The rapid advancement of intelligent technology has led to the development of optimization algorithms that leverage natural behaviors to address complex issues. Among these, the Rat Swarm Optimizer (RSO), inspired by rats' social and behavioral characteristics, has demonstrated potential in various domains, although its convergence precision and exploration capabilities are limited. To address these shortcomings, this study introduces the Modified Rat Swarm Optimizer (MRSO), designed to enhance the balance between exploration and exploitation. MRSO incorporates unique modifications to improve search efficiency and durability, making it suitable for challenging engineering problems such as welded beam, pressure vessel, and gear train design. Extensive testing with classical benchmark functions shows that MRSO significantly improves performance, avoiding local optima and achieving higher accuracy in six out of nine multimodal functions and in all seven fixed-dimension multimodal functions. In the CEC 2019 benchmarks, MRSO outperforms the standard RSO in six out of ten functions, demonstrating superior global search capabilities. When applied to engineering design problems, MRSO consistently delivers better average results than RSO, proving its effectiveness. Additionally, we compared our approach with eight recent and well-known algorithms using both classical and CEC-2019 bench-marks. MRSO outperforms each of these algorithms, achieving superior results in six out of 23 classical benchmark functions and in four out of ten CEC-2019 benchmark functions. These results further demonstrate MRSO's significant contributions as a reliable and efficient tool for optimization tasks in engineering applications.
Multi-objective optimization is a common problem in practical applications, and multi-objective evolutionary algorithm (MOEA) is considered as one of the effective methods to solve these problems. However, their randomness sometimes prevents algorithms from rapidly converging to global optimization, and the design of their genetic operators often requires complicated manual tuning. To overcome this challenge, this study proposes a new framework that combines a large language model (LLM) with traditional evolutionary algorithms to enhance the algorithm's search capability and generalization performance.In our framework, we employ adaptive and hybrid mechanisms to integrate the LLM with the MOEA, thereby accelerating algorithmic convergence. Specifically, we leverage an auxiliary evaluation function and automated prompt construction within the adaptive mechanism to flexibly adjust the utilization of the LLM, generating high-quality solutions that are further refined and optimized through genetic operators.Concurrently, the hybrid mechanism aims to minimize interaction costs with the LLM as much as possible.
This paper presents an overview of the Burer-Monteiro method (BM), a technique that has been applied to solve robot perception problems to certifiable optimality in real-time. BM is often used to solve semidefinite programming relaxations, which can be used to perform global optimization for non-convex perception problems. Specifically, BM leverages the low-rank structure of typical semidefinite programs to dramatically reduce the computational cost of performing optimization. This paper discusses BM in certifiable perception, with three main objectives: (i) to consolidate information from the literature into a unified presentation, (ii) to elucidate the role of the linear independence constraint qualification (LICQ), a concept not yet well-covered in certifiable perception literature, and (iii) to share practical considerations that are discussed among practitioners but not thoroughly covered in the literature. Our general aim is to offer a practical primer for applying BM towards certifiable perception.
While previous years have seen great progress in the 3D reconstruction of humans from monocular videos, few of the state-of-the-art methods are able to handle loose garments that exhibit large non-rigid surface deformations during articulation. This limits the application of such methods to humans that are dressed in standard pants or T-shirts. Our method, ReLoo, overcomes this limitation and reconstructs high-quality 3D models of humans dressed in loose garments from monocular in-the-wild videos. To tackle this problem, we first establish a layered neural human representation that decomposes clothed humans into a neural inner body and outer clothing. On top of the layered neural representation, we further introduce a non-hierarchical virtual bone deformation module for the clothing layer that can freely move, which allows the accurate recovery of non-rigidly deforming loose clothing. A global optimization jointly optimizes the shape, appearance, and deformations of the human body and clothing via multi-layer differentiable volume rendering. To evaluate ReLoo, we record subjects with dynamically deforming garments in a multi-view capture studio. This evaluation, both on existing and our novel dataset, demonstrates ReLoo's clear superiority over prior art on both indoor datasets and in-the-wild videos.
Efficient water management in agriculture is important for mitigating the growing freshwater scarcity crisis. Mixed-integer Model Predictive Control (MPC) has emerged as an effective approach for addressing the complex scheduling problems in agricultural irrigation. However, the computational complexity of mixed-integer MPC still poses a significant challenge, particularly in large-scale applications. This study proposes an approach to enhance the computational efficiency of mixed-integer MPC-based irrigation schedulers by employing ReLU surrogate models to describe the soil moisture dynamics of the agricultural field. By leveraging the mixed-integer linear representation of the ReLU operator, the proposed approach transforms the mixed-integer MPC-based scheduler with a quadratic cost function into a mixed-integer quadratic program, which is the simplest class of mixed-integer nonlinear programming problems that can be efficiently solved using global optimization solvers. The effectiveness of this approach is demonstrated through comparative studies conducted on a large-scale agricultural field across two growing seasons, involving other machine learning surrogate models, specifically Long Short-Term Memory (LSTM) networks, and the widely used triggered irrigation scheduling method. The ReLU-based approach significantly reduces solution times -- by up to 99.5\% -- while achieving comparable performance to the LSTM approach in terms of water savings and Irrigation Water Use Efficiency (IWUE). Moreover, the ReLU-based approach maintains enhanced performance in terms of total prescribed irrigation and IWUE compared to the widely-used triggered irrigation scheduling method.
We propose a combined global-local control approach to regulate voltage and minimize power losses in distribution networks with high integration of distributed energy resources (DERs). Local controllers embed the fast acting proportional volt-var-watt control law and have their gain (slope) coefficients updated regularly by a global optimization problem at a slower time-scale. Design of optimal coefficients preserve overall system stability and encapsulate inverter and energy limits of controllable DERs. The proposed approach is formulated based on a linear network model (LinDistFlow) and suitable approximations to produce a convex multi-period optimization formulation. Numerical simulations with real-world customer data and two different distribution feeders revealed that our approach provides substantial voltage regulation, while reducing losses by 11 per cent and peak substation power by 26 per cent compared to other state-of-the-art algorithms.
Surgical navigation based on multimodal image registration has played a significant role in providing intraoperative guidance to surgeons by showing the relative position of the target area to critical anatomical structures during surgery. However, due to the differences between multimodal images and intraoperative image deformation caused by tissue displacement and removal during surgery, effective registration of preoperative and intraoperative multimodal images faces significant challenges. To address the multimodal image registration challenges in Learn2Reg 2024, an unsupervised multimodal medical image registration method based on multilevel correlation balanced optimization (MCBO) is designed to solve these problems. First, the features of each modality are extracted based on the modality independent neighborhood descriptor, and the multimodal images are mapped to the feature space. Second, a multilevel pyramidal fusion optimization mechanism is designed to achieve global optimization and local detail complementation of the deformation field through dense correlation analysis and weight-balanced coupled convex optimization for input features at different scales. For preoperative medical images in different modalities, the alignment and stacking of valid information between different modalities is achieved by the maximum fusion between deformation fields. Our method focuses on the ReMIND2Reg task in Learn2Reg 2024, and to verify the generality of the method, we also tested it on the COMULIS3DCLEM task. Based on the results, our method achieved second place in the validation of both two tasks. The code is available at https://github.com/wjiazheng/MCBO.
Data augmentation has become an integral part of deep learning, as it is known to improve the generalization capabilities of neural networks. Since the most effective set of image transformations differs between tasks and domains, automatic data augmentation search aims to alleviate the extreme burden of manually finding the optimal image transformations. However, current methods are not able to jointly optimize all degrees of freedom: (1) the number of transformations to be applied, their (2) types, (3) order, and (4) magnitudes. Many existing methods risk picking the same transformation more than once, limit the search to two transformations only, or search for the number of transformations exhaustively or iteratively in a myopic manner. Our approach, FreeAugment, is the first to achieve global optimization of all four degrees of freedom simultaneously, using a fully differentiable method. It efficiently learns the number of transformations and a probability distribution over their permutations, inherently refraining from redundant repetition while sampling. Our experiments demonstrate that this joint learning of all degrees of freedom significantly improves performance, achieving state-of-the-art results on various natural image benchmarks and beyond across other domains. Project page at https://tombekor.github.io/FreeAugment-web
LLM-based autonomous agents often fail to execute complex web tasks that require dynamic interaction due to the inherent uncertainty and complexity of these environments. Existing LLM-based web agents typically rely on rigid, expert-designed policies specific to certain states and actions, which lack the flexibility and generalizability needed to adapt to unseen tasks. In contrast, humans excel by exploring unknowns, continuously adapting strategies, and resolving ambiguities through exploration. To emulate human-like adaptability, web agents need strategic exploration and complex decision-making. Monte Carlo Tree Search (MCTS) is well-suited for this, but classical MCTS struggles with vast action spaces, unpredictable state transitions, and incomplete information in web tasks. In light of this, we develop WebPilot, a multi-agent system with a dual optimization strategy that improves MCTS to better handle complex web environments. Specifically, the Global Optimization phase involves generating a high-level plan by breaking down tasks into manageable subtasks and continuously refining this plan, thereby focusing the search process and mitigating the challenges posed by vast action spaces in classical MCTS. Subsequently, the Local Optimization phase executes each subtask using a tailored MCTS designed for complex environments, effectively addressing uncertainties and managing incomplete information. Experimental results on WebArena and MiniWoB++ demonstrate the effectiveness of WebPilot. Notably, on WebArena, WebPilot achieves SOTA performance with GPT-4, achieving a 93% relative increase in success rate over the concurrent tree search-based method. WebPilot marks a significant advancement in general autonomous agent capabilities, paving the way for more advanced and reliable decision-making in practical environments.
3D object detection in driving scenarios faces the challenge of complex road environments, which can lead to the loss or incompleteness of key features, thereby affecting perception performance. To address this issue, we propose an advanced detection framework called Co-Fix3D. Co-Fix3D integrates Local and Global Enhancement (LGE) modules to refine Bird's Eye View (BEV) features. The LGE module uses Discrete Wavelet Transform (DWT) for pixel-level local optimization and incorporates an attention mechanism for global optimization. To handle varying detection difficulties, we adopt multi-head LGE modules, enabling each module to focus on targets with different levels of detection complexity, thus further enhancing overall perception capability. Experimental results show that on the nuScenes dataset's LiDAR benchmark, Co-Fix3D achieves 69.4\% mAP and 73.5\% NDS, while on the multimodal benchmark, it achieves 72.3\% mAP and 74.7\% NDS. The source code is publicly available at \href{https://github.com/rubbish001/Co-Fix3d}{https://github.com/rubbish001/Co-Fix3d}.
Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way problems requiring a polynomial number of calls to an oracle in $\Sigma_n^p$ (that is, problems in $\Delta_{n+1}^p$). Such problems include, in particular, optimization problems. In this paper we propose an extension of ASP(Q), in which component programs may contain weak constraints. Weak constraints can be used both for expressing local optimization within quantified component programs and for modeling global optimization criteria. We showcase the modeling capabilities of the new formalism through various application scenarios. Further, we study its computational properties obtaining complexity results and unveiling non-obvious characteristics of ASP(Q) programs with weak constraints.
This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness and numerical efficiency, frequently struggle with selecting optimal base kernels and parameter tuning, especially with gradient-based methods prone to local optima. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions, thereby achieving more reliable and precise learning of dynamical systems. Through comprehensive numerical experiments on the Logistic Map, Henon Map, and Lorentz System, KSOS is shown to consistently outperform gradient descent in minimizing the relative-$\rho$ metric and improving kernel accuracy. These results highlight KSOS's effectiveness in predicting the behavior of chaotic dynamical systems, demonstrating its capability to adapt kernels to underlying dynamics and enhance the robustness and predictive power of kernel-based approaches, making it a valuable asset for time series analysis in various scientific fields.
Reconstructing the 3D shape of a deformable environment from the information captured by a moving depth camera is highly relevant to surgery. The underlying challenge is the fact that simultaneously estimating camera motion and tissue deformation in a fully deformable scene is an ill-posed problem, especially from a single arbitrarily moving viewpoint. Current solutions are often organ-specific and lack the robustness required to handle large deformations. Here we propose a multi-viewpoint global optimization framework that can flexibly integrate the output of low-level perception modules (data association, depth, and relative scene flow) with kinematic and scene-modeling priors to jointly estimate multiple camera motions and absolute scene flow. We use simulated noisy data to show three practical examples that successfully constrain the convergence to a unique solution. Overall, our method shows robustness to combined noisy input measures and can process hundreds of points in a few milliseconds. MultiViPerFrOG builds a generalized learning-free scaffolding for spatio-temporal encoding that can unlock advanced surgical scene representations and will facilitate the development of the computer-assisted-surgery technologies of the future.
Exploring the capabilities of Neural Radiance Fields (NeRF) and Gaussian-based methods in the context of 3D scene reconstruction, this study contrasts these modern approaches with traditional Simultaneous Localization and Mapping (SLAM) systems. Utilizing datasets such as Replica and ScanNet, we assess performance based on tracking accuracy, mapping fidelity, and view synthesis. Findings reveal that NeRF excels in view synthesis, offering unique capabilities in generating new perspectives from existing data, albeit at slower processing speeds. Conversely, Gaussian-based methods provide rapid processing and significant expressiveness but lack comprehensive scene completion. Enhanced by global optimization and loop closure techniques, newer methods like NICE-SLAM and SplaTAM not only surpass older frameworks such as ORB-SLAM2 in terms of robustness but also demonstrate superior performance in dynamic and complex environments. This comparative analysis bridges theoretical research with practical implications, shedding light on future developments in robust 3D scene reconstruction across various real-world applications.
This paper presents a novel framework for inferring timed temporal logic properties from data. The dataset comprises pairs of finite-time system traces and corresponding labels, denoting whether the traces demonstrate specific desired behaviors, e.g. whether the ship follows a safe route or not. Our proposed approach leverages decision-tree-based methods to infer Signal Temporal Logic classifiers using primitive formulae. We formulate the inference process as a mixed integer linear programming optimization problem, recursively generating constraints to determine both data classification and tree structure. Applying a max-flow algorithm on the resultant tree transforms the problem into a global optimization challenge, leading to improved classification rates compared to prior methodologies. Moreover, we introduce a technique to reduce the number of constraints by exploiting the symmetry inherent in STL primitives, which enhances the algorithm's time performance and interpretability. To assess our algorithm's effectiveness and classification performance, we conduct three case studies involving two-class, multi-class, and complex formula classification scenarios.
This paper focuses on hyperparameter optimization for autonomous driving strategies based on Reinforcement Learning. We provide a detailed description of training the RL agent in a simulation environment. Subsequently, we employ Efficient Global Optimization algorithm that uses Gaussian Process fitting for hyperparameter optimization in RL. Before this optimization phase, Gaussian process interpolation is applied to fit the surrogate model, for which the hyperparameter set is generated using Latin hypercube sampling. To accelerate the evaluation, parallelization techniques are employed. Following the hyperparameter optimization procedure, a set of hyperparameters is identified, resulting in a noteworthy enhancement in overall driving performance. There is a substantial increase of 4\% when compared to existing manually tuned parameters and the hyperparameters discovered during the initialization process using Latin hypercube sampling. After the optimization, we analyze the obtained results thoroughly and conduct a sensitivity analysis to assess the robustness and generalization capabilities of the learned autonomous driving strategies. The findings from this study contribute to the advancement of Gaussian process based Bayesian optimization to optimize the hyperparameters for autonomous driving in RL, providing valuable insights for the development of efficient and reliable autonomous driving systems.
We introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov Chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.
Audio-Visual Segmentation (AVS) aims to achieve pixel-level localization of sound sources in videos, while Audio-Visual Semantic Segmentation (AVSS), as an extension of AVS, further pursues semantic understanding of audio-visual scenes. However, since the AVSS task requires the establishment of audio-visual correspondence and semantic understanding simultaneously, we observe that previous methods have struggled to handle this mashup of objectives in end-to-end training, resulting in insufficient learning and sub-optimization. Therefore, we propose a two-stage training strategy called \textit{Stepping Stones}, which decomposes the AVSS task into two simple subtasks from localization to semantic understanding, which are fully optimized in each stage to achieve step-by-step global optimization. This training strategy has also proved its generalization and effectiveness on existing methods. To further improve the performance of AVS tasks, we propose a novel framework Adaptive Audio Visual Segmentation, in which we incorporate an adaptive audio query generator and integrate masked attention into the transformer decoder, facilitating the adaptive fusion of visual and audio features. Extensive experiments demonstrate that our methods achieve state-of-the-art results on all three AVS benchmarks. The project homepage can be accessed at https://gewu-lab.github.io/stepping_stones/.
Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion planning is composability -- different motion constraints can be easily combined by adding corresponding potentials. However, constructing motion paths from potentials requires solving a global optimization across configuration space potential landscape, which is often prone to local minima. We propose a new approach towards learning potential based motion planning, where we train a neural network to capture and learn an easily optimizable potentials over motion planning trajectories. We illustrate the effectiveness of such approach, significantly outperforming both classical and recent learned motion planning approaches and avoiding issues with local minima. We further illustrate its inherent composability, enabling us to generalize to a multitude of different motion constraints.
Structured Sentiment Analysis (SSA) was cast as a problem of bi-lexical dependency graph parsing by prior studies. Multiple formulations have been proposed to construct the graph, which share several intrinsic drawbacks: (1) The internal structures of spans are neglected, thus only the boundary tokens of spans are used for relation prediction and span recognition, thus hindering the model's expressiveness; (2) Long spans occupy a significant proportion in the SSA datasets, which further exacerbates the problem of internal structure neglect. In this paper, we treat the SSA task as a dependency parsing task on partially-observed dependency trees, regarding flat spans without determined tree annotations as latent subtrees to consider internal structures of spans. We propose a two-stage parsing method and leverage TreeCRFs with a novel constrained inside algorithm to model latent structures explicitly, which also takes advantages of joint scoring graph arcs and headed spans for global optimization and inference. Results of extensive experiments on five benchmark datasets reveal that our method performs significantly better than all previous bi-lexical methods, achieving new state-of-the-art.