Robotic manipulation demands precise control over both contact forces and motion trajectories. While force control is essential for achieving compliant interaction and high-frequency adaptation, it is limited to operations in close proximity to the manipulated object and often fails to maintain stable orientation during extended motion sequences. Conversely, optimization-based motion planning excels in generating collision-free trajectories over the robot's configuration space but struggles with dynamic interactions where contact forces play a crucial role. To address these limitations, we propose a multi-modal control framework that combines force control and optimization-augmented motion planning to tackle complex robotic manipulation tasks in a sequential manner, enabling seamless switching between control modes based on task requirements. Our approach decomposes complex tasks into subtasks, each dynamically assigned to one of three control modes: Pure optimization for global motion planning, pure force control for precise interaction, or hybrid control for tasks requiring simultaneous trajectory tracking and force regulation. This framework is particularly advantageous for bimanual and multi-arm manipulation, where synchronous motion and coordination among arms are essential while considering both the manipulated object and environmental constraints. We demonstrate the versatility of our method through a range of long-horizon manipulation tasks, including single-arm, bimanual, and multi-arm applications, highlighting its ability to handle both free-space motion and contact-rich manipulation with robustness and precision.

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer's core design in solving VRPs.

This paper presents a robust cascaded control architecture for over-actuated multirotors. It extends the Incremental Nonlinear Dynamic Inversion (INDI) control combined with structured H_inf control, initially proposed for under-actuated multirotors, to a broader range of multirotor configurations. To achieve precise and robust attitude and position tracking, we employ a weighted least-squares geometric guidance control allocation method, formulated as a quadratic optimization problem, enabling full-pose tracking. The proposed approach effectively addresses key challenges, such as preventing infeasible pose references and enhancing robustness against disturbances, as well as considering multirotor's actual physical limitations. Numerical simulations with an over-actuated hexacopter validate the method's effectiveness, demonstrating its adaptability to diverse mission scenarios and its potential for real-world aerial applications.

Recent advancements in large language models (LLMs) have highlighted their potential across a variety of tasks, but their performance still heavily relies on the design of effective prompts. Existing methods for automatic prompt optimization face two challenges: lack of diversity, limiting the exploration of valuable and innovative directions and semantic drift, where optimizations for one task can degrade performance in others. To address these issues, we propose Residual Optimization Tree (RiOT), a novel framework for automatic prompt optimization. RiOT iteratively refines prompts through text gradients, generating multiple semantically diverse candidates at each step, and selects the best prompt using perplexity. Additionally, RiOT incorporates the text residual connection to mitigate semantic drift by selectively retaining beneficial content across optimization iterations. A tree structure efficiently manages the optimization process, ensuring scalability and flexibility. Extensive experiments across five benchmarks, covering commonsense, mathematical, logical, temporal, and semantic reasoning, demonstrate that RiOT outperforms both previous prompt optimization methods and manual prompting.

Legged robots, such as quadrupeds and humanoids, require high-performance actuators for efficient locomotion. Quasi-Direct-Drive (QDD) actuators with single-stage planetary gearboxes offer low inertia, high efficiency, and transparency. Among planetary gearbox architectures, Internal (ISSPG) and External Single-Stage Planetary Gearbox (ESSPG) are the two predominant designs. While ISSPG is often preferred for its compactness and high torque density at certain gear ratios, no objective comparison between the two architectures exists. Additionally, existing designs rely on heuristics rather than systematic optimization. This paper presents a design framework for optimally selecting actuator parameters based on given performance requirements and motor specifications. Using this framework, we generate and analyze various optimized gearbox designs for both architectures. Our results demonstrate that for the T-motor U12, ISSPG is the superior choice within the lower gear ratio range of 5:1 to 7:1, offering a lighter design. However, for gear ratios exceeding 7:1, ISSPG becomes infeasible, making ESSPG the better option in the 7:1 to 11:1 range. To validate our approach, we designed and optimized two actuators for manufacturing: an ISSPG with a 6.0:1 gear ratio and an ESSPG with a 7.2:1 gear ratio. Their respective masses closely align with our optimization model predictions, confirming the effectiveness of our methodology.

Increasing global energy demand and renewable integration complexity have placed buildings at the center of sustainable energy management. We present a three-step reinforcement learning(RL)-based Building Energy Management System (BEMS) that combines clustering, forecasting, and constrained policy learning to address scalability, adaptability, and safety challenges. First, we cluster non-shiftable load profiles to identify common consumption patterns, enabling policy generalization and transfer without retraining for each new building. Next, we integrate an LSTM based forecasting module to anticipate future states, improving the RL agents' responsiveness to dynamic conditions. Lastly, domain-informed action masking ensures safe exploration and operation, preventing harmful decisions. Evaluated on real-world data, our approach reduces operating costs by up to 15% for certain building types, maintains stable environmental performance, and quickly classifies and optimizes new buildings with limited data. It also adapts to stochastic tariff changes without retraining. Overall, this framework delivers scalable, robust, and cost-effective building energy management.

Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Matérn and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the domain of the function, which may limit their applicability in bounded domains. To address the limitation, we introduce the Beta kernel, a non-stationary kernel induced by a product of Beta distribution density functions. Such a formulation allows our kernel to naturally model functions on bounded domains. We present statistical evidence supporting the hypothesis that the kernel exhibits an exponential eigendecay rate, based on empirical analyses of its spectral properties across different settings. Our experimental results demonstrate the robustness of the Beta kernel in modeling functions with optima located near the faces or vertices of the unit hypercube. The experiments show that our kernel consistently outperforms a wide range of kernels, including the well-known Matérn and RBF, in different problems, including synthetic function optimization and the compression of vision and language models.

With the rise of distributed energy resources and sector coupling, distributed optimization can be a sensible approach to coordinate decentralized energy resources. Further, district heating, heat pumps, cogeneration, and sharing concepts like local energy communities introduce the potential to optimize heating and electricity output simultaneously. To solve this issue, we tackle the distributed multi-energy scheduling optimization problem, which describes the optimization of distributed energy generators over multiple time steps to reach a specific target schedule. This work describes a novel distributed hybrid algorithm as a solution approach. This approach is based on the heuristics of gossiping and local search and can simultaneously optimize the private objective of the participants and the collective objective, considering multiple energy sectors. We show that the algorithm finds globally near-optimal solutions while protecting the stakeholders' economic goals and the plants' technical properties. Two test cases representing pure electrical and gas-based technologies are evaluated.

Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph. This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions. Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.

Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.