OBJECTIVE:To develop a patient-level simulation model of type 1 diabetes (T1D) covering both childhood and adulthood. The goal is to identify and evaluate the cost-effectiveness of optimal screening for pre-symptomatic T1D. METHODS:We developed a Python-based simulation model to track 100,000 participants screened in childhood, capturing a subset of those at risk and transitioning to T1D, to estimate the incremental cost-effectiveness per life year gained of screening versus no screening. Our multi-objective optimisation approach sought to minimise three objectives: incremental cost effectiveness ratio, diabetic ketoacidosis (DKA) events at onset and the maximum number of screening tests a child can have with the healthcare system. The NSGA-II algorithm is used to explore the set of possible screening strategies from combinations of genetic risk score (GRS) and islet autoantibody (IA) measurements at different ages and frequencies during the first 15 years of life. Data for transition probabilities include large scale screening studies such as The Environmental Determinants of Diabetes in the Young, TrialNet, published risk functions, clinical trials and epidemiologic studies. RESULTS:We illustrate the use of multi-objective optimisation in patient-level simulations by estimating an optimal subset of T1D screening strategies in the USA. We identify four screening strategies with incremental cost-effectiveness ratios that meet commonly cited cost-effectiveness thresholds, which require, respectively, a maximum of 1, 2 3 and 4 islet autoantibody (IA) tests. CONCLUSIONS:This article and corresponding model code can be used as a reference for implementing a multi-objective optimisation pipeline in patient-level simulation models.

Neural mass models (NMMs) are often used to help understand the circuitry that underpins observed brain dynamics in basic and clinical research. A key step is to fuse models with data so that model parameter values can be inferred for a given data set-a process called model fitting or model calibration. This can shed light on putative physiological mechanisms underlying the observed signals. Calibration is notoriously challenging in biology since models are often non-identifiable, high-dimensional, and nonlinear. Established methods such as dynamic causal modelling (DCM) circumvent some of these issues, for example, by incorporating prior information and employing fast local search methods in the space of feasible parameter values ("parameter space"). However, it is pertinent to better understand the potential limitations of these methods so that we can increase our confidence in the use of models to interpret brain activity, and to develop new approaches as required. Here, we use tools from dynamical systems theory to illustrate some of the complexities of model calibration in an archetypal NMM. We use this information to motivate the use of calibration methods that work across large regions of parameter space, rather than focusing on informative priors or localised search methods. We subsequently evaluate the performance of approximate Bayesian computation (ABC) and evolutionary search metaheuristics (ESMs) for mapping feasible sets of parameters for which an NMM can recreate electroencephalographic recordings during an eyes-closed resting state. Our results demonstrate the superiority of ESMs in terms of computational efficiency and accuracy. Furthermore, we elucidate potential reasons why ESMs are able to perform better than ABC, that is, that they are less susceptible to biases induced by the complexity of underlying cost landscapes. These results highlight the importance of incorporating ESMs in future efforts to model brain dynamics.

Local Optima Networks (LONs) are established graph-based models for landscape analysis, yet their methodological maturity in continuous optimisation lags behind their combinatorial counterparts. This study investigates the challenges of constructing LONs for the Black-Box Optimisation Benchmark (BBOB) suite using a basin-hopping framework. We first identify a critical sampling anomaly—spurious local optima on theoretically unimodal functions—and suggest that vanishing gradients are the primary cause, proposing specific parameters to mitigate this behaviour. To improve high-dimensional interpretability, we introduce an integrated topographic visualisation that superimposes the LON graph onto a reconstructed fitness surface. This approach extends the intuition of 2d heatmaps to higher dimensions, capturing both connectivity and topography. Finally, we characterise the 5d BBOB suite using an expanded set of LON features. Comparative analysis reveals that LON-derived metrics outperform traditional landscape features for 3 of the 4 optimisers tested, suggesting that graph-based models capture structural nuances distinct from traditional metrics. These results contribute to establish the LON framework as a complementary quantitative and visualisation tool to characterise continuous optimisation landscapes.

Local optima networks (LONs) are a compact graph-based visualisation and characterisation approach to represent the fitness landscape of an optimisation problem. LONs are most frequently generated for combinatorial problems, where neighbourhoods can be crisply defined. A handful of approaches exist for continuous spaces, e.g. using derivatives-based local search approaches and basin-hopping, or by discretising the continuous space via gridding. Here we propose a new approach. Neighbourhoods are defined as balls around quasi-random samples from the search space. Basins and local optima are identified by greedily traversing these sampled neighbourhoods. One interpretation of such a formulation is that it approximates the LON induced by a (1+λ ) –Evolution Strategy (ES) with a ball mutation. The proposal allows the generation of LONs for problems with non-linear constraints, and discontinuous functions. We detail construction methods and illustrate the effective landscapes for some different objective functions using both the proposed methodology and derivatives-based alternatives.

Recent work on expensive single-objective Computational Fluid Dynamics (CFD) design problems has identified a trio of surrogate assisted evolutionary algorithms (LSADE, TS-DDEO and ESA) as being particularly strong performers. In this work, we contrast their performance on multi-objective optimisation, embedding eight different popular scalarising functions within their pipelines to facilitate their use in this domain, and compare them to a Bayesian optimisation (BO) alternative on a range of synthetic problems. We End that for bi-objective problems ESA and TS-DDEO outperform the others, but as the number of objectives increases the ranking reverses and BO becomes the dominant performer. Interestingly, the older scalarisation approaches tend to perform better in the configurations used, though again performance is seen to vary as the number of objectives increases. We introduce a new real world multi-objective CFD design benchmark, that of optimising a sand trap geometry, and observe that performance on the collection of synthetic test functions is not predictive on this practical problem highlighting the need to add such practical test cases to the benchmarking suits in this domain.

Abstract. General circulation models (GCMs) face significant uncertainties in estimating Earth's radiative budget due to aerosol-cloud interactions (ACI). To improve the representation of ACI in GCMs it is crucial to constrain processes controlling the aerosol lifecycle and the resulting size distribution. This is challenging due to the complexity and number of competing atmospheric processes that interact over large spatial and temporal scales which require untangling to elucidate dominant processes controlling aerosol properties. This study aims to (a) develop a generic explainable AI framework from air-mass history to build an accurate representation of processes controlling aerosol properties, from this, (b) identify key relationships between aerosol processes and their impacts on observed aerosol number concentrations, and (c) provide robust process-based observational constraints to aid in the isolation of GCM structural uncertainties. This is achieved by developing XGBoost regression models to simulate Aitken and accumulation mode number concentrations for receptor surface stations and application of TreeSHAP to identify key processes from explanatory variables describing meteorological and aerosol processes collocated to Lagrangian air-mass trajectories. The fidelity of this framework is demonstrated for the Antarctic station Trollhaugen, situated in a pristine region in which GCMs exhibit significant biases. Aerosol number concentrations at Trollhaugen were shown to be dominated by marine sources as well as transport from the free troposphere. The contribution from aloft dominates aerosol burden of the Aitken mode in the transitions between summer and winter, in contrast to a larger contribution in the summer from local marine sources from transport in the boundary layer.

In this paper we look at the experimental design for multi-objective problems, where the objectives can be evaluated independently (decoupled) and thus it may make sense to evaluate different solutions for each objective if the objectives have different evaluation costs and/or different landscape characteristics. We propose to iteratively add design points in a way that minimises the total integrated mean squared prediction error assuming a Gaussian process response surface model, and show that allowing decoupled evaluations can lead to significantly better Pareto front estimations than a coupled design of experiments if the evaluation costs of the objectives are different. We also find that our approach of minimising mean squared prediction error yields significantly better results than standard Latin Hypercube designs even if the evaluation costs and landscape characteristics of the objectives are the same.

Local Optima Networks (LON)s have been used extensively to understand the global structure of optimisation problems and to study algorithm behaviour. The central idea is to compress the search space into a graph object capturing the local optima along with information on their basins of attraction and the connections between them. This enables the visualisation of high dimensional search spaces, and the extraction of metrics for characterising and contrasting different problem instances. In this paper we extend the canonical LON definition to encompass search spaces with constraints. We use a well-known pairwise comparison operator for constrained problems, and capture the features of the constraint violation landscape that present a challenge for such an operator, such as infeasible local traps. The concept of a constrained LON is illustrated through a range of problem instances. Most problems in the context of real-world applications have constraints. By including the notion of feasibility and constraint violation into the definition of LONs, it becomes possible to use this powerful analysis tool on a much wider range of real-world problems.

This work presents the experimental setup for the GECCO 2024 competition on benchmarking niching methods for multimodal optimization. It employs 16 recently developed scalable composite problems to evaluate different aspects of multimodal optimization methods. These test problems are available in Python and MATLAB.

The shape of a hydrodynamic particle separator has been optimized using a parallelized and robust formulation of Bayesian optimization, with data from an unsteady Eulerian flow field coupled with Lagrangian particle tracking. The uncertainty due to the mesh, initial conditions, and stochastic dispersion in the Eulerian-Lagrangian simulations was minimized and quantified. This was then translated across to the error term in the Gaussian process model and the minimum probability of improvement infill criterion. An existing parallelization strategy was modified for the infill criterion and customized to prefer exploitation in the decision space. In addition, a new strategy was developed for hidden constraints using Voronoi penalization. In the approximate Pareto Front, an absolute improvement over the base design of 14% in the underflow collection efficiency and 10% in the total collection efficiency was achieved, which resulted in the filing of a patent.* The corresponding designs were attributed to the effective distribution of residence time between the trays via the removal of a vertical plume. The plume also reduced both efficiencies by creating a flow path in a direction that acted against effective settling. The concave down and offset tray shapes demonstrated the value of Bayesian optimization in producing useful and non-intuitive designs.

This study introduces novel tunable benchmark test problems for continuous box-constrained multimodal optimization (MMO). It first introduces a new approach to control the non-uniformity of distribution of global minima, a notable challenge in MMO. Then, it builds upon an existing procedure to create composite functions in which the severity of two distinguishable groups of MMO challenges can be controlled: i) challenges shared with global optimization (GO), such as ill-conditioning, and ii) challenges specific to MMO, such as non-uniform distribution of global minima. Eight new scalable and tunable MMO functions are then proposed, based on which a test suite of 16 continuous MMO test problems is suggested. This test suite is designed to be i) comprehensive, which means they simulate most, if not all, prominent challenges associated with MMO, ii) discriminating, which means test problems can disclose the gap between the performance of diverse MMO methods, and iii) illuminating, which means test problems can reveal and compare strengths and weaknesses of MMO methods. The code of these problems is made available in two different programming languages to encourage its adoption by the research community.

Deep learning models, despite their remarkable success in various tasks, have been shown to be vulnerable to adversarial perturbations. Although robust learning techniques that consider adversarial risks against worst-case perturbations can effectively increase a model’s robustness, they may not always be the most suitable approach. This is due to the fact that in certain scenarios, perturbations are more likely to occur probabilistically rather than being intentionally crafted by attackers. To address this challenge, we propose a novel risk-averse robust learning method based on entropic value-at-risk, called PRASS (Probabilistical Risk-Averse Robust Learning with Stochastic Search). Our approach leverages principles of stochastic optimisation and considers perturbing distributions rather than solely worst-case adversaries. By applying adaptive stochastic search to parameterised distributions, we further enhance the scalability of PRASS to handle distributional robustness. Empirical experiments demonstrate that PRASS outperforms existing state-of-the-art baselines.

Abstract The shape of a hydrodynamic particle separator has been optimised using unsteady computational fluid dynamics, coupled with Lagrangian particle tracking, combined with a parallelised and robust formulation of Bayesian optimisation. The noise present in the models of the separator required the use of the minimum probability of improvement infill criterion for optimisation of the geometry. This allowed direct inclusion of the objective noise via homoscedastic Gaussian process models. The wall clock time for the fluid modelling suggested that the Bayesian sampling should be parallelised. An existing parallelisation strategy was modified for the infill criterion being used and customised to favour exploitation in the decision space in order to deal with the cliff-edge type landscape that the infill criterion created. A new strategy was developed for convergence failures using Voronoi penalisation, while the approach for handling hardware failures was by manual restart. The presence of unsteady flow in the separator was addressed by time-resolving the flow fields in an Eulerian-Lagrangian manner. The optimisation generated an approximate Pareto front of solutions, which included novel and unexpected geometric shapes, demonstrating the value of Bayesian optimisation in producing innovative designs, which resulted in the filing of a patent.

In safety-critical deep learning applications robustness measurement is a vital pre-deployment phase. However, existing robustness verification methods are not sufficiently practical for deploying machine learning systems in the real world. On the one hand, these methods attempt to claim that no perturbations can “fool” deep neural networks (DNNs), which may be too stringent in practice. On the other hand, existing works rigorously consider L_p bounded additive perturbations on the pixel space, although perturbations, such as colour shifting and geometric transformations, are more practically and frequently occurring in the real world. Thus, from the practical standpoint, we present a novel and general probabilistic robustness assessment method (PRoA) based on the adaptive concentration, and it can measure the robustness of deep learning models against functional perturbations. PRoA can provide statistical guarantees on the probabilistic robustness of a model, i.e., the probability of failure encountered by the trained model after deployment. Our experiments demonstrate the effectiveness and flexibility of PRoA in terms of evaluating the probabilistic robustness against a broad range of functional perturbations, and PRoA can scale well to various large-scale deep neural networks compared to existing state-of-the-art baselines. For the purpose of reproducibility, we release our tool on GitHub: < https://github.com/TrustAI/PRoA>.

A key concern when undertaking any form of optimisation is how to characterise the quality of the putative solution returned. In many-objective optimisation an added complication is that such measures are on a set of trade-off solutions. We present and discuss the commonly used quality measures for many-objective optimisation, which are a subset of those used in multi-objective optimisation. We discuss the computational aspects and theoretical properties of these measures, highlighting measures for both a posteriori and a priori approaches, where the latter incorporate preference information from a decision maker (DM). We also discuss open areas in this field and forms of many-objective optimisation which are relatively under-explored, and where appropriate quality measures are much less developed including challenges related to developing measures for interactive methods.

The 2022 Genetic and Evolutionary Computation Conference (GECCO 2022) took place in Boston, on July 9th--13th, 2022, as the first-ever "hybrid" GECCO. Hybrid here meant that about half of the attendees were physically present in Boston, while the others joined online. In the following, we provide statistics about submissions and authorship, and some comments about the evolution and growth of GECCO.

Gaussian processes (GPs) serve as powerful surrogate models in optimisation by providing a flexible data-driven framework for representing complex fitness landscapes. We provide an analysis of realisations drawn from GP models of fitness landscapes-which represent alternative coherent fits to the data-and use a network-based approach to investigate their induced landscape consistency. We consider the variation of constructed local optima networks (LONs: which provide a condensed representation of landscapes), analyse the fitness landscapes of GP realisations, and delve into the uncertainty associated with graph metrics of LONs. Our findings contribute to the understanding and practical application of GPs in optimisation and landscape analysis. Particularly that landscape consistency between GP realisations can vary considerably dependent on the model fit and underlying landscape complexity of the optimisation problem.