Tootfinder

Solving the Market Split Problem with Lattice Enumeration
Alfred Wassermann
https://arxiv.org/abs/2508.08702 https://arxiv.org/pdf/2508.08702

Solving the Market Split Problem with Lattice Enumeration
The market split problem was proposed by Cornuéjols and Dawande in 1998 as benchmark problem for algorithms solving linear systems with binary variables. The recent (2025) Quantum Optimization Benchmark Library (QOBLIB) contains a set of feasible instances of the market split problem. The market split problem seems to be difficult to solve with the conventional branch-and-bound approach of integer linear programming software which reportedly can handle QOBLIB instances up to $m=7$. In contra…

Solving Set Constraints with Comprehensions and Bounded Quantifiers
Mudathir Mohamed, Nick Feng, Andrew Reynolds, Cesare Tinelli, Clark Barrett, Marsha Chechik
https://arxiv.org/abs/2508.08496

Solving Set Constraints with Comprehensions and Bounded Quantifiers
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have been developed to tackle this. However, SMT solvers still struggle with quantified formulas generated by some applications. In this paper, we discuss the use of set-bounded quantifiers, quantifiers whose variable ranges over a finite set. These quantifiers can…

Teaching Problem Solving in Undergraduate Physics Courses: An Endorsement for Deliberate Practice
Kelly Miller, Olivia Miller, Georgia Lawrence
https://arxiv.org/abs/2508.08133 …

Teaching Problem Solving in Undergraduate Physics Courses: An Endorsement for Deliberate Practice
Developing expert-like problem-solving skills is a central goal of undergraduate physics education. In this study, we investigate the impact of teaching explicit problem-solving frameworks, combined with deliberate practice, on students' problem-solving approaches. Using multidimensional scaling to analyze students' decision-making patterns, we compare the similarity of students taught with these methods to physics experts and to students taught with traditional repeated practice. Our results s…

Material Fingerprinting: A shortcut to material model discovery without solving optimization problems
Moritz Flaschel, Denisa Martonov\'a, Carina Veil, Ellen Kuhl
https://arxiv.org/abs/2508.07831

Material Fingerprinting: A shortcut to material model discovery without solving optimization problems
We propose Material Fingerprinting, a new method for the rapid discovery of mechanical material models from direct or indirect data that avoids solving potentially non-convex optimization problems. The core assumption of Material Fingerprinting is that each material exhibits a unique response when subjected to a standardized experimental setup. We can interpret this response as the material's fingerprint, essentially a unique identifier that encodes all pertinent information about the material'…

Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
Francesco Dell'Accio, Luca Desiderio, Allal Guessab, Federico Nudo
https://arxiv.org/abs/2508.07238

Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
In this paper, we propose weighted and unweighted enrichment strategies to enhance the accuracy of the linear lagrangian finite element for solving the Poisson problem with Dirichlet boundary conditions. We first recall key examples of admissible enrichment functions, specifically designed to overcome the limitations of the linear lagrangian finite element in capturing solution features such as sharp gradients and boundary-layer phenomena. We then introduce two novel three-parameter families of…

Triple-S: A Collaborative Multi-LLM Framework for Solving Long-Horizon Implicative Tasks in Robotics
Zixi Jia, Hongbin Gao, Fashe Li, Jiqiang Liu, Hexiao Li, Qinghua Liu
https://arxiv.org/abs/2508.07421

Triple-S: A Collaborative Multi-LLM Framework for Solving Long-Horizon Implicative Tasks in Robotics
Leveraging Large Language Models (LLMs) to write policy code for controlling robots has gained significant attention. However, in long-horizon implicative tasks, this approach often results in API parameter, comments and sequencing errors, leading to task failure. To address this problem, we propose a collaborative Triple-S framework that involves multiple LLMs. Through In-Context Learning, different LLMs assume specific roles in a closed-loop Simplification-Solution-Summary process, effectivel…

Plug-and-play Diffusion Models for Image Compressive Sensing with Data Consistency Projection
Xiaodong Wang, Ping Wang, Zhangyuan Li, Xin Yuan
https://arxiv.org/abs/2509.09365 h…

Plug-and-play Diffusion Models for Image Compressive Sensing with Data Consistency Projection
We explore the connection between Plug-and-Play (PnP) methods and Denoising Diffusion Implicit Models (DDIM) for solving ill-posed inverse problems, with a focus on single-pixel imaging. We begin by identifying key distinctions between PnP and diffusion models-particularly in their denoising mechanisms and sampling procedures. By decoupling the diffusion process into three interpretable stages: denoising, data consistency enforcement, and sampling, we provide a unified framework that integrates…

Enhancing Decision Space Diversity in Multi-Objective Evolutionary Optimization for the Diet Problem
Gustavo V. Nascimento, Ivan R. Meneghini, Val\'eria Santos, Eduardo Luz, Gladston Moreira
https://arxiv.org/abs/2508.07077

Enhancing Decision Space Diversity in Multi-Objective Evolutionary Optimization for the Diet Problem
Multi-objective evolutionary algorithms (MOEAs) are essential for solving complex optimization problems, such as the diet problem, where balancing conflicting objectives, like cost and nutritional content, is crucial. However, most MOEAs focus on optimizing solutions in the objective space, often neglecting the diversity of solutions in the decision space, which is critical for providing decision-makers with a wide range of choices. This paper introduces an approach that directly integrates a H…

Global Nonconvex Optimization with Integer Variables
Dimitris Bertsimas, Danique de Moor, Thodoris Koukouvinos, Demetrios Kriezis
https://arxiv.org/abs/2508.07018 https://

Global Nonconvex Optimization with Integer Variables
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. introduce a novel approach for solving continuous nonconvex optimization problems to provable optimality, called the Relaxation Perspectification Technique - Branch and Bound (RPT-BB). In this paper, we extend the …

Learning to control inexact Benders decomposition via reinforcement learning
Zhe Li, Bernard T. Agyeman, Ilias Mitrai, Prodromos Daoutidis
https://arxiv.org/abs/2508.06700 https…

Learning to control inexact Benders decomposition via reinforcement learning
Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf application to online settings can be computationally inefficient due to the repeated solution of the master problem. An approach to reduce the solution time is to solve the master problem to local optimality. However, identifying the level of suboptimality at each i…