EURO Journal on Computational Optimization最新文献

英文中文

A compact model for the home healthcare routing and scheduling problem 家庭医疗保健路由和调度问题的紧凑模型

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2024.100101

Roberto Montemanni , Sara Ceschia , Andrea Schaerf

Home healthcare has become more and more central in the last decades, due to the advantages it can bring to both healthcare institutions and patients. Planning activities in this context, however, presents significant challenges related to route planning and mutual synchronization of caregivers.

In this paper we propose a new compact model for the combined optimization of scheduling (of the activities) and routing (of the caregivers) characterized by fewer variables and constraints when compared with the models previously available in the literature. The new model is solved by a constraint programming solver and compared experimentally with the exact and metaheuristic approaches available in the literature on the common datasets adopted by the community. The results show that the new model provides improved lower bounds for the vast majority of the instances, while producing at the same time high quality heuristic solutions, comparable to those of tailored metaheuristics, for small/medium size instances.

在过去的几十年里，家庭医疗变得越来越重要，因为它可以给医疗机构和患者带来好处。然而，在这种情况下，规划活动提出了与路线规划和护理人员相互同步相关的重大挑战。在本文中，我们提出了一个新的紧凑模型，用于活动安排和照顾者路线的组合优化，与文献中已有的模型相比，该模型具有更少的变量和约束。新模型通过约束规划求解器求解，并与文献中采用的基于公共数据集的精确方法和元启发式方法进行了实验比较。结果表明，新模型为绝大多数实例提供了改进的下界，同时对中小型实例产生了高质量的启发式解决方案，可与定制元启发式解决方案相媲美。

引用次数: 0

Interior point methods in the year 2025 2025年的内部点法

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100105

Jacek Gondzio

Interior point methods (IPMs) have hugely influenced the field of optimization. Their fast development has been triggered by the seminal paper of Narendra Karmarkar published in 1984 which delivered a polynomial algorithm for linear programming and suggested that it might be implemented into a very efficient method in practice. Indeed, this has been demonstrated within a few years after 1984 and has gained IPMs a status of exceptionally powerful optimization tool. Linear Programming (LP) is at the centre of many operational research techniques including mixed-integer programming, network optimization and various decomposition techniques. Therefore, any progress in LP has far-reaching consequences. IPMs certainly did not disappoint in this context: they have become a heavily used methodology in modern optimization and operational research. Their accuracy, efficiency and reliability have been particularly appreciated when IPMs are applied to truly large scale problems which challenge any alternative approaches.

In this survey we will discuss several issues related to interior point methods. We will recall techniques which provide the building blocks of IPMs, and observe that actually at least some of them have been developed before 1984. We will briefly comment on the worst-case complexity results for different variants of IPMs and then focus on key aspects of their implementation. We will also address some of the most spectacular features of IPMs and discuss their potential advantages when applied in decomposition algorithms, cutting planes scheme and column generation technique.

内点法对优化领域产生了巨大的影响。1984年，纳伦德拉·卡马卡发表了一篇开创性的论文，提出了线性规划的多项式算法，并表明它可能在实践中被实现成一种非常有效的方法，从而引发了线性规划的快速发展。事实上，这在1984年之后的几年内得到了证明，并使ipm获得了异常强大的优化工具的地位。线性规划（LP）是许多运筹学技术的核心，包括混合整数规划、网络优化和各种分解技术。因此，LP的任何进展都具有深远的影响。在这种情况下，ipm当然没有让人失望：它们已经成为现代优化和运筹学中大量使用的方法。当ipm应用于挑战任何替代方法的真正大规模问题时，它们的准确性、效率和可靠性尤其受到赞赏。在本次调查中，我们将讨论与内点法有关的几个问题。我们将回顾提供ipm构建模块的技术，并观察到实际上至少有一些技术是在1984年之前开发的。我们将简要介绍ipm不同变体的最坏情况复杂性结果，然后关注其实现的关键方面。我们还将讨论ipm的一些最引人注目的特征，并讨论它们在分解算法、切割平面方案和列生成技术中应用时的潜在优势。

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引用次数: 0

Speed planning by minimizing travel time and energy consumption 通过最小化旅行时间和能量消耗来规划速度

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100112

Stefano Ardizzoni, Luca Consolini, Mattia Laurini, Marco Locatelli

In this paper we address the speed planning problem for a vehicle over an assigned path with the aim of minimizing a weighted sum of travel time and energy consumption under suitable constraints (maximum allowed speed, maximum traction or braking force, maximum power consumption). The resulting mathematical model is a non-convex optimization problem. We prove that, under some mild assumptions, a convex reformulation of the non-convex problem is exact. In particular, the convex reformulation is a Second Order Cone Programming (SOCP) problem, for which efficient solvers exist. Through the numerical experiments we confirm that the convex relaxation can be solved very efficiently and, moreover, we also provide the Pareto front of the trade-off between the two objectives (travel time and energy consumption).

在本文中，我们解决了车辆在指定路径上的速度规划问题，其目的是在适当的约束条件下（最大允许速度，最大牵引力或制动力，最大功率消耗）最小化行驶时间和能量消耗的加权总和。所得到的数学模型是一个非凸优化问题。我们证明，在一些温和的假设下，非凸问题的凸重新表述是精确的。特别地，凸重构是一个二阶锥规划（SOCP）问题，存在有效的解。通过数值实验，我们证实了凸松弛可以非常有效地求解，并且我们还提供了两个目标（旅行时间和能量消耗）之间权衡的帕累托前沿。

引用次数: 0

Efficient use of optimality conditions in Interval Branch and Bound methods 区间分支和定界方法中最优性条件的有效利用

IF 2.6 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100108

Mihály Gencsi, Boglárka G.-Tóth

The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems where a rigorous solution is required. The method uses Interval Arithmetic (IA) to handle rounding errors in calculations. In the literature, a wide range of variations of IBB exists. However, few IBB implementations use the Karush-Kuhn-Tucker (KKT) or the Fritz-John (FJ) optimality conditions to eliminate non-optimal boxes. The application of the FJ conditions implies to solve a system of interval linear equations, which is often challenging due to overestimation of the boxes. This study focuses on the geometric perspective of the FJ optimality conditions. A preliminary test is introduced, namely the Geometrical Test, which tries to decide when the optimality conditions cannot hold or whether it is convenient to compute the Fritz-John Test. Furthermore, a test case generator is presented that transforms unconstrained problems into constrained test cases by setting a given number of active and inactive constraints at a global optimizer. The efficiency of the Geometrical Test was considered through computational experiments on the generated benchmark. Six variations of the IBB were compared, with or without the FJ condition system and Geometrical Test. The best methods for solving the 272 generated test cases use the designed Geometrical Test with the Lagrange estimator and the Newton step on the normalized interval FJ conditions in most cases.

区间分支定界法（IBB）是求解非线性规划问题的一种广泛使用的方法。该方法使用区间算术（IA）来处理计算中的舍入错误。在文献中，IBB存在着广泛的变异。然而，很少有IBB实现使用Karush-Kuhn-Tucker （KKT）或Fritz-John （FJ）最优性条件来消除非最优框。FJ条件的应用意味着求解一个区间线性方程组，这通常是具有挑战性的，因为盒子的高估。本文主要从几何角度研究FJ最优性条件。引入了一种初步检验，即几何检验，它试图确定最优性条件何时不成立或是否便于计算Fritz-John检验。此外，提出了一个测试用例生成器，通过在全局优化器上设置给定数量的活动和非活动约束，将未受约束的问题转换为受约束的测试用例。在生成的基准上进行计算实验，考虑几何测试的效率。在FJ条件系统和几何试验条件下，对6种不同的IBB进行了比较。在大多数情况下，求解272个生成的测试用例的最佳方法是使用设计的几何测试，在归一化区间FJ条件下使用拉格朗日估计量和牛顿步。

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引用次数: 0

A combined linear and nonlinear presolve for nonlinear optimization 非线性优化的线性和非线性组合解

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100119

Yi Zhang , Nikolaos V. Sahinidis

Presolve techniques have been experimentally shown to significantly accelerate the performance of optimization solvers, achieving speedups of several orders of magnitude in widely used benchmarks. Building on the success of these techniques in linear and mixed-integer linear optimization problems, we introduce novel presolve methods specifically designed for nonlinear optimization. These methods aim to reduce model size and nonlinearity while preserving convexity and ensuring global optimality. We propose a combined linear and nonlinear presolve approach that integrates classical linear presolve strategies with novel methods for reformulating nonlinear expressions and simplifying models. For instance, monotonicity arguments are used to fix nonlinear variables, and linear constraints are exploited to tighten bilinear products. Computational experiments on diverse nonlinear benchmarks and continuous relaxations of discrete nonlinear problems demonstrate the efficacy of our approach. The results show that the proposed methods significantly enhance the performance of one global and four local nonlinear optimization solvers.

解决技术已经被实验证明可以显著加快优化求解器的性能，在广泛使用的基准测试中实现了几个数量级的速度。基于这些技术在线性和混合整数线性优化问题中的成功，我们引入了专门为非线性优化设计的新颖求解方法。这些方法旨在减小模型尺寸和非线性，同时保持凸性和全局最优性。我们提出了一种线性和非线性相结合的求解方法，该方法将经典的线性求解策略与重新表述非线性表达式和简化模型的新方法相结合。例如，单调性参数用于固定非线性变量，线性约束用于收紧双线性乘积。各种非线性基准和离散非线性问题的连续松弛的计算实验证明了我们的方法的有效性。结果表明，所提方法显著提高了一个全局和四个局部非线性优化解的性能。

引用次数: 0

On two vectorization schemes for set-valued optimization 集值优化的两种向量化方案

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100120

Gabriele Eichfelder, Tobias Gerlach, Ernest Quintana, Stefan Rocktäschel

In this paper, we investigate two known solution approaches for set-valued optimization problems, both of which are based on so-called vectorization strategies. These strategies consist of deriving a parametric family of multi-objective optimization problems whose optimal solution sets approximate those of the original set-valued problem with arbitrary accuracy in a certain sense. Thus, these approaches can serve as a basis for the numerical solution of set-valued optimization problems using established solution algorithms from multi-objective optimization. We show that many properties that have already been obtained for one of the two vectorization schemes also hold for the other similarly. Thereby, it turns out that under certain assumptions there exist problem classes for both vectorization schemes in which the set-valued initial problems are even equivalent to the corresponding multi-objective replacement problems. This property is fulfilled, for example, for set-valued optimization problems with a finite feasible set, a polytope-valued objective map, or a convex graph. This was already known for one of the two vectorization schemes, and could now also be shown for the other scheme.

在本文中，我们研究了两种已知的集值优化问题的求解方法，它们都是基于所谓的向量化策略。这些策略包括导出多目标优化问题的参数族，这些问题的最优解集在一定意义上以任意精度近似于原集值问题的最优解集。因此，这些方法可以作为利用多目标优化中已建立的求解算法对集值优化问题进行数值求解的基础。我们证明了两种矢量化方案中的一种已经获得的许多性质同样适用于另一种。由此证明，在一定的假设下，两种向量化方案都存在集值初始问题甚至等价于相应的多目标替换问题的问题类。例如，对于具有有限可行集、多面体值目标映射或凸图的集值优化问题，可以实现这一性质。这在两种向量化方案中的一种方案中已经知道了，现在也可以在另一种方案中得到证明。

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引用次数: 0

Robust personalized pricing under uncertainty of purchase probabilities 购买概率不确定下的鲁棒个性化定价

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100114

Shunnosuke Ikeda , Naoki Nishimura , Noriyoshi Sukegawa , Yuichi Takano

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable prediction errors that can negatively impact the realized revenues and profits. To resolve this challenge, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with the golden section search to efficiently find high-quality solutions to large-scale problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.

本文关注的是个性化定价模型，其目的是最大化单个项目的预期收入或利润。虽然预测每个消费者的购买概率对于个性化定价至关重要，但这些预测值本质上受到不可避免的预测误差的影响，这些预测误差可能会对实现的收入和利润产生负面影响。为了解决这一挑战，我们专注于鲁棒优化技术，为不确定性优化问题提供可靠的解决方案。具体来说，我们提出了一个稳健的个性化定价优化模型，该模型考虑了预测购买概率的不确定性。该模型可表述为一个混合整数线性优化问题，可以用数学优化求解器精确求解。我们还开发了一种结合黄金分割搜索的拉格朗日分解算法，以有效地找到大规模问题的高质量解。实验结果证明了鲁棒优化模型的有效性，并突出了拉格朗日分解算法在计算效率和解质量方面的实用性。

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引用次数: 0

Investigating the Monte-Carlo Tree Search approach for the job shop scheduling problem 研究了作业车间调度问题的蒙特卡洛树搜索方法

IF 1.7 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

EURO Journal on Computational Optimization

Pub Date : 2025-01-01 DOI: 10.1016/j.ejco.2025.100118

Laurie Boveroux, Damien Ernst, Quentin Louveaux

The Job Shop Scheduling Problem (JSSP) is a well-known optimization problem in manufacturing, where the goal is to determine the optimal sequence of jobs across different machines to minimize a given objective. In this work, we focus on minimizing the weighted sum of job completion times. We explore the potential of Monte Carlo Tree Search (MCTS), a heuristic-based reinforcement learning technique, to solve large-scale JSSPs, especially those with recirculation. We propose several Markov Decision Process (MDP) formulations to model the JSSP for the MCTS algorithm. In addition, we introduce a new synthetic benchmark derived from real manufacturing data, which captures the computational burden of large, non-rectangular instances often encountered in practice. Our experimental results show that MCTS effectively produces good-quality solutions for large-scale JSSP instances, outperforming our constraint programming approach.

作业车间调度问题（Job Shop Scheduling Problem， JSSP）是制造业中一个众所周知的优化问题，其目标是确定跨不同机器的最佳作业序列，以最小化给定目标。在这项工作中，我们的重点是最小化任务完成时间的加权总和。我们探索了蒙特卡罗树搜索（MCTS）的潜力，这是一种基于启发式的强化学习技术，用于解决大规模的jsp，特别是那些具有再循环的jsp。我们提出了几种马尔可夫决策过程（MDP）公式来为MCTS算法建模JSSP。此外，我们引入了一个新的合成基准，该基准来源于真实的制造数据，它捕获了在实践中经常遇到的大型非矩形实例的计算负担。我们的实验结果表明，MCTS有效地为大规模JSSP实例生成高质量的解决方案，优于我们的约束规划方法。

引用次数: 0

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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