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Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty 交货时间不确定情况下全渠道多快递员订单履行的情境随机优化
arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.06918
Tinghan Ye, Sikai Cheng, Amira Hijazi, Pascal Van Hentenryck
{"title":"Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty","authors":"Tinghan Ye, Sikai Cheng, Amira Hijazi, Pascal Van Hentenryck","doi":"arxiv-2409.06918","DOIUrl":"https://doi.org/arxiv-2409.06918","url":null,"abstract":"The paper studies a large-scale order fulfillment problem for a leading\u0000e-commerce company in the United States. The challenge involves selecting\u0000fulfillment centers and shipping carriers with observational data only to\u0000efficiently process orders from a vast network of physical stores and\u0000warehouses. The company's current practice relies on heuristic rules that\u0000choose the cheapest fulfillment and shipping options for each unit, without\u0000considering opportunities for batching items or the reliability of carriers in\u0000meeting expected delivery dates. The paper develops a data-driven Contextual\u0000Stochastic Optimization (CSO) framework that integrates distributional\u0000forecasts of delivery time deviations with stochastic and robust order\u0000fulfillment optimization models. The framework optimizes the selection of\u0000fulfillment centers and carriers, accounting for item consolidation and\u0000delivery time uncertainty. Validated on a real-world data set containing tens\u0000of thousands of products, each with hundreds of fulfillment options, the\u0000proposed CSO framework significantly enhances the accuracy of meeting\u0000customer-expected delivery dates compared to current practices. It provides a\u0000flexible balance between reducing fulfillment costs and managing delivery time\u0000deviation risks, emphasizing the importance of contextual information and\u0000distributional forecasts in order fulfillment. This is the first paper that\u0000studies the omnichannel multi-courier order fulfillment problem with delivery\u0000time uncertainty through the lens of contextual optimization, fusing machine\u0000learning and optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Indirect Dynamic Negotiation in the Nash Demand Game 纳什需求博弈中的间接动态谈判
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06566
Tatiana V. Guy, Jitka Homolová, Aleksej Gaj
{"title":"Indirect Dynamic Negotiation in the Nash Demand Game","authors":"Tatiana V. Guy, Jitka Homolová, Aleksej Gaj","doi":"arxiv-2409.06566","DOIUrl":"https://doi.org/arxiv-2409.06566","url":null,"abstract":"The paper addresses a problem of sequential bilateral bargaining with\u0000incomplete information. We proposed a decision model that helps agents to\u0000successfully bargain by performing indirect negotiation and learning the\u0000opponent's model. Methodologically the paper casts heuristically-motivated\u0000bargaining of a self-interested independent player into a framework of Bayesian\u0000learning and Markov decision processes. The special form of the reward\u0000implicitly motivates the players to negotiate indirectly, via closed-loop\u0000interaction. We illustrate the approach by applying our model to the Nash\u0000demand game, which is an abstract model of bargaining. The results indicate\u0000that the established negotiation: i) leads to coordinating players' actions;\u0000ii) results in maximising success rate of the game and iii) brings more\u0000individual profit to the players.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proceedings of the XIII International Workshop on Locational Analysis and Related Problems 第十三届定位分析及相关问题国际研讨会论文集
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06397
Marta Baldomero-Naranjo, Ricardo Gázquez, Miguel Martínez-Antón, Luisa I. Martínez-Merino, Juan M. Muñoz-Ocaña, Francisco Temprano, Alberto Torrejón, Carlos Valverde, Nicolás Zerega
{"title":"Proceedings of the XIII International Workshop on Locational Analysis and Related Problems","authors":"Marta Baldomero-Naranjo, Ricardo Gázquez, Miguel Martínez-Antón, Luisa I. Martínez-Merino, Juan M. Muñoz-Ocaña, Francisco Temprano, Alberto Torrejón, Carlos Valverde, Nicolás Zerega","doi":"arxiv-2409.06397","DOIUrl":"https://doi.org/arxiv-2409.06397","url":null,"abstract":"The topics of interest are location analysis and related problems. This\u0000includes location models, networks, transportation, logistics, exact and\u0000heuristic solution methods, and computational geometry, among many others.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frequency range non-Lipschitz parametric optimization of a noise absorption 噪声吸收的频率范围非 Lipschitz 参数优化
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06292
Frederic MagoulesMICS, Mathieu MenouxMICS, Anna Rozanova-PierratMICS
{"title":"Frequency range non-Lipschitz parametric optimization of a noise absorption","authors":"Frederic MagoulesMICS, Mathieu MenouxMICS, Anna Rozanova-PierratMICS","doi":"arxiv-2409.06292","DOIUrl":"https://doi.org/arxiv-2409.06292","url":null,"abstract":"In the framework of the optimal wave energy absorption, we solve\u0000theoretically and numerically a parametric shape optimization problem to find\u0000the optimal distribution of absorbing material in the reflexive one defined by\u0000a characteristic function in the Robin-type boundary condition associated with\u0000the Helmholtz equation. Robin boundary condition can be given on a part or the\u0000all boundary of a bounded ($epsilon$, $infty$)-domain of R n . The geometry\u0000of the partially absorbing boundary is fixed, but allowed to be non-Lipschitz,\u0000for example, fractal. It is defined as the support of a d-upper regular measure\u0000with d $in$]n -2, n[. Using the well-posedness properties of the model, for\u0000any fixed volume fraction of the absorbing material, we establish the existence\u0000of at least one optimal distribution minimizing the acoustical energy on a\u0000fixed frequency range of the relaxation problem. Thanks to the shape derivative\u0000of the energy functional, also existing for non-Lipschitz boundaries, we\u0000implement (in the two-dimensional case) the gradient descent method and find\u0000the optimal distribution with 50% of the absorbent material on a frequency\u0000range with better performances than the 100% absorbent boundary. The same type\u0000of performance is also obtained by the genetic method.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems KANtrol：用于解决多维和分数最优控制问题的物理信息型科尔莫戈罗夫-阿诺德网络框架
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06649
Alireza Afzal Aghaei
{"title":"KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems","authors":"Alireza Afzal Aghaei","doi":"arxiv-2409.06649","DOIUrl":"https://doi.org/arxiv-2409.06649","url":null,"abstract":"In this paper, we introduce the KANtrol framework, which utilizes\u0000Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving\u0000continuous time variables. We explain how Gaussian quadrature can be employed\u0000to approximate the integral parts within the problem, particularly for\u0000integro-differential state equations. We also demonstrate how automatic\u0000differentiation is utilized to compute exact derivatives for integer-order\u0000dynamics, while for fractional derivatives of non-integer order, we employ\u0000matrix-vector product discretization within the KAN framework. We tackle\u0000multi-dimensional problems, including the optimal control of a 2D heat partial\u0000differential equation. The results of our simulations, which cover both forward\u0000and parameter identification problems, show that the KANtrol framework\u0000outperforms classical MLPs in terms of accuracy and efficiency.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks Learn2Aggregate：使用图神经网络监督生成 Chvátal-Gomory 剪切
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06559
Arnaud Deza, Elias B. Khalil, Zhenan Fan, Zirui Zhou, Yong Zhang
{"title":"Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks","authors":"Arnaud Deza, Elias B. Khalil, Zhenan Fan, Zirui Zhou, Yong Zhang","doi":"arxiv-2409.06559","DOIUrl":"https://doi.org/arxiv-2409.06559","url":null,"abstract":"We present $textit{Learn2Aggregate}$, a machine learning (ML) framework for\u0000optimizing the generation of Chv'atal-Gomory (CG) cuts in mixed integer linear\u0000programming (MILP). The framework trains a graph neural network to classify\u0000useful constraints for aggregation in CG cut generation. The ML-driven CG\u0000separator selectively focuses on a small set of impactful constraints,\u0000improving runtimes without compromising the strength of the generated cuts. Key\u0000to our approach is the formulation of a constraint classification task which\u0000favours sparse aggregation of constraints, consistent with empirical findings.\u0000This, in conjunction with a careful constraint labeling scheme and a hybrid of\u0000deep learning and feature engineering, results in enhanced CG cut generation\u0000across five diverse MILP benchmarks. On the largest test sets, our method\u0000closes roughly $textit{twice}$ as much of the integrality gap as the standard\u0000CG method while running 40$% faster. This performance improvement is due to our\u0000method eliminating 75% of the constraints prior to aggregation.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bi-level regularization via iterative mesh refinement for aeroacoustics 通过迭代网格细化实现航空声学的双级正则化
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06854
Christian Aarset, Tram Thi Ngoc Nguyen
{"title":"Bi-level regularization via iterative mesh refinement for aeroacoustics","authors":"Christian Aarset, Tram Thi Ngoc Nguyen","doi":"arxiv-2409.06854","DOIUrl":"https://doi.org/arxiv-2409.06854","url":null,"abstract":"In this work, we illustrate the connection between adaptive mesh refinement\u0000for finite element discretized PDEs and the recently developed emph{bi-level\u0000regularization algorithm}. By adaptive mesh refinement according to data noise,\u0000regularization effect and convergence are immediate consequences. We moreover\u0000demonstrate its numerical advantages to the classical Landweber algorithm in\u0000term of time and reconstruction quality for the example of the Helmholtz\u0000equation in an aeroacoustic setting.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Policy Iteration Method for Inverse Mean Field Games 逆均值场博弈的策略迭代法
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06184
Kui Ren, Nathan Soedjak, Shanyin Tong
{"title":"A Policy Iteration Method for Inverse Mean Field Games","authors":"Kui Ren, Nathan Soedjak, Shanyin Tong","doi":"arxiv-2409.06184","DOIUrl":"https://doi.org/arxiv-2409.06184","url":null,"abstract":"We propose a policy iteration method to solve an inverse problem for a\u0000mean-field game model, specifically to reconstruct the obstacle function in the\u0000game from the partial observation data of value functions, which represent the\u0000optimal costs for agents. The proposed approach decouples this complex inverse\u0000problem, which is an optimization problem constrained by a coupled nonlinear\u0000forward and backward PDE system in the MFG, into several iterations of solving\u0000linear PDEs and linear inverse problems. This method can also be viewed as a\u0000fixed-point iteration that simultaneously solves the MFG system and inversion.\u0000We further prove its linear rate of convergence. In addition, numerical\u0000examples in 1D and 2D, along with performance comparisons to a direct\u0000least-squares method, demonstrate the superior efficiency and accuracy of the\u0000proposed method for solving inverse MFGs.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fourier series-based algorithm for control optimization in pendulum capsule drive: an integrated computational and experimental study 基于傅立叶级数的摆式胶囊驱动控制优化算法：计算与实验综合研究
arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI: arxiv-2409.06824
Sandra Zarychta, Marek Balcerzak, Katarzyna Wojdalska, Rafał Dolny, Jerzy Wojewoda
{"title":"Fourier series-based algorithm for control optimization in pendulum capsule drive: an integrated computational and experimental study","authors":"Sandra Zarychta, Marek Balcerzak, Katarzyna Wojdalska, Rafał Dolny, Jerzy Wojewoda","doi":"arxiv-2409.06824","DOIUrl":"https://doi.org/arxiv-2409.06824","url":null,"abstract":"Pendulum-driven systems have emerged as a notable modification of\u0000vibro-impact mechanisms, replacing the conventional mass-on-spring oscillator\u0000with a pendulum. Such systems exhibit intricate behavior resulting from the\u0000interplay of directional dynamics, pendulum motion, and contact forces between\u0000the designed device and the underlying surface. This paper delves into the\u0000application of a Fourier series-based greedy algorithm for control optimization\u0000in pendulum capsule drives, which hold potential for diverse scenarios,\u0000including endoscopy capsule robots, pipeline inspection, and rescue operations\u0000in confined spaces. The emphasis is placed on experimental studies involving\u0000prototype development to validate the system's efficacy with previous\u0000computational simulations. Empirical findings closely align (<2% loss) with\u0000numerical investigations, showcasing the pendulum capsule drive's ability to\u0000achieve average speeds of 2.48 cm/s and 2.58 cm/s for three and six harmonics,\u0000respectively. These results are reinforced by high-quality signal-tracking\u0000accuracy, which demonstrates resilience against potential disturbances during\u0000motion. The authors envision the Fourier series-based control optimization\u0000method as a significant step towards ensuring enhanced locomotion performance\u0000in discontinuous systems, effectively handling the non-linearities arising from\u0000dry friction.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constant Payoff Property in Zero-Sum Stochastic Games with a Finite Horizon 有限地平线零和随机博弈中的恒定回报特性
arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05683
Thomas Ragel, Bruno Ziliotto
{"title":"Constant Payoff Property in Zero-Sum Stochastic Games with a Finite Horizon","authors":"Thomas Ragel, Bruno Ziliotto","doi":"arxiv-2409.05683","DOIUrl":"https://doi.org/arxiv-2409.05683","url":null,"abstract":"This paper examines finite zero-sum stochastic games and demonstrates that\u0000when the game's duration is sufficiently long, there exists a pair of\u0000approximately optimal strategies such that the expected average payoff at any\u0000point in the game remains close to the value. This property, known as the\u0000textit{constant payoff property}, was previously established only for\u0000absorbing games and discounted stochastic games.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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