[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122787-en":3,"doc-seo-122787-105":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},122787,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition - Abstract","Mixed integer Model Predictive Control (MPC) enables simultaneous discrete and continuous decisions to mitigate disturbances, but solving the resulting mixed integer optimization online is computationally challenging. This work presents a machine learning-based branch-and-check Generalized Benders Decomposition method for mixed integer MPC arising in chemical processes. It provably returns feasible solutions whenever the MPC problem is feasible and sharply reduces solution time (up to 97% or 50×) while keeping errors around 1% versus standard and accelerated approaches. ","2023  \nComputationally efficient solution of mixed integer model predictive control problems via  \nmachine learning aided Benders Decomposition  \nIlias Mitrai, Prodromos Daoutidis 1  \nDepartment of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455  \nAbstract  \nMixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient and robust online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for  \n28  \nchemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50×) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition.  \nKeywords: Benders decomposition, Machine learning, Mixed integer MPC, Mixed integer optimization  \nOC]  \narXiv :2309 . 16508v1  \njective function is optimized subject to constraints that describe the behavior of the system [1] . MPC has usually been applied to continuous dynamical systems, with the objective being either the control performance or some economic metric leading to the so-called economic MPC [2] . The implementation of MPC relies on the efficient and robust online solution of the underlying optimization problem. Significant advances have been made in the solution of continuous optimization problems, yet the solution of mixed integer optimization problems [3, 4], i.e., problems that consider both continuous and discrete (integer) variables, remains a challenge.  \nDiscrete variables can arise either due to the hybrid nature of the dynamic system (e.g., piece-wise affine dynamics) or due to the presence of discrete variables related to the operation of the system [5] . Typical examples of the latter include the operation of energy systems where a unit is either on or off [6], chemical processes that can operate only at specific operating points [7], motion planning in the presence of obstacles [8], and fuel cell operation [9] . These problems are formally known as mixed integer optimal control problems [5, 10] and are formulated as Mixed Integer Dynamic Optimization problems (MIDO) . A common approach to solving such problems is to discretize the differential equations that describe the system  \nEmail address: [daout001@umn.edu](daout001@umn.edu) (Prodromos Daoutidis)  \n1Corresponding author  \nand then use mathematical optimization techniques to solve the resulting Mixed Integer Programming (MIP) problem.  \nSolving such MIP problems online can be a daunting computational task and thus a major limitation for the implementation of mixed integer MPC. Branch and Bound is a standard solution strategy, where branching is performed either on the integer variables or on the spatial domain of the feasible region for nonconvex problems [11, 12, 13, 14, 15, 16, 17, 18] . This approach can guarantee global optimality, yet it is generally slow for online applications, especially when the underlying problem is a Mixed Integer Nonlinear Programming (MINLP) problem. Multiparametric programming can be used to efficiently determine the optimal solution of a MIP problem [19, 20, 21, 22] . However, computing the critical regions, i.e., the optimal solution, for every value of the parameters of the MIP problem is computationally expensive for nonlinear systems with many states. Another solution approach is to exploit the underlying structure of the problem and use decomposition-based solution algorithms, such as the combinatorial integral approximation (CIA) [2","cbCaiqd6R1C51plL","https://ap.wps.com/l/cbCaiqd6R1C51plL","pdf",2130706,1,12,"English","en",105,"# Abstract\n## Problem background: mixed integer MPC and online optimization\n## Mixed integer optimal control formulation (MIDO/MIP)\n## Baseline methods and limitations (branch-and-bound, multiparametric)\n## Decomposition approach: Generalized Benders Decomposition (GBD)\n## Challenges in online GBD implementation\n## Role of machine learning in mixed integer MPC","[{\"question\":\"What makes mixed integer MPC problems difficult to solve online?\",\"answer\":\"They require efficient, robust online solutions of mixed integer optimization problems that combine continuous and discrete decisions, which are generally computationally hard and can lead to slow methods such as branch-and-bound.\"},{\"question\":\"How does Generalized Benders Decomposition (GBD) help in mixed integer optimization?\",\"answer\":\"GBD fixes complicating variables to decompose the problem into a master problem (integer variables) and a continuous subproblem, coordinating them iteratively using cuts that capture the subproblem response.\"},{\"question\":\"What improvement does the proposed machine learning aided branch-and-check GBD provide?\",\"answer\":\"The method always finds feasible solutions when the mixed integer MPC problem is feasible and substantially reduces solution time (up to 97% or 50×) with small errors on the order of 1% compared with standard and accelerated GBD.\"}]","Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition - Abstract | PDF",1785812889,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"computationally-efficient-solution-of-mixed-integer-model-predictive-control-problems-via-machine-learning-aided-benders-decomposition-abstract","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/computationally-efficient-solution-of-mixed-integer-model-predictive-control-problems-via-machine-learning-aided-benders-decomposition-abstract/122787/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What makes mixed integer MPC problems difficult to solve online?","Question",{"text":75,"@type":76},"They require efficient, robust online solutions of mixed integer optimization problems that combine continuous and discrete decisions, which are generally computationally hard and can lead to slow methods such as branch-and-bound.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does Generalized Benders Decomposition (GBD) help in mixed integer optimization?",{"text":80,"@type":76},"GBD fixes complicating variables to decompose the problem into a master problem (integer variables) and a continuous subproblem, coordinating them iteratively using cuts that capture the subproblem response.",{"name":82,"@type":73,"acceptedAnswer":83},"What improvement does the proposed machine learning aided branch-and-check GBD provide?",{"text":84,"@type":76},"The method always finds feasible solutions when the mixed integer MPC problem is feasible and substantially reduces solution time (up to 97% or 50×) with small errors on the order of 1% compared with standard and accelerated GBD.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]