Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether or not an item can be placed feasibly at a certain position, and the optimization challenge of finding a good solution according to some objective function. Until now, those tackling such problems have had to address both challenges simultaneously, requiring two distinct sets of expertise and a lot of research & development effort. One way to lower this barrier is to decouple the two challenges. In this paper we introduce a powerful collision detection engine (CDE) for 2D irregular C&P problems which assumes full responsibility for the geometric challenge. The CDE (i) allows users to focus with full confidence on their optimization challenge by abstracting geometry away and (ii) enables independent advances to propagate to all optimization algorithms built atop it. We present a set of core principles and design philosophies to model a general and adaptable CDE focused on maximizing performance, accuracy and robustness. These principles are accompanied by a concrete open-source implementation called jagua-rs. This paper together with its implementation serves as a catalyst for future advances in irregular C&P problems by providing a solid foundation which can either be used as it currently exists or be further improved upon. Funding: This research was supported by the Research Foundation -- Flanders (FWO) under grant number 1S71222N and K804824N.

Abstract--Genetic programming (GP) has demonstrated strong effectiveness in evolving tree-structured heuristics for complex optimization problems. Y et, in dynamic and large-scale scenarios, the most effective heuristics are often highly complex, hindering interpretability, slowing convergence, and limiting transferability across tasks. T o address these challenges, we present EvoSpeak, a novel framework that integrates GP with large language models (LLMs) to enhance the efficiency, transparency, and adaptability of heuristic evolution. EvoSpeak learns from high-quality GP heuristics, extracts knowledge, and leverages this knowledge to (i) generate warm-start populations that accelerate convergence, (ii) translate opaque GP trees into concise natural-language explanations that foster interpretability and trust, and (iii) enable knowledge transfer and preference-aware heuristic generation across related tasks. We verify the effectiveness of EvoSpeak through extensive experiments on dynamic flexible job shop scheduling (DFJSS), under both single-and multi-objective formulations. The results demonstrate that EvoSpeak produces more effective heuristics, improves evolutionary efficiency, and delivers human-readable reports that enhance usability. EURISTICS are indispensable tools for solving complex decision-making and optimization problems, with applications spanning scheduling [1], routing [2], and resource allocation [3]. They are designed to provide adaptive, domain-specific solutions that balance solution quality and computational efficiency, enabling practitioners to make near-optimal decisions in real time. Among the diverse methodologies for heuristic design, Genetic Programming (GP) [4] has emerged as a particularly powerful paradigm, capable of evolving interpretable symbolic rules that adapt to different problem structures [5]. GP-generated heuristics often rival, and sometimes surpass, learning-based methods such as neural combinatorial optimization [6], especially in terms of transparency and adaptability. Meng Xu is with the Singapore Institute of Manufacturing Technology, Agency for Science, Technology and Research, Singapore (e-mail: xu_meng@simtech.a-star.edu.sg). Jiao Liu is with the College of Computing & Data Science, Nanyang Technological University, Singapore (e-mail: jiao.liu@ntu.edu.sg). Y ew Soon Ong is with the College of Computing and Data Science, Nanyang Technological University, and the Centre for Frontier AI Research, Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore (e-mail: asysong@ntu.edu.sg). Despite these advantages, the practical deployment of GPevolved heuristics faces two persistent challenges: complexity and transferability.

We consider the simplest possible case that still allows for nonlinear dynamics.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes several approaches to sample from a Gibbs distribution over a discrete space by solving randomly perturbed combinatorial optimization problems (MAP inference) over the same space. The starting point is a known result [5] that allows to do sampling (in principle, using high dimensional perturbations with exponential complexity) by solving a single optimization problem. In this paper they propose to 1) use more efficient low-dimensional random perturbations to do approximate sampling (with probabilistic accuracy guarantees on tree structured models) 2) estimate (conditional) marginals using ratios of partition function estimates, and sequentially sample variables. They propose a clever rejection strategy based on self reduction that guarantees unbiasedness of the samples.

Neural Information Processing Systems http://nips.cc/

It is defined w.r.t. a finite number of finite sets, all of the same cardinality. A feasible solution consists in as many bijections as there are pairs of distinct sets. These bijections are constrained to be consistent in the following sense: For any three sets, A, B, C, if a in A is mapped to b in B and b in B is mapped to c in C, then a needs to be mapped to c. The objective function is defined w.r.t.

Meta-learning, or 'learning to learn' [ However, it can be any useful knowledge which can be learned in the meta-training stage. This setting is intuitive and theoretically sound.

The optimal first-order algorithm of Nesterov has linear convergence for such problem but the constant depends on the square root of the condition number k. The authors consider the situation where one has access to the expensive full gradient of the objective as well as a cheap stochastic gradient oracle. They propose a hybrid algorithm which only requires O(log 1/eps) calls to the full gradient oracle (independent of the condition number) and O(k^2 log(1/eps)) calls to the cheaper stochastic gradient oracle -- as long as the condition number is not too big, this could be faster in theory. The main idea behind their algorithm(called Epoch Mixed Gradient Descent - EMGD) is to replace a full gradient step (called an epoch) with a fixed number O(k^2) of mixed gradient steps which use a combination of the full gradient (computed once for the epoch) and stochastic gradients (which vary within an epoch). By taking the average of the O(k^2) iterates within an epoch, they can show a constant decrease of the suboptimality *independent* of the condition number, which is why the number of required full gradient step computations (the number of epochs) is independent from the condition number. They provide a simple and complete self-contained proof of their convergence rate, but no experiment.