Multi-task optimization is typically characterized by a fixed and finite set of optimization tasks. The present paper relaxes this condition by considering a non-fixed and potentially infinite set of optimization tasks defined in a parameterized, continuous and bounded task space. We refer to this unique problem setting as parametric multi-task optimization (PMTO). Assuming the bounds of the task parameters to be ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$), a novel ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$)-PMTO algorithm is crafted to enable joint search over tasks and their solutions. This joint search is supported by two approximation models: (1) for mapping solutions to the objective spaces of all tasks, which provably accelerates convergence by acting as a conduit for inter-task knowledge transfers, and (2) for probabilistically mapping tasks to the solution space, which facilitates evolutionary exploration of under-explored regions of the task space. At the end of a full ($\boldsymbol{\theta}_l$, $\boldsymbol{\theta}_u$)-PMTO run, the acquired models enable rapid identification of optimized solutions for any task lying within the specified bounds. This outcome is validated on both synthetic test problems and practical case studies, with the significant real-world applicability of PMTO shown towards fast reconfiguration of robot controllers under changing task conditions. The potential of PMTO to vastly speedup the search for solutions to minimax optimization problems is also demonstrated through an example in robust engineering design.

With the advancement of multi-robot technology, cooperative exploration tasks have garnered increasing attention. This paper presents a comprehensive review of multi-robot cooperative exploration systems. First, we review the evolution of robotic exploration and introduce a modular research framework tailored for multi-robot cooperative exploration. Based on this framework, we systematically categorize and summarize key system components. As a foundational module for multi-robot exploration, the localization and mapping module is primarily introduced by focusing on global and relative pose estimation, as well as multi-robot map merging techniques. The cooperative motion module is further divided into learning-based approaches and multi-stage planning, with the latter encompassing target generation, task allocation, and motion planning strategies. Given the communication constraints of real-world environments, we also analyze the communication module, emphasizing how robots exchange information within local communication ranges and under limited transmission capabilities. Finally, we discuss the challenges and future research directions for multi-robot cooperative exploration in light of real-world trends. This review aims to serve as a valuable reference for researchers and practitioners in the field.

This paper introduces BSPA, a parallel algorithm that leverages beam search to address the two-dimensional strip packing problem. The study begins with a comprehensive review of existing approaches and methodologies, followed by a detailed presentation of the BSPA algorithm. Experimental results demonstrate the effectiveness of the proposed method. To facilitate further research, both the code and datasets are publicly available.

Abstract: This paper presents a pipeline that combines high-resolution orthomosaic maps generated from UAS imagery with GPS-based global navigation to guide a skid-steered ground robot. We evaluated three path planning strategies: A* Graph search, Deep Q-learning (DQN) model, and Heuristic search, benchmarking them on planning time and success rate in realistic simulation environments. Experimental results reveal that the Heuristic search achieves the fastest planning times (0.28 ms) and a 100% success rate, while the A* approach delivers nearoptimal performance, and the DQN model, despite its adaptability, incurs longer planning delays and occasional suboptimal routing. These results highlight the advantages of deterministic rulebased methods in geometrically constrained crop-row environments and lay the groundwork for future hybrid strategies in precision agriculture. Keywords: Path planning, autonomous control, crop rows, autonomous nitrate sampling 1. INTRODUCTION Autonomous navigation in agricultural fields is challenging due to structured layouts with unstructured variability.

Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Preference Optimization for Combinatorial Optimization (POCO), a training paradigm that leverages solution preferences via objective values. It introduces: (1) an efficient preference pair construction for better explore and exploit solutions, and (2) a novel loss function that adaptively scales gradients via objective differences, removing reliance on reward models or reference policies. Experiments on Job-Shop Scheduling (JSP), Traveling Salesman (TSP), and Flexible Job-Shop Scheduling (FJSP) show POCO outperforms state-of-the-art neural methods, reducing optimality gaps impressively with efficient inference. POCO is architecture-agnostic, enabling seamless integration with existing NCO models, and establishes preference optimization as a principled framework for combinatorial optimization.

In this study, we present a block-based heuristic search algorithm to address the nuclear waste container packing problem in the context of real-world nuclear power plants. Additionally, we provide a dataset comprising 1600 problem instances for future researchers to use. Experimental results on this dataset demonstrate that the proposed algorithm effectively enhances the disposal pool's space utilization while minimizing the radiation dose within the pool. The code and data employed in this study are publicly available to facilitate reproducibility and further investigation.

This work suggests faster and space-efficient index construction algorithms for LSH for Euclidean distance (\textit{a.k.a.}~\ELSH) and cosine similarity (\textit{a.k.a.}~\SRP). The index construction step of these LSHs relies on grouping data points into several bins of hash tables based on their hashcode. To generate an $m$-dimensional hashcode of the $d$-dimensional data point, these LSHs first project the data point onto a $d$-dimensional random Gaussian vector and then discretise the resulting inner product. The time and space complexity of both \ELSH~and \SRP~for computing an $m$-sized hashcode of a $d$-dimensional vector is $O(md)$, which becomes impractical for large values of $m$ and $d$. To overcome this problem, we propose two alternative LSH hashcode generation algorithms both for Euclidean distance and cosine similarity, namely, \CSELSH, \HCSELSH~and \CSSRP, \HCSSRP, respectively. \CSELSH~and \CSSRP~are based on count sketch \cite{count_sketch} and \HCSELSH~and \HCSSRP~utilize higher-order count sketch \cite{shi2019higher}. These proposals significantly reduce the hashcode computation time from $O(md)$ to $O(d)$. Additionally, both \CSELSH~and \CSSRP~reduce the space complexity from $O(md)$ to $O(d)$; ~and \HCSELSH, \HCSSRP~ reduce the space complexity from $O(md)$ to $O(N \sqrt[N]{d})$ respectively, where $N\geq 1$ denotes the size of the input/reshaped tensor. Our proposals are backed by strong mathematical guarantees, and we validate their performance through simulations on various real-world datasets.

The problem of finding a minimum vertex cover (MVC) in a graph is a well-known NP-hard problem with significant practical applications in optimization and scheduling. Its complexity, combined with the increasing scale of problems, underscores the need for efficient and effective algorithms. However, existing heuristic algorithms for MVC often rely on simplistic initialization strategies and overlook the impact of edge attributes and neighborhood information on vertex selection. In this paper, we introduce GCNIVC, a novel heuristic search algorithm designed to address the limitations of existing methods for solving MVC problems in large-scale graphs. Our approach features two main innovations. First, it utilizes a Graph Convolutional Network (GCN) to capture the global structure of graphs, which enables the generation of high-quality initial solutions that enhance the efficiency of the subsequent search process. Second, GCNIVC introduces a new heuristic that employs three containers and the concept of double-covered edges (dc-edges), improving search efficiency and providing greater flexibility for adding and removing operations based on edge attributes. Through extensive experiments on benchmark datasets, we demonstrate that GCNIVC outperforms state-of-the-art MVC algorithms in terms of both accuracy and efficiency. Our results highlight the effectiveness of GCNIVC's GCN-assisted initialization and its edge-informed search strategy. This study not only advances the understanding of MVC problem-solving but also contributes a new tool for addressing large-scale graph optimization challenges.

According to the recently introduced theory of artistic support tools, creativity support tools exert normative influences over artistic production, instantiating a normative ground that shapes both the process and product of artistic expression. We argue that the normative ground of most existing automated writing tools is misaligned with writerly values and identify a potential alternative frame-material writing support-for experimental poetry tools that flexibly support the finding, processing, transforming, and shaping of text(s). Based on this frame, we introduce Phraselette, an artistic material writing support interface that helps experimental poets search for words and phrases. To provide material writing support, Phraselette is designed to counter the dominant mode of automated writing tools, while offering language model affordances in line with writerly values. We further report on an extended expert evaluation involving 10 published poets that indicates support for both our framing of material writing support and for Phraselette itself.

We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems in the framework of diffusion models. The exploration of the graph is carried out by the forward process, while finding the target nodes is done by the inverse backward process. This systematizes the discussion and suggests many generalizations. To improve exploration, we propose a ``reversed score'' ansatz which substantially improves over previous comparable algorithms.