In this paper, we investigate a multi-agent target guarding problem in which a single defender seeks to capture multiple attackers aiming to reach a high-value target area. In contrast to previous studies, the attackers herein are assumed to be heterogeneous in the sense that they have not only different speeds but also different weights representing their respective degrees of importance (e.g., the amount of allocated resources). The objective of the attacker team is to jointly minimize the weighted sum of their final levels of proximity to the target area, whereas the defender aims to maximize the same value. Using geometric arguments, we construct candidate equilibrium control policies that require the solution of a (possibly nonconvex) optimization problem. Subsequently, we validate the optimality of the candidate control policies using parametric optimization techniques. Lastly, we provide numerical examples to illustrate how cooperative behaviors emerge within the attacker team due to their heterogeneity.

In this paper, we formulate the hyperparameter tuning problem in machine learning as a bilevel program. The bilevel program is solved using a micro genetic algorithm that is enhanced with a linear program. While the genetic algorithm searches over discrete hyperparameters, the linear program enhancement allows hyper local search over continuous hyperparameters. The major contribution in this paper is the formulation of a linear program that supports fast search over continuous hyperparameters, and can be integrated with any hyperparameter search technique. It can also be applied directly on any trained machine learning or deep learning model for the purpose of fine-tuning. We test the performance of the proposed approach on two datasets, MNIST and CIFAR-10. Our results clearly demonstrate that using the linear program enhancement offers significant promise when incorporated with any population-based approach for hyperparameter tuning.

Tree ensemble methods represent a popular machine learning model, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned for their interpretability properties. However, tree ensemble methods do not reliably exhibit interpretable output. Our work aims to extract an optimized list of rules from a trained tree ensemble, providing the user with a condensed, interpretable model that retains most of the predictive power of the full model. Our approach consists of solving a clean and neat set partitioning problem formulated through Integer Programming. The proposed method works with either tabular or time series data, for both classification and regression tasks, and does not require parameter tuning under the most common setting. Through rigorous computational experiments, we offer statistically significant evidence that our method is competitive with other rule extraction methods and effectively handles time series.

Exploring the limits of quadruped robot agility, particularly in the context of rapid and real-time planning and execution of omnidirectional jump trajectories, presents significant challenges due to the complex dynamics involved, especially when considering significant impulse contacts. This paper introduces a new framework to enable fast, omnidirectional jumping capabilities for quadruped robots. Utilizing minimum jerk technology, the proposed framework efficiently generates jump trajectories that exploit its analytical solutions, ensuring numerical stability and dynamic compatibility with minimal computational resources. The virtual model control is employed to formulate a Quadratic Programming (QP) optimization problem to accurately track the Center of Mass (CoM) trajectories during the jump phase. The whole-body control strategies facilitate precise and compliant landing motion. Moreover, the different jumping phase is triggered by time-schedule. The framework's efficacy is demonstrated through its implementation on an enhanced version of the open-source Mini Cheetah robot. Omnidirectional jumps-including forward, backward, and other directional-were successfully executed, showcasing the robot's capability to perform rapid and consecutive jumps with an average trajectory generation and tracking solution time of merely 50 microseconds.

Quantum computing is regarded as a promising paradigm that may overcome the current computational power bottlenecks in the post-Moore era. The increasing maturity of quantum processors, especially superconducting ones, provides more possibilities for the development and implementation of quantum algorithms. As the crucial stages for quantum algorithm implementation, the logic circuit design and quantum compiling have also received significant attention, which covers key technologies such as quantum logic circuit synthesis (also widely known as quantum architecture search) and optimization, as well as qubit mapping and routing. Recent studies suggest that the scale and precision of related algorithms are steadily increasing, especially with the integration of artificial intelligence methods. In this survey, we systematically review and summarize a vast body of literature, exploring the feasibility of an integrated design and optimization scheme that spans from the algorithmic level to quantum hardware, combining the steps of logic circuit design and compilation optimization. Leveraging the exceptional cognitive and learning capabilities of AI algorithms, one can reduce manual design costs, enhance the precision and efficiency of execution, and facilitate the implementation and validation of the superiority of quantum algorithms on hardware.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in white-box and black-box prompt learning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown in both reasoning and image generation tasks, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in \url{https://github.com/research4pan/Plum}.

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.

When applying nonnegative matrix factorization (NMF), generally the rank parameter is unknown. Such rank in NMF, called the nonnegative rank, is usually estimated heuristically since computing the exact value of it is NP-hard. In this work, we propose an approximation method to estimate such rank while solving NMF on-the-fly. We use sum-of-norm (SON), a group-lasso structure that encourages pairwise similarity, to reduce the rank of a factor matrix where the rank is overestimated at the beginning. On various datasets, SON-NMF is able to reveal the correct nonnegative rank of the data without any prior knowledge nor tuning. SON-NMF is a nonconvx nonsmmoth non-separable non-proximable problem, solving it is nontrivial. First, as rank estimation in NMF is NP-hard, the proposed approach does not enjoy a lower computational complexity. Using a graph-theoretic argument, we prove that the complexity of the SON-NMF is almost irreducible. Second, the per-iteration cost of any algorithm solving SON-NMF is possibly high, which motivated us to propose a first-order BCD algorithm to approximately solve SON-NMF with a low per-iteration cost, in which we do so by the proximal average operator. Lastly, we propose a simple greedy method for post-processing. SON-NMF exhibits favourable features for applications. Beside the ability to automatically estimate the rank from data, SON-NMF can deal with rank-deficient data matrix, can detect weak component with small energy. Furthermore, on the application of hyperspectral imaging, SON-NMF handle the issue of spectral variability naturally.

The dispatch optimization of coal mine integrated energy system is challenging due to high dimensionality, strong coupling constraints, and multiobjective. Existing constrained multiobjective evolutionary algorithms struggle with locating multiple small and irregular feasible regions, making them inaplicable to this problem. To address this issue, we here develop a multitask evolutionary algorithm framework that incorporates the dispatch correlated domain knowledge to effectively deal with strong constraints and multiobjective optimization. Possible evolutionary multitask construction strategy based on complex constraint relationship analysis and handling, i.e., constraint coupled spatial decomposition, constraint strength classification and constraint handling technique, is first explored. Within the multitask evolutionary optimization framework, two strategies, i.e., an elite guided knowledge transfer by designing a special crowding distance mechanism to select dominant individuals from each task, and an adaptive neighborhood technology based mutation to effectively balance the diversity and convergence of each optimized task for the differential evolution algorithm, are further developed. The performance of the proposed algorithm in feasibility, convergence, and diversity is demonstrated in a case study of a coal mine integrated energy system by comparing with CPLEX solver and seven constrained multiobjective evolutionary algorithms.

In this paper, we introduce a novel approach for large language model merging via black-box multi-objective optimization algorithms. The goal of model merging is to combine multiple models, each excelling in different tasks, into a single model that outperforms any of the individual source models. However, model merging faces two significant challenges: First, existing methods rely heavily on human intuition and customized strategies. Second, parameter conflicts often arise during merging, and while methods like DARE [1] can alleviate this issue, they tend to stochastically drop parameters, risking the loss of important delta parameters. To address these challenges, we propose the MM-MO method, which automates the search for optimal merging configurations using multi-objective optimization algorithms, eliminating the need for human intuition. During the configuration searching process, we use estimated performance across multiple diverse tasks as optimization objectives in order to alleviate the parameter conflicting between different source models without losing crucial delta parameters. We conducted comparative experiments with other mainstream model merging methods, demonstrating that our method consistently outperforms them. Moreover, our experiments reveal that even task types not explicitly targeted as optimization objectives show performance improvements, indicating that our method enhances the overall potential of the model rather than merely overfitting to specific task types. This approach provides a significant advancement in model merging techniques, offering a robust and plug-and-play solution for integrating diverse models into a unified, high-performing model.