models that approximate fitness (surface surrogate models) and a novel way to connect classification models (pairwise surrogate models). The pairwise approach can be directly exploited by some algorithms, such as Differential Evolution, in which the fitness value is not actually needed to drive the search, and it is sufficient to know whether a solution is better than another one or not. Based on these modelling approaches, we have conducted a multidimensional analysis of surrogate models under different configurations: different machine learning algorithms (regularised regression, neural networks, decision trees, boosting methods, and random forests), different surrogate strategies (encouraging diversity or relaxing prediction thresholds), and compare them for both surface and pairwise surrogate models. The experimental part of the article includes the benchmark problems already proposed for the SOCO2011 competition in continuous optimisation and a simulation problem included in the recent GECCO2021 Industrial Challenge. This paper shows that the performance of the overall search, when using online machine learning-based surrogate models, depends not only on the accuracy of the predictive model but also on both the kind of bias towards positive or negative cases and how the optimisation uses those predictions to decide whether to execute the actual fitness function.

As AI solutions enter safety-critical products, the explainability and interpretability of solutions generated by AI products become increasingly important. In the long term, such explanations are the key to gaining users' acceptance of AI-based systems' decisions. We report on applying a model-driven-based optimisation to search for an interpretable and explainable policy that solves the game 2048. This paper describes a solution to the GECCO'24 Interpretable Control Competition using the open-source software EvoAl. We aimed to develop an approach for creating interpretable policies that are easy to adapt to new ideas.

For this paper, a prediction study of cloud computing energy consumption was conducted by optimising the data regression algorithm based on the horned lizard optimisation algorithm for Convolutional Neural Networks-Bi-Directional Gated Recurrent Units. Firstly, through Spearman correlation analysis of CPU, usage, memory usage, network traffic, power consumption, number of instructions executed, execution time and energy efficiency, we found that power consumption has the highest degree of positive correlation with energy efficiency, while CPU usage has the highest degree of negative correlation with energy efficiency. In our experiments, we introduced a random forest model and an optimisation model based on the horned lizard optimisation algorithm for testing, and the results show that the optimisation algorithm has better prediction results compared to the random forest model. Specifically, the mean square error (MSE) of the optimisation algorithm is 0.01 smaller than that of the random forest model, and the mean absolute error (MAE) is 0.01 smaller than that of the random forest.3 The results of the combined metrics show that the optimisation algorithm performs more accurately and reliably in predicting energy efficiency. This research result provides new ideas and methods to improve the energy efficiency of cloud computing systems. This research not only expands the scope of application in the field of cloud computing, but also provides a strong support for improving the energy use efficiency of the system.

The intersection of chemistry and Artificial Intelligence (AI) is an active area of research focused on accelerating scientific discovery. While using large language models (LLMs) with scientific modalities has shown potential, there are significant challenges to address, such as improving training efficiency and dealing with the out-of-distribution problem. Focussing on the task of automated language-molecule translation, we are the first to use state-of-the art (SOTA) human-centric optimisation algorithms in the cross-modal setting, successfully aligning cross-language-molecule modals. We empirically show that we can augment the capabilities of scientific LLMs without the need for extensive data or large models. We conduct experiments using only 10% of the available data to mitigate memorisation effects associated with training large models on extensive datasets. We achieve significant performance gains, surpassing the best benchmark model trained on extensive in-distribution data by a large margin and reach new SOTA levels. Additionally we are the first to propose employing non-linear fusion for mixing cross-modal LLMs which further boosts performance gains without increasing training costs or data needs. Finally, we introduce a fine-grained, domain-agnostic evaluation method to assess hallucination in LLMs and promote responsible use.