EURO Journal on Computational Optimization最新文献

英文中文

A diving heuristic for mixed-integer problems with unbounded semi-continuous variables 具有无界半连续变量的混合整数问题的潜水启发式

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100107

Katrin Halbig , Alexander Hoen , Ambros Gleixner , Jakob Witzig , Dieter Weninger

Semi-continuous decision variables arise naturally in many real-world applications. They are defined to take either value zero or any value within a specified range, and occur mainly to prevent small nonzero values in the solution. One particular challenge that can come with semi-continuous variables in practical models is that their upper bound may be large or even infinite. In this article, we briefly discuss these challenges, and present a new diving heuristic tailored for mixed-integer optimization problems with general semi-continuous variables. The heuristic is designed to work independently of whether the semi-continuous variables are bounded from above, and thus circumvents the specific difficulties that come with unbounded semi-continuous variables. We conduct extensive computational experiments on three different test sets, integrating the heuristic in an open-source MIP solver. The results indicate that this heuristic is a successful tool for finding high-quality solutions in negligible time. At the root node the primal gap is reduced by an average of 5% up to 21%, and considering the overall performance improvement, the primal integral is reduced by 2% to 17% on average.

半连续决策变量在许多实际应用中自然出现。它们被定义为取零值或指定范围内的任何值，主要是为了防止解中出现小的非零值。在实际模型中，半连续变量可能面临的一个特殊挑战是，它们的上界可能很大，甚至是无限的。在本文中，我们简要地讨论了这些挑战，并提出了一种针对一般半连续变量的混合整数优化问题的新的潜水启发式算法。启发式被设计为独立于半连续变量是否从上面有界工作，从而规避了无界半连续变量带来的特定困难。我们在三个不同的测试集上进行了大量的计算实验，并将启发式算法集成到一个开源的MIP求解器中。结果表明，这种启发式方法是在可忽略不计的时间内找到高质量解的成功工具。在根节点，原始间隙平均减少了5%到21%，考虑到整体性能的提高，原始积分平均减少了2%到17%。

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引用次数: 0

Unsupervised learning with GNNs for QUBO-based combinatorial optimization 基于gnn的无监督学习基于qubo的组合优化

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100116

Olga Krylova , Frank Phillipson

Recent advances in deep learning techniques pose a question of whether they can facilitate the task of finding good quality solutions to combinatorial optimization (CO) problems in a practically relevant solution time. Specifically, it is of practical relevance to determine to what extent graph neural networks (GNNs) can be applied to CO problems that can be formulated as QUBOs and thus be naturally interpreted as graph problems. In this research a GNN solver is applied to two classical CO problems–the maximum cut problem and maximum independent set problem–in an unsupervised learning setting. We show that while GNN solver consistently finds good quality solutions for the Max Cut problem irrespective of the size and density of the graph, solving MIS problems is challenging for all but very sparse graphs. We further show how this problem can be addressed by embedding transfer between these two problems and compare two different GNN architectures–GCN and GraphSAGE on their robustness with respect to graph density and symmetry. Finally we demonstrate that changing the widely used Adam optimizer to Rprop optimizer can lead to considerable reduction in solution times.

深度学习技术的最新进展提出了一个问题，即它们是否能够在实际相关的解决时间内为组合优化（CO）问题找到高质量的解决方案。具体来说，确定图神经网络（gnn）在多大程度上可以应用于CO问题具有实际意义，这些问题可以表述为qubo，从而自然地解释为图问题。本文将GNN求解器应用于无监督学习环境下的两个经典CO问题——最大割问题和最大独立集问题。我们表明，尽管无论图的大小和密度如何，GNN求解器始终能够为Max Cut问题找到高质量的解，但除了非常稀疏的图外，解决MIS问题对所有图都具有挑战性。我们进一步展示了如何通过在这两个问题之间嵌入转移来解决这个问题，并比较了两种不同的GNN架构——gcn和GraphSAGE在图密度和对称性方面的鲁棒性。最后，我们证明了将广泛使用的Adam优化器更改为Rprop优化器可以大大减少解决时间。

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引用次数: 0

Decentralised convex optimisation with probability-proportional-to-size quantization 概率比例量化的分散凸优化

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100113

D.A. Pasechnyuk , P. Dvurechensky , C.A. Uribe , A.V. Gasnikov

Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical distribution with probabilities proportional to values at those components. Then, we propose a primal and a primal-dual accelerated stochastic gradient methods that use our proposed quantization, and derive their convergence rates in terms of probabilities of large deviations. We focus on affine-constrained convex optimisation and its application to decentralised distributed optimisation problems. To illustrate the work of our algorithm, we apply it to the decentralised computation of semi-discrete entropy regularized Wasserstein barycentre's.

通信是分布式优化和学习的瓶颈之一。为了克服这一瓶颈，我们提出了一种新的量化方法，该方法将向量转换为从分类分布中提取的组件指标样本，其概率与这些组件的值成正比。然后，我们提出了一种原始和原始对偶加速随机梯度方法，它们使用我们提出的量化，并根据大偏差的概率推导出它们的收敛速度。我们关注仿射约束凸优化及其在分散分布式优化问题中的应用。为了说明我们的算法的工作，我们将其应用于半离散熵正则化Wasserstein质心的分散计算。

引用次数: 0

A robust twin parametric margin support vector machine for multiclass classification 多类分类的鲁棒双参数余量支持向量机

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100115

Renato De Leone , Francesca Maggioni , Andrea Spinelli

In this paper, we introduce novel Twin Parametric Margin Support Vector Machine (TPMSVM) models designed to address multiclass classification tasks under feature uncertainty. To handle data perturbations, we construct bounded-by-norm uncertainty sets around each training observation and derive the robust counterparts of the deterministic models using robust optimization techniques. To capture complex data structures, we explore both linear and kernel-induced classifiers, providing computationally tractable reformulations of the resulting robust models. Additionally, we propose two alternatives for the final decision function, enhancing models’ flexibility. Finally, we validate the effectiveness of the proposed robust multiclass TPMSVM methodology on real-world datasets, showing the good performance of the approach in the presence of uncertainty.

本文提出了一种新的双参数边界支持向量机（TPMSVM）模型，用于解决特征不确定性下的多类分类任务。为了处理数据扰动，我们在每个训练观测值周围构建了范数有界的不确定性集，并使用鲁棒优化技术推导出确定性模型的鲁棒对应物。为了捕获复杂的数据结构，我们探索了线性和核诱导分类器，提供了计算上易于处理的鲁棒模型的重新表述。此外，我们提出了最终决策函数的两种备选方案，增强了模型的灵活性。最后，我们在真实数据集上验证了所提出的鲁棒多类TPMSVM方法的有效性，表明该方法在存在不确定性的情况下具有良好的性能。

引用次数: 0

On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations 基于方向归一化的dantzigg - wolfe分解和Fenchel分解的集成

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100122

François Lamothe , Alain Haït , Emmanuel Rachelson , Claudio Contardo , Bernard Gendron

Strengthening linear relaxations and the bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit strong dual bounds to discard unpromising regions of the feasible space. In this paper, we consider the strengthening of linear programs via a composite of Dantzig-Wolfe and Fenchel decompositions. We provide geometric interpretations of these two standard methods. Motivated by these geometric interpretations, we introduce a novel approach for solving Fenchel sub-problems and propose a novel algorithmic method that originally combines Dantzig-Wolfe and Fenchel decompositions. We carry out extensive computational experiments assessing the performance of the novel method on the unsplittable flow problem. This new approach yields very promising results when compared to usual decomposition methods.

几十年来，强化线性松弛和混合整数线性规划的界一直是一个活跃的研究课题。基于枚举的整数规划方法，如基于线性规划的分支定界方法，利用强对偶界来丢弃可行空间中没有希望的区域。在本文中，我们考虑通过dantzigg - wolfe和Fenchel分解的组合来增强线性规划。我们提供了这两种标准方法的几何解释。在这些几何解释的激励下，我们引入了一种求解Fenchel子问题的新方法，并提出了一种将dantzigg - wolfe分解和Fenchel分解相结合的新算法。我们进行了大量的计算实验，以评估新方法在不可分割流动问题上的性能。与通常的分解方法相比，这种新方法产生了非常有希望的结果。

引用次数: 0

Randomized block coordinate DC algorithm 随机块坐标DC算法

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100123

Hoomaan Maskan , Paniz Halvachi , Suvrit Sra , Alp Yurtsever

We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For

n

coordinate-blocks and

k

iterations, our main result proves a non-asymptotic convergence rate of

O (n / k)

in expectation, with respect to a stationarity measure based on a Forward-Backward envelope. Furthermore, leveraging the connection between DCA and Expectation Maximization (EM), we propose a randomized block coordinate EM algorithm.

本文以随机分块坐标方法的形式，对可分离结构问题的凸差分算法进行了扩展。对于n个坐标块和k次迭代，我们的主要结果证明了期望的非渐近收敛率为O(n/k)，相对于基于前向向后包络的平稳性度量。此外，利用DCA和期望最大化（EM）之间的联系，我们提出了一种随机块坐标EM算法。

引用次数: 0

A tutorial on properties of the epigraph reformulation 关于铭文改写的性质的教程

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100109

Oliver Stein

This paper systematically surveys useful properties of the epigraph reformulation for optimization problems, and complements them by some new results. We focus on the complete compatibility of the original formulation and the epigraph reformulation with respect to solvability and unsolvability, the compatibility with respect to some, but not all, basic constraint qualifications, the formulation of first-order optimality conditions for problems with max-type objective function, and the interpretation of feasibility and optimality cuts along epigraphs in the framework of cutting plane methods. Finally we introduce a generalized epigraph reformulation which is particularly useful for treating nonsmooth summands of objective and constraint functions independently in the reformulation.

本文系统地考察了铭文重构在优化问题中的一些有用性质，并补充了一些新的结果。我们重点研究了原始公式与金字改写公式在可解性和不可解性方面的完全相容，对一些但不是全部的基本约束条件的相容，最大型目标函数问题的一阶最优性条件的表述，以及在切割平面方法的框架下金字可行性和最优性切割的解释。最后，我们引入了一种广义的铭文重构，它特别适用于在重构中单独处理目标函数和约束函数的非光滑求和。

引用次数: 0

In memoriam: Marguerite Straus Frank (1927–2024) 纪念：玛格丽特·斯特劳斯·弗兰克（1927-2024）

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100104

Immanuel Bomze, Anna Nagurney

引用次数: 0

Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms 2025年的直接搜索方法：理论保证和算法范式

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100110

K.J. Dzahini , F. Rinaldi , C.W. Royer , D. Zeffiro

Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of implementation, even though its theoretical underpinnings are not always easy to grasp.

In this work, we survey contemporary direct-search algorithms from a theoretical viewpoint, with the aim of highlighting the key theoretical features of these methods. We provide a basic introduction to the main classes of direct-search methods, including line-search techniques that have received little attention in earlier surveys. We also put a particular emphasis on probabilistic direct-search techniques and their application to noisy problems, a topic that has undergone significant algorithmic development in recent years. Finally, we complement existing surveys by reviewing the main theoretical advances for solving constrained and multiobjective optimization using direct-search algorithms.

在不使用导数的情况下优化函数是一个具有挑战性的范例，它排除了使用非线性优化的经典算法，因此可能看起来很难，而不是使用启发式。尽管如此，无导数优化领域已经成功地产生了不依赖于导数但又具有收敛性保证的算法。这类方法中有一类被称为直接搜索方法，由于其实现简单而特别受欢迎，尽管其理论基础并不总是容易掌握。在这项工作中，我们从理论角度调查了当代直接搜索算法，目的是突出这些方法的关键理论特征。我们提供了直接搜索方法的主要类别的基本介绍，包括在早期调查中很少受到关注的线搜索技术。我们还特别强调了概率直接搜索技术及其在噪声问题中的应用，这是近年来经历了重大算法发展的主题。最后，我们通过回顾使用直接搜索算法解决约束和多目标优化的主要理论进展来补充现有的调查。

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引用次数: 0

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100117

Héctor G.-de-Alba , Samuel Nucamendi-Guillén , Oliver Avalos-Rosales , Francisco Ángel-Bello

This paper addresses with minimizing the makespan in unrelated parallel machines with sequence and machine-dependent setup times involving a non-overlapping shared resource. The shared resource corresponds to an operator who can service one machine at a time to perform setup operations when it is necessary to change the type of job to be processed. We develop two Mixed Integer Linear Programming (MILP) formulations and a metaheuristic algorithm that combines an Iterated Greedy scheme with Variable Neighborhood Descent (IG + VND). Both approaches were compared with existing models and algorithms from the literature. The results indicate that the proposed formulation outperforms previous models present in the literature in instances of up to 14 jobs and 4 machines. The algorithm reported average deviations within 5 % of the solutions obtained by the model, but performed up to 3 orders of magnitude faster. Similarly, the proposed IG+VND outperformed the other algorithms in the literature, particularly for instances of up to 40 jobs and 6 machines, and obtained solutions for instances of up to 60 jobs and up to 6 machines.

本文讨论了在不重叠的共享资源中，具有序列和机器相关设置时间的不相关并行机中最小化最大完工时间的问题。共享资源对应于一个操作员，当需要更改要处理的作业类型时，操作员可以一次为一台机器提供服务，以执行设置操作。我们提出了两个混合整数线性规划（MILP）公式和一个结合迭代贪心方案和可变邻域下降（IG + VND）的元启发式算法。将这两种方法与文献中的现有模型和算法进行比较。结果表明，在多达14个工作和4台机器的情况下，提出的公式优于文献中出现的先前模型。该算法报告的平均偏差在模型得到的解决方案的5%以内，但执行速度高达3个数量级。同样，所提出的IG+VND算法优于文献中的其他算法，特别是在多达40个作业和6台机器的情况下，并获得了最多60个作业和最多6台机器的解决方案。

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EURO Journal on Computational Optimization

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