One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a hierarchy with increasing fidelity, associated with lower error, but increasing cost. In this paper, we compare different multi-fidelity methods employed in constructing Gaussian process surrogates for regression. Non-linear autoregressive methods in the existing literature are primarily confined to two-fidelity models, and we extend these methods to handle more than two levels of fidelity. Additionally, we propose enhancements for an existing method incorporating delay terms by introducing a structured kernel. We demonstrate the performance of these methods across various academic and real-world scenarios. Our findings reveal that multi-fidelity methods generally have a smaller prediction error for the same computational cost as compared to the single-fidelity method, although their effectiveness varies across different scenarios.

Bayesian optimization (BO) algorithm is very popular for solving low-dimensional expensive optimization problems. Extending Bayesian optimization to high dimension is a meaningful but challenging task. One of the major challenges is that it is difficult to find good infill solutions as the acquisition functions are also high-dimensional. In this work, we propose the expected coordinate improvement (ECI) criterion for high-dimensional Bayesian optimization. The proposed ECI criterion measures the potential improvement we can get by moving the current best solution along one coordinate. The proposed approach selects the coordinate with the highest ECI value to refine in each iteration and covers all the coordinates gradually by iterating over the coordinates. The greatest advantage of the proposed ECI-BO (expected coordinate improvement based Bayesian optimization) algorithm over the standard BO algorithm is that the infill selection problem of the proposed algorithm is always a one-dimensional problem thus can be easily solved. Numerical experiments show that the proposed algorithm can achieve significantly better results than the standard BO algorithm and competitive results when compared with five state-of-the-art high-dimensional BOs. This work provides a simple but efficient approach for high-dimensional Bayesian optimization.

We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: i) they cannot provide optimality guarantees and can suffer from learning sub-optimal models; ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We overcome these shortcomings and develop a computationally efficient mixed-integer programming framework for learning medium-sized problems that accounts for arbitrary heteroscedastic noise. We present an early stopping criterion under which we can terminate the branch-and-bound procedure to achieve an asymptotically optimal solution and establish the consistency of this approximate solution. In addition, we show via numerical experiments that our method outperforms three state-of-the-art algorithms and is robust to noise heteroscedasticity, whereas the performance of the competing methods deteriorates under strong violations of the identifiability assumption. The software implementation of our method is available as the Python package \emph{micodag}.

The diversity optimization is the class of optimization problems, in which we aim at finding a diverse set of good solutions. One of the frequently used approaches to solve such problems is to use evolutionary algorithms which evolve a desired diverse population. This approach is called evolutionary diversity optimization (EDO). In this paper, we analyse EDO on a 3-objective function LOTZ$_k$, which is a modification of the 2-objective benchmark function (LeadingOnes, TrailingZeros). We prove that the GSEMO computes a set of all Pareto-optimal solutions in $O(kn^3)$ expected iterations. We also analyze the runtime of the GSEMO$_D$ (a modification of the GSEMO for diversity optimization) until it finds a population with the best possible diversity for two different diversity measures, the total imbalance and the sorted imbalances vector. For the first measure we show that the GSEMO$_D$ optimizes it asymptotically faster than it finds a Pareto-optimal population, in $O(kn^2\log(n))$ expected iterations, and for the second measure we show an upper bound of $O(k^2n^3\log(n))$ expected iterations. We complement our theoretical analysis with an empirical study, which shows a very similar behavior for both diversity measures that is close to the theory predictions.

Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully applied in optimizing chance-constrained monotone submodular problems. However, the difference in performance between algorithms using the surrogates and those employing the direct sampling-based evaluation remains unclear. Within the paper, a sampling-based method is proposed to directly evaluate the chance constraint. Furthermore, to address the problems with more challenging settings, an enhanced GSEMO algorithm integrated with an adaptive sliding window, called ASW-GSEMO, is introduced. In the experiments, the ASW-GSEMO employing the sampling-based approach is tested on the chance-constrained version of the maximum coverage problem with different settings. Its results are compared with those from other algorithms using different surrogate functions. The experimental findings indicate that the ASW-GSEMO with the sampling-based evaluation approach outperforms other algorithms, highlighting that the performances of algorithms using different evaluation methods are comparable. Additionally, the behaviors of ASW-GSEMO are visualized to explain the distinctions between it and the algorithms utilizing the surrogate functions.

High-performance catalysts are crucial for sustainable energy conversion and human health. However, the discovery of catalysts faces challenges due to the absence of efficient approaches to navigating vast and high-dimensional structure and composition spaces. In this study, we propose a high-throughput computational catalyst screening approach integrating density functional theory (DFT) and Bayesian Optimization (BO). Within the BO framework, we propose an uncertainty-aware atomistic machine learning model, UPNet, which enables automated representation learning directly from high-dimensional catalyst structures and achieves principled uncertainty quantification. Utilizing a constrained expected improvement acquisition function, our BO framework simultaneously considers multiple evaluation criteria. Using the proposed methods, we explore catalyst discovery for the CO2 reduction reaction. The results demonstrate that our approach achieves high prediction accuracy, facilitates interpretable feature extraction, and enables multicriteria design optimization, leading to significant reduction of computing power and time (10x reduction of required DFT calculations) in high-performance catalyst discovery.

The rapidly changing landscapes of modern optimization problems require algorithms that can be adapted in real-time. This paper introduces an Adaptive Metaheuristic Framework (AMF) designed for dynamic environments. It is capable of intelligently adapting to changes in the problem parameters. The AMF combines a dynamic representation of problems, a real-time sensing system, and adaptive techniques to navigate continuously changing optimization environments. Through a simulated dynamic optimization problem, the AMF's capability is demonstrated to detect environmental changes and proactively adjust its search strategy. This framework utilizes a differential evolution algorithm that is improved with an adaptation module that adjusts solutions in response to detected changes. The capability of the AMF to adjust is tested through a series of iterations, demonstrating its resilience and robustness in sustaining solution quality despite the problem's development. The effectiveness of AMF is demonstrated through a series of simulations on a dynamic optimization problem. Robustness and agility characterize the algorithm's performance, as evidenced by the presented fitness evolution and solution path visualizations. The findings show that AMF is a practical solution to dynamic optimization and a major step forward in the creation of algorithms that can handle the unpredictability of real-world problems.

Abstract--Sampling-based model-predictive controllers have become a powerful optimization tool for planning and control problems in various challenging environments. In this paper, we show how the default choice of uncorrelated Gaussian distributions can be improved upon with the use of a colored noise distribution. Our choice of distribution allows for the emphasis on low frequency control signals, which can result in smoother and more exploratory samples. We use this frequency-based sampling distribution with Model Predictive Path Integral (MPPI) in both hardware and simulation experiments to show better or equal performance on systems with various speeds of input response. S autonomous systems grow in interest, the choice of methods and algorithms used to do real-time motion planning and control becomes critical to achieve complex tasks.

Inspired by the utilization of dogs in sled-pulling for transportation, we introduce a cable-trailer system with a quadruped robot. The motion planning of the proposed robot system presents challenges arising from the nonholonomic constraints of the trailer, system underactuation, and hybrid interaction through the cable. To tackle these challenges, we develop a hybrid dynamics model that accounts for the cable's taut/slack status. Since it is computationally intense to directly optimize the trajectory, we first propose a search algorithm to compute a sub-optimal trajectory as the initial solution. Then, a novel collision avoidance constraint based on the geometric shapes of objects is proposed to formulate the trajectory optimization problem for the hybrid system. The proposed trajectory planning method is implemented on a Unitree A1 quadruped robot with a customized cable-trailer and validated through experiments.

Similarly to many other inference problems in planted models, we are interested in understanding the fundamental information-theoretical limits as well as the computational hardness of graph alignment. First, we study the Gaussian setting, when the graphs are complete and the signal lies on correlated Gaussian edges weights. We prove that the exact recovery task exhibits a sharp information-theoretic threshold (and characterize it), and study a simple and natural spectral method for recovery, EIG1, which consists in aligning the leading eigenvectors of the adjacency matrices of the two graphs. While most of the recent work on the subject was dedicated to recovering the hidden signal in dense graphs, we next explore graph alignment in the sparse regime, where the mean degree of the nodes are constant, not scaling with the graph size. In this particularly challenging setting, for sparse Erdős-Rényi graphs, only a fraction of the nodes can be correctly matched by any algorithm.