[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117838-en":3,"doc-seo-117838-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117838,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","A Machine Learning Approach to Two-Stage Adaptive Robust Optimization","An approach is presented using machine learning to solve two-stage linear adaptive robust optimization problems with binary here-and-now decisions and polyhedral uncertainty sets. The method encodes here-and-now choices, the worst-case scenarios linked to those choices, and wait-and-see actions into a unified strategy representation. Multiple similar instances are solved offline to build a training set via column-and-constraint generation. A trained model then predicts high-quality strategies for all decision stages, while an additional algorithm reduces the number of target classes required for training. Applications include facility location, multi-item inventory control, and unit commitment, achieving major speedups with high accuracy.","arXiv :2307 . 12409v 1 [ cs .LG] 23 Jul 2023  \nA Machine Learning Approach to Two-Stage Adaptive Robust Optimization  \nDimitris Bertsimasa,􀀃, Cheol Woo Kimb  \naSloan School of Management, Massachusetts Institute of Technology, 100 Main Street, Cambridge, 02142, United  \nStates  \nb Operations Research Center, Massachusetts Institute of Technology, 1 Amherst Street, Cambridge, 02142, United  \nStates  \nAbstract  \nWe propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote asthe strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train a machine learning model that predicts high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. We also introduce an algorithm to reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.  \nKeywords: Machine Learning, Adaptive Robust Optimization, Articifial Intelligence  \n1. Introduction  \nRobust optimization (RO) has become increasingly popular as a method to account for parameter uncertainty. Compared to more conventional methods such as stochastic optimization, which can be computationally intensive in high dimensions, RO offers a significant computational advantage (Ben-Tal & Nemirovski, 2002; Bertsimas & den Hertog, 2022; Bertsimas et al., 2011; Ben-Tal et al. , 2009) .  \nAdaptive robust optimization (ARO) is an important extension of RO that allows certain decision variables, referred to as the wait-and-see variables, to be determined after the uncertainty is revealed. In ARO, the wait-and-see decisions are mathematically modeled as functions of uncertain parameters, enabling them to adapt to the realization of those parameters. ARO is particularly useful in multistage decision-making problems, where decision-makers may be uncertain about future parameter values, and where decisions may need to be made sequentially over time. Compared to RO, ARO provides greater modeling flexibility and often results in superior solutions that are better able to adapt to changing conditions (Bertsimas & den Hertog, 2022; Yanıkoğlu et al., 2019; Ben-Tal et al. ,  \n􀀃 Corresponding author  \nEmail addresses: [dbertsim@mit.edu](dbertsim@mit.edu) (Dimitris Bertsimas), [acwkim@mit.edu](acwkim@mit.edu) (Cheol Woo Kim)  \nPreprint submitted to European Journal of Operations Research July 28, 2023  \n2004) . Application areas include energy (Sun & Lorca, 2015; Bertsimas et al., 2013; Moreira et al. , 2015), inventory management (See & Sim, 2009; Ang et al., 2012) , portfolio management (Fliedner & Liesiö, 2016) among many others (Yanıkoğlu et al., 2019) .  \nDespite its many benefits, ARO poses significant computational challenges that distinguish it from RO. One of the primary challenges arises from the fact that ARO is an infinite-dimensional optimization problem, as the wait-and-see variables are functions of the uncertain parameters. To overcome this issue, approximation methods have been proposed that restrict the wait-and-see variables to a limited set of functions, such as affine functions (Bertsimas & den Hertog, 2022; Ben-Tal et al., 2004) . However, while these methods may be able to reformulate ARO into RO, there is no guarantee that the resulting approximation will be near-optimal or even feasible (Ben-Talet al., 2","cbCaisX3fEPyhokr","https://ap.wps.com/l/cbCaisX3fEPyhokr","pdf",793986,1,30,"English","en",105,"# Introduction\n## Robust optimization and adaptive robust optimization\n## Computational challenges in ARO\n## Related machine learning approaches and paper contributions","[{\"question\":\"What problem does the paper address?\",\"answer\":\"It addresses two-stage linear adaptive robust optimization with binary here-and-now decisions and polyhedral uncertainty sets.\"},{\"question\":\"How is the machine learning component trained?\",\"answer\":\"The method generates a training set by solving multiple similar ARO instances in advance using a column-and-constraint generation algorithm, then learning to predict high-quality strategies.\"},{\"question\":\"Which applications are used to demonstrate the approach?\",\"answer\":\"Facility location, multi-item inventory control, and unit commitment are used to evaluate the proposed method.\"}]","A Machine Learning Approach to Two-Stage Adaptive Robust Optimization | 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problem does the paper address?","Question",{"text":75,"@type":76},"It addresses two-stage linear adaptive robust optimization with binary here-and-now decisions and polyhedral uncertainty sets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the machine learning component trained?",{"text":80,"@type":76},"The method generates a training set by solving multiple similar ARO instances in advance using a column-and-constraint generation algorithm, then learning to predict high-quality strategies.",{"name":82,"@type":73,"acceptedAnswer":83},"Which applications are used to demonstrate the approach?",{"text":84,"@type":76},"Facility location, multi-item inventory control, and unit commitment are used to evaluate the proposed 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