编者按

在本系列文章中，我们梳理了运筹学顶刊Operations Research在2024年3月份发布的18篇文章的基本信息，旨在帮助读者快速洞察领域新动态。本文为第一部分。

推荐文章1

● 题目：Optimal Diagonal Preconditioning 

最优对角预条件化

● 原文链接：https://doi.org/10.1287/opre.2022.0592

● 作者：Zhaonan Qu, Wenzhi Gao, Oliver Hinder, Yinyu Ye, Zhengyuan Zhou

● 发布时间：2024/03/04

● 摘要：

• Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice, most lack guarantees on reductions in condition number, and the degree to which we can improve over existing heuristic preconditioners remains an important question. In this paper, we study the problem of optimal diagonal preconditioning that achieves maximal reduction in the condition number of any full-rank matrix by scaling its rows and/or columns with positive numbers. We first reformulate the problem as a quasiconvex optimization problem and provide a simple algorithm based on bisection. Then, we develop an interior point algorithm with O(log(1/ϵ)) iteration complexity, where each iteration consists of a Newton update based on the Nesterov-Todd direction. Next, we specialize in one-sided optimal diagonal preconditioning problems and demonstrate that they can be formulated as standard dual semidefinite program (SDP) problems. We then develop efficient customized solvers for the SDP approach and study the empirical performance of our optimal diagonal preconditioning procedures through extensive experiments. Our findings suggest that optimal diagonal preconditioners can significantly improve upon existing heuristics-based diagonal preconditioners at reducing condition numbers, and our SDP approach can find such optimal preconditioners efficiently. We also extend our SDP approach to compute optimal mixtures of heuristic preconditioners, which further improves its scalability and applicability.

• 预条件化技术长期以来一直是优化领域的基本技术，常用于降低矩阵的条件数并加速算法的收敛。尽管在实践中有许多流行的预条件化技术，但大多数技术缺乏在减少条件数方面的保证，我们能在多大程度上改善现有启发式预处理器仍是一个重要问题。在本文中，我们研究了通过用正数缩放其行和/或列来实现任何满秩矩阵的条件数最大降低的最优对角预条件化问题。我们首先将问题重新表述为一个准凸优化问题，并提供了一个基于二分法的简单算法。然后，我们开发了一个内点算法，其迭代复杂度为O(log(1/ϵ))，其中每次迭代包括基于Nesterov-Todd方向的牛顿更新。接下来，我们专注于单侧最优对角预处理问题，并证明它们可以被表述为标准对偶半定规划（SDP）问题。我们随后为SDP方法开发了高效的定制求解器，并通过广泛的实验研究了我们的最优对角预条件化程序的经验性能。我们的发现表明，最优对角预条件化器可以显著改善现有基于启发式的对角预条件化器在减少条件数方面的性能，而我们的SDP方法能够高效地找到这样的最优预条件化器。我们还将我们的SDP方法扩展到计算启发式预条件化器的最优混合，这进一步提高了其可扩展性和适用性。

推荐文章2

● 题目：Technical Note—On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization 

技术说明——关于梯度随机优化的随机逼近的收敛速率

● 原文链接：https://doi.org/10.1287/opre.2023.0055

● 作者：Jiaqiao Hu, Michael C. Fu

● 发布时间：2024/03/08

● 摘要：

• We consider stochastic optimization via gradient-based search. Under a stochastic approximation framework, we apply a recently developed convergence rate analysis to provide a new finite-time error bound for a class of problems with convex differentiable structures. For noisy black-box functions, our main result allows us to derive finite-time bounds in the setting where the gradients are estimated via finite-difference estimators, including those based on randomized directions such as the simultaneous perturbation stochastic approximation algorithm. In particular, the convergence rate analysis sheds light on when it may be advantageous to use such randomized gradient estimates in terms of problem dimension and noise levels.

• 我们考虑通过基于梯度的搜索进行随机优化。在随机逼近框架下，我们应用了最近发展的收敛率分析，为具有凸可微结构的一类问题提供了新的有限时间误差界限。对于噪声黑盒函数，在梯度通过有限差分估计器估计的设置中，我们的主要结果允许我们导出有限时间界限，包括那些基于随机方向的估计器（例如，同时扰动随机逼近算法）。特别是，收敛率分析揭示了在问题维度和噪声水平方面，使用这种随机梯度估计何时可能更有优势。

推荐文章3

● 题目：Quantile Optimization via Multiple-Timescale Local Search for Black-Box Functions 

基于多时间尺度局部搜索的黑箱函数分位数优化

● 原文链接：https://doi.org/10.1287/opre.2022.0534

● 作者：Jiaqiao Hu, Meichen Song, Michael C. Fu

● 发布时间：2024/03/12

● 摘要：

• We consider quantile optimization of black-box functions that are estimated with noise. We propose two new iterative three-timescale local search algorithms. The first algorithm uses an appropriately modified finite-difference-based gradient estimator that requires 2d + 1 samples of the black-box function per iteration of the algorithm, where d is the number of decision variables (dimension of the input vector). For higher-dimensional problems, this algorithm may not be practical if the black-box function estimates are expensive. The second algorithm employs a simultaneous-perturbation-based gradient estimator that uses only three samples for each iteration regardless of problem dimension. Under appropriate conditions, we show the almost sure convergence of both algorithms. In addition, for the class of strongly convex functions, we further establish their (finite-time) convergence rate through a novel fixed-point argument. Simulation experiments indicate that the algorithms work well on a variety of test problems and compare well with recently proposed alternative methods.

• 我们考虑对被带有噪声估计的黑箱函数进行分位数优化。我们提出了两种新的迭代式“三时间尺度”局部搜索算法。第一个算法使用了适当修改的基于有限差分的梯度估计器，每次算法迭代需要2d+1个黑箱函数的样本，其中d是决策变量的数量（输入向量的维度）。对于高维问题，如果黑箱函数估计代价昂贵，这个算法可能不实用。第二个算法采用基于同时扰动的梯度估计器，每次迭代只需要三个样本，无论问题维度如何。在适当条件下，我们展示了两种算法的几乎肯定收敛性。此外，对于强凸函数类，我们通过一种新的不动点论证，进一步建立了它们的（有限时间）收敛率。模拟实验表明，这些算法在各种测试问题上表现良好，并且与最近提出的替代方法相比有良好的竞争力。

推荐文章4

● 题目：Designing Service Menus for Bipartite Queueing Systems 

为双边排队系统设计服务菜单

● 原文链接：https://doi.org/10.1287/opre.2022.0179

● 作者：René Caldentey, Lisa Aoki Hillas, Varun Gupta

● 发布时间：2024/03/12

● 摘要：

• We consider a multiclass, multiserver queueing system, in which customers of different types have heterogeneous preferences over the many servers available. The goal of the service provider is to design a menu of service classes that balances two competing objectives: (1) maximize customers’ average matching reward and (2) minimize customers’ average waiting time. A service class corresponds to a single queue served by a subset of servers under a first come, first served–assign longest idle server service discipline. Customers act as rational self-interested utility-maximizing agents when choosing which service class to join. In particular, they join the class that maximizes their expected ex ante net utility, which is given by the difference between the server-dependent service reward they receive and a disutility based on the mean steady-state waiting time of the service class they join. We study the problem under (conventional) heavy-traffic conditions: that is, in the limit as the traffic intensity of the system approaches one from below. For the case of two servers, we provide a complete characterization of the possible menus and their delay-reward trade-offs. For a general number of servers, we prove that if the service provider only cares about minimizing average delay or maximizing total matching reward, then very simple menus are optimal. Finally, we provide mixed-integer linear programming formulations for optimizing the delay-reward trade-off within fairly rich and practically relevant families of menus, which we term partitioned and tailored.

• 我们研究了一个多类别、多服务员的排队系统，在该系统中，不同类型的顾客对众多可用服务员有着各异的偏好。服务提供者的目标是设计一个服务类别菜单，平衡两个相互竞争的目标：（1）最大化顾客的平均匹配奖励和（2）最小化顾客的平均等待时间。一个服务类别对应一个由部分服务员的队列，其服务规则为在先到先服务的基础上，分配最长闲置服务员。顾客作为理性的、自利的、追求最大化效用的智能体，在选择加入哪个服务类别时表现出来。特别是，他们加入能最大化他们预期的净效用的类别，这个预期的净效用由他们收到的，依赖服务员的服务奖励与基于他们所在服务类别的平均稳态等待时间，这两者的不适用性之差给出。我们在（常规的）重流量条件下研究这个问题：即，随着系统的流量强度从下方接近一的极限。对于两个服务员的情况，我们提供了可能菜单及其延迟-奖励权衡的完整特征化。对于一般数量的服务员，我们证明了如果服务提供者只关心最小化平均延迟或最大化总匹配奖励，则非常简单的菜单是最优的。最后，在相当丰富且实际相关的菜单家族内，我们为优化延迟-奖励权衡提供了混合整数线性规划的建模，称之为分区和定制菜单。

推荐文章5

● 题目：Branch-and-Price for Prescriptive Contagion Analytics 

分支定价法在决策性传染分析中的应用

● 原文链接：https://doi.org/10.1287/opre.2023.0308

● 作者：Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé, Kai Wang

● 发布时间：2024/03/13

● 摘要：

• Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by continuous-time contagion dynamics. These problems feature a large-scale mixed-integer nonconvex optimization structure with constraints governed by ordinary differential equations. This paper develops a branch-and-price methodology for this class of problems based on (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a state-clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a tripartite branching scheme to circumvent nonlinearities. We apply the methodology to four real-world cases: vaccine distribution, vaccination centers deployment, content promotion, and congestion mitigation. Extensive experiments show that the algorithm scales to large and otherwise-intractable instances, outperforming state-of-the-art benchmarks. Our methodology provides practical benefits in contagion systems—In particular, we show that it can increase the effectiveness of a vaccination campaign in a setting replicating the rollout of COVID-19 vaccines in 2021. We provide an open-source implementation of the methodology to enable replication.

• 传染模型在流行病学、社会科学、工程和管理学中无处不在。本文构建了一个决策性传染分析模型，决策者在此模型中跨多个人群段分配共享资源，每个段都受连续时间传染动态的约束。这些问题具有大规模混合整数非凸优化结构，受常微分方程约束。本文基于以下几点开发了一种针对此类问题的分支定价方法：（i）一种集合分割重构；（ii）列生成分解；（iii）针对离散决策连续状态动态规划的状态聚类算法；及（iv）一种三部分分支方案以规避非线性问题。我们将该方法应用于四个现实案例：疫苗分配、疫苗接种中心部署、内容推广和拥堵缓解。广泛的实验表明，该算法能够处理大规模且其他方法难以处理的实例，超越了现有技术水平的基准。我们的方法在传染系统中提供了实际效益——特别是，我们展示了它如何在模拟2021年COVID-19疫苗推出的设置中提高疫苗接种活动的有效性。我们提供了方法的开源实现，以便于复制。

推荐文章6

● 题目：Shipping Emission Control Area Optimization Considering Carbon Emission Reduction 

考虑碳排放减少的船舶排放控制区优化

● 原文链接：https://doi.org/10.1287/opre.2022.0361

● 作者：Dan Zhuge, Shuaian Wang, Lu Zhen

● 发布时间：2024/03/15

● 摘要：

• Sulfur emission control areas (ECAs) are crucial for reducing global shipping emissions and protecting the environment. The main plank of an ECA policy is usually a fuel sulfur limit. However, the approaches to setting sulfur limits are relatively subjective and lack scientific support. This paper investigates the design of ECA policies, especially sulfur limits, for sailing legs with ECAs. The objective is to minimize the social costs of shipping operations, local sulfur oxides (SOx) emissions, and global carbon dioxide (CO2) emissions. First, a case with a no-ECA policy and a case with the current ECA policy are analyzed. Then, two new voyage-dependent ECA policies with sulfur limits, designated sailing paths, and speed limits are proposed. Stackelberg game models are developed to solve the research problem with the two proposed policies and two players: the ECA regulator and a shipping company aiming to minimize social costs and company costs, respectively. The ECA regulator determines the sulfur limit, sailing path, and speed limit, and the shipping company optimizes the sailing speed accordingly. We also compare and analyze each type of cost under different ECA policies (i.e., no ECA, the current ECA policy, and the proposed ECA policies). The research problem is then extended from a sailing leg to a shipping network to improve the practicality of the findings. A dynamic programming-based algorithm is developed to optimize the ECA policies for the shipping network from the perspective of the ECA regulator. Mathematical derivation shows that the proposed ECA policies can reduce the social costs of shipping. The results of extensive numerical experiments further demonstrate the ability of the proposed policies to reduce social costs, providing important insights for voyage-dependent ECA policy design.

• 硫磺排放控制区（ECA）对于减少全球航运排放和保护环境至关重要。ECA政策的主要内容通常是燃料硫含量限制。然而，设定硫限制的方法相对主观，缺乏科学支持。本文研究了ECA政策的设计，特别是对航行段中ECA的硫限制。目标是最小化航运操作的社会成本、局部硫氧化物（SOx）排放和全球二氧化碳（CO2）排放。首先，分析了无ECA政策情况和当前ECA政策情况。然后，提出了两种新的依航程的ECA政策，包括硫限制、指定航道和速度限制。我们开发了Stackelberg博弈模型来解决研究问题，模型中包含两种提议的政策和两个玩家：ECA监管者和旨在分别最小化社会成本和公司成本的航运公司。ECA监管者确定硫限制、航道和速度限制，而航运公司据此优化航速。我们还比较和分析了不同ECA政策（即无ECA、当前ECA政策和提议的ECA政策）下各类成本。然后，研究问题从航行段扩展到航运网络，以提高研究发现的实用性。我们从ECA监管者的角度，开发了一种基于动态规划的算法来优化航运网络的ECA政策。数学推导表明，提出的ECA政策能够减少航运的社会成本。大量数值实验的结果进一步证明了提议政策减少社会成本的能力，为依航程的ECA政策设计提供了重要见解。

推荐文章7

● 题目：Randomized Assortment Optimization 

随机化的产品组合优化

● 原文链接：https://doi.org/10.1287/opre.2022.0129

● 作者：Zhengchao Wang, Heikki Peura, Wolfram Wiesemann

● 发布时间：2024/03/18

● 摘要：

• When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. Recent work has addressed this issue using robust optimization, where the true parameter values are assumed unknown and the firm chooses an assortment that maximizes its worst-case expected revenues over an uncertainty set of likely parameter values, thus mitigating estimation errors. In this paper, we introduce the concept of randomization into the robust assortment optimization literature. We show that the standard approach of deterministically selecting a single assortment to offer is not always optimal in the robust assortment optimization problem. Instead, the firm can improve its worst-case expected revenues by selecting an assortment randomly according to a prudently designed probability distribution. We demonstrate this potential benefit of randomization both theoretically in an abstract problem formulation as well as empirically across three popular choice models: the multinomial logit model, the Markov chain model, and the preference ranking model. We show how an optimal randomization strategy can be determined exactly and heuristically. Besides the superior in-sample performance of randomized assortments, we demonstrate improved out-of-sample performance in a data-driven setting that combines estimation with optimization. Our results suggest that more general versions of the assortment optimization problem—incorporating business constraints, more flexible choice models and/or more general uncertainty sets—tend to be more receptive to the benefits of randomization.

• 当一家公司选择要向客户提供的产品组合时，它会使用选择模型来预测顾客购买每个产品的概率。在实践中，这些模型的估计受到统计误差的影响，这可能导致明显次优的产品组合决策。最近的工作通过使用鲁棒优化来解决这一问题，其中真实参数值被假定为未知，公司选择一个产品组合，以最大化其在一个可能参数值的不确定集上的最坏情况预期收入，从而缓解估计误差。在本文中，我们将随机化的概念引入鲁棒产品组合优化文献中。我们展示了在鲁棒产品组合优化问题中，确定性选择单一产品组合并不总是最优的。相反，公司可以通过根据精心设计的概率分布随机选择产品组合来提高其最坏情况预期收益。我们不仅在抽象问题表述中理论上展示了随机化的潜在好处，也在三个流行的选择模型中经验性地展示了这一点：多元Logit模型、马尔可夫链模型和偏好排名模型。我们展示了如何准确和启发式地确定最优随机化策略。除了随机化产品组合的优越内样本表现外，我们还在一个结合估计和优化的数据驱动设置中展示了改进的外样本表现。我们的结果表明，更一般版本的产品组合优化问题——纳入商业约束、更灵活的选择模型和/或更一般的不确定集——更倾向于接受随机化的好处。

推荐文章8

● 题目：A Mutual Catastrophe Insurance Framework for Horizontal Collaboration in Prepositioning Strategic Reserves 

横向合作中预置战略储备的相互灾害保险框架

● 原文链接：https://doi.org/10.1287/opre.2021.0141

● 作者：Hani Zbib, Burcu Balcik, Marie-Ève Rancourt, Gilbert Laporte

● 发布时间：2024/03/18

● 摘要：

• We develop a mutual catastrophe insurance framework for the prepositioning of strategic reserves to foster horizontal collaboration in preparedness against low-probability high-impact natural disasters. The framework consists of a risk-averse insurer pooling the risks of a portfolio of risk-averse policyholders. It encompasses the operational functions of planning the prepositioning network in preparedness for incoming insurance claims, in the form of units of strategic reserves, setting coverage deductibles and limits of policyholders, and providing insurance coverage to the claims in the emergency response phase. It also encompasses the financial functions of ensuring the insurer’s solvency by efficiently managing its capital and allocating yearly premiums among policyholders. We model the framework as a very large-scale nonlinear multistage stochastic program, and solve it through a Benders decomposition algorithm. We study the case of Caribbean countries establishing a horizontal collaboration for hurricane preparedness. Our results show that the collaboration is more effective when established over a longer planning horizon, and is more beneficial when outsourcing becomes expensive. Moreover, the correlation of policyholders affected simultaneously under the extreme realizations and the position of their claims in their global claims distribution directly affects which policyholders get deductibles and limits. This underlines the importance of prenegotiating policyholders’ indemnification policies at the onset of collaboration.

• 我们开发了一个相互灾害保险框架，用于预置战略储备，以促进针对低概率高影响自然灾害的横向合作准备。该框架由一个风险厌恶型保险人组成，它汇集了一组风险厌恶型保单持有者的风险。它包括规划预置网络的操作功能，以准备迎接保险索赔，形式为战略储备单位，设定保单持有者的免赔额和限额，并在紧急响应阶段提供保险覆盖。它还包括通过有效管理其资本和在保单持有者之间分配年度保费来确保保险人的偿付能力的财务功能。我们将该框架建模为一个非常大规模的非线性多阶段随机规划，并通过Benders分解算法来解决它。我们研究了加勒比国家为飓风准备建立横向合作的案例。我们的结果显示，当在更长的规划期限上建立合作时，合作更为有效，并且当外包变得昂贵时，合作更为有益。此外，保单持有者在极端情况下同时受影响的相关性，以及他们的索赔在全球索赔分布中的位置，直接影响哪些保单持有者获得免赔额和限额。这强调了在合作开始时预先协商保单持有者的赔偿政策的重要性。

推荐文章9

● 题目：Optimal Impact Portfolios with General Dependence and Marginals 

带有一般依赖性和边缘分布的最优影响力投资组合

● 原文链接：https://doi.org/10.1287/opre.2023.0400

● 作者：Andrew W. Lo, Lan Wu, Ruixun Zhang, Chaoyi Zhao

● 发布时间：2024/03/20

● 摘要：

• We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. The distribution of induced order statistics can be represented by a mixture of order statistics and uniformly distributed random variables, where the mixture function is determined by the dependence structure between residual returns and impact factors—characterized by copulas—and the marginal distribution of residual returns. This representation theorem allows us to explicitly and efficiently compute optimal portfolio weights under any copula. This framework provides a systematic approach for constructing and quantifying the performance of optimal impact portfolios with arbitrary dependence structures and return distributions.

• 我们开发了一个数学框架，用于构建最优影响力投资组合，并通过使用诱导顺序统计量和copulas来表征影响力排名资产的回报，以此量化它们的财务表现。诱导顺序统计量的分布可以通过顺序统计量和均匀分布随机变量的混合来表示，其中混合函数由残余回报和影响因素之间的依赖结构决定——通过copulas表征——以及残余回报的边缘分布。这一表示定理使我们能够在任何copula下显式且高效地计算最优投资组合权重。该框架为构建和量化具有任意依赖结构和回报分布的最优影响力投资组合提供了一种系统方法。