ref_integer_and_mixed_integer.bib

@article{takapouiSimpleEffectiveHeuristic2020,
  title = {A Simple Effective Heuristic for Embedded Mixed-Integer Quadratic Programming},
  author = {Takapoui, Reza and Moehle, Nicholas and Boyd, Stephen and Bemporad, Alberto},
  year = {2020},
  month = jan,
  journal = {International Journal of Control},
  volume = {93},
  number = {1},
  pages = {2--12},
  publisher = {Taylor \& Francis},
  issn = {0020-7179},
  doi = {10.1080/00207179.2017.1316016},
  url = {https://doi.org/10.1080/00207179.2017.1316016},
  urldate = {2020-11-04},
  abstract = {In this paper, we propose a fast optimisation algorithm for approximately minimising convex quadratic functions over the intersection of affine and separable constraints (i.e. the Cartesian product of possibly nonconvex real sets). This problem class contains many NP-hard problems such as mixed-integer quadratic programming. Our heuristic is based on a variation of the alternating direction method of multipliers (ADMM), an algorithm for solving convex optimisation problems. We discuss the favourable computational aspects of our algorithm, which allow it to run quickly even on very modest computational platforms such as embedded processors. We give several examples for which an approximate solution should be found very quickly, such as management of a hybrid-electric vehicle drivetrain and control of switched-mode power converters. Our numerical experiments suggest that our method is very effective in finding a feasible point with small objective value; indeed, we see that in many cases, it finds the global solution.}
}

@book{chenAppliedIntegerProgramming2010,
  title = {Applied {{Integer Programming}}: {{Modeling}} and {{Solution}}},
  shorttitle = {Applied {{Integer Programming}}},
  author = {Chen, Der-San and Batson, Robert G. and Dang, Yu},
  year = {2010},
  month = jan,
  publisher = {Wiley},
  address = {Hoboken, N.J},
  abstract = {An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.},
  isbn = {978-0-470-37306-4},
  langid = {english}
}

@book{confortiIntegerProgramming2014,
  title = {Integer {{Programming}}},
  author = {Conforti, Michele and Cornu{\'e}jols, G{\'e}rard and Zambelli, Giacomo},
  year = {2014},
  month = dec,
  series = {Graduate {{Texts}} in {{Mathematics}}},
  number = {271},
  publisher = {Springer},
  address = {New York},
  isbn = {978-3-319-11007-3},
  langid = {english}
}

@book{wolseyIntegerProgramming2021,
  title = {Integer {{Programming}}},
  author = {Wolsey, Laurence A.},
  year = {2021},
  edition = {2},
  publisher = {Wiley},
  address = {Hoboken, NJ},
  isbn = {978-1-119-60653-6},
  langid = {english}
}

@book{williamsModelBuildingMathematical2013,
  title = {Model {{Building}} in {{Mathematical Programming}}},
  author = {Williams, H. Paul},
  year = {2013},
  month = mar,
  edition = {5},
  publisher = {Wiley},
  address = {Hoboken, N.J},
  isbn = {978-1-118-44333-0},
  langid = {english}
}

@book{korteCombinatorialOptimizationTheory2018,
  title = {Combinatorial {{Optimization}}: {{Theory}} and {{Algorithms}}},
  shorttitle = {Combinatorial {{Optimization}}},
  author = {Korte, Bernhard and Vygen, Jens},
  year = {2018},
  month = mar,
  series = {Algorithms and {{Combinatorics}}},
  edition = {6},
  number = {21},
  publisher = {Springer},
  address = {New York, NY},
  url = {http://www.or.uni-bonn.de/~vygen/co.html},
  isbn = {978-3-662-56038-9},
  langid = {english}
}

@article{klotzPracticalGuidelinesSolving2013,
  title = {Practical Guidelines for Solving Difficult Mixed Integer Linear Programs},
  author = {Klotz, Ed and Newman, Alexandra M.},
  year = {2013},
  month = oct,
  journal = {Surveys in Operations Research and Management Science},
  volume = {18},
  number = {1},
  pages = {18--32},
  issn = {1876-7354},
  doi = {10.1016/j.sorms.2012.12.001},
  url = {https://www.sciencedirect.com/science/article/pii/S1876735413000020},
  urldate = {2021-11-26},
  abstract = {Even with state-of-the-art hardware and software, mixed integer programs can require hours, or even days, of run time and are not guaranteed to yield an optimal (or near-optimal, or any!) solution. In this paper, we present suggestions for appropriate use of state-of-the-art optimizers and guidelines for careful formulation, both of which can vastly improve performance.},
  langid = {english}
}

@phdthesis{axehillIntegerQuadraticProgramming2008,
  title = {Integer {{Quadratic Programming}} for {{Control}} and {{Communication}}},
  author = {Axehill, Daniel},
  year = {2008},
  address = {Link{\"o}ping, Sweden},
  url = {http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10642},
  urldate = {2022-12-07},
  abstract = {DiVA portal is a finding tool for research publications and student theses written at the following 50 universities and research institutions.},
  langid = {english},
  school = {Link{\"o}ping University}
}

@book{taillardDesignHeuristicAlgorithms2023,
  title = {Design of {{Heuristic Algorithms}} for {{Hard Optimization}}: {{With Python Codes}} for the {{Travelling Salesman Problem}}},
  shorttitle = {Design of {{Heuristic Algorithms}} for {{Hard Optimization}}},
  author = {Taillard, {\'E}ric D.},
  year = {2023},
  publisher = {Springer Nature},
  doi = {10.1007/978-3-031-13714-3},
  url = {https://library.oapen.org/handle/20.500.12657/59365},
  urldate = {2022-12-08},
  abstract = {This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content.},
  isbn = {978-3-031-13714-3},
  langid = {english}
}

@book{balasDisjunctiveProgramming2018,
  title = {Disjunctive {{Programming}}},
  author = {Balas, Egon},
  year = {2018},
  month = dec,
  publisher = {Springer},
  address = {Cham},
  url = {https://doi.org/10.1007/978-3-030-00148-3},
  isbn = {978-3-030-00147-6},
  langid = {english}
}

@book{williamsLogicIntegerProgramming2009,
  title = {Logic and {{Integer Programming}}},
  author = {Williams, H. Paul},
  year = {2009},
  month = apr,
  series = {International {{Series}} in {{Operations Research}} \& {{Management Science}}},
  publisher = {Springer},
  langid = {english}
}

@book{floudasNonlinearMixedIntegerOptimization1995,
  title = {Nonlinear and {{Mixed-Integer Optimization}}: {{Fundamentals}} and {{Applications}}},
  shorttitle = {Nonlinear and {{Mixed-Integer Optimization}}},
  author = {Floudas, Christodoulos A.},
  year = {1995},
  publisher = {Oxford University Press},
  address = {New York},
  url = {https://doi.org/10.1093/oso/9780195100563.001.0001},
  isbn = {978-0-19-510056-3},
  langid = {english}
}

@article{cavalierModelingIntegerProgramming1990,
  title = {Modeling and Integer Programming Techniques Applied to Propositional Calculus},
  author = {Cavalier, Tom M. and Pardalos, Panos M. and Soyster, Allen L.},
  year = {1990},
  month = jan,
  journal = {Computers \& Operations Research},
  volume = {17},
  number = {6},
  pages = {561--570},
  issn = {0305-0548},
  doi = {10.1016/0305-0548(90)90062-C},
  url = {https://www.sciencedirect.com/science/article/pii/030505489090062C},
  urldate = {2022-12-30},
  abstract = {This paper discusses alternative methods for constructing a 0--1 integer programming problem from a propositional calculus problem and the use of the resulting mathematical program to solve the related logic problem. This paper also identifies some special structures associated with the constraint sets and discusses several fundamental results concerning methods of preprocessing the logical inferences into constraints.},
  langid = {english}
}

@inproceedings{vielmaMixedIntegerConic2019,
  title = {Mixed {{Integer Conic Optimization}} Using {{Julia}} and {{JuMP}}},
  booktitle = {3rd {{Los Alamos National Laboratory Grid Science Winter School}} \& {{Conference}}},
  author = {Vielma, Juan Pablo},
  year = {2019},
  month = jan,
  address = {Santa Fe, NM},
  url = {https://cnls.lanl.gov/external/gsslides2019/Vielma.pdf},
  urldate = {2023-02-20}
}

@article{bertsimasOnlineMixedIntegerOptimization2022,
  title = {Online {{Mixed-Integer Optimization}} in {{Milliseconds}}},
  author = {Bertsimas, Dimitris and Stellato, Bartolomeo},
  year = {2022},
  month = jul,
  journal = {INFORMS Journal on Computing},
  volume = {34},
  number = {4},
  pages = {2229--2248},
  publisher = {INFORMS},
  issn = {1091-9856},
  doi = {10.1287/ijoc.2022.1181},
  url = {https://pubsonline.informs.org/doi/abs/10.1287/ijoc.2022.1181},
  urldate = {2023-09-20},
  abstract = {We propose a method to approximate the solution of online mixed-integer optimization (MIO) problems at very high speed using machine learning. By exploiting the repetitive nature of online optimization, we can greatly speed up the solution time. Our approach encodes the optimal solution into a small amount of information denoted as strategy using the voice of optimization framework. In this way, the core part of the optimization routine becomes a multiclass classification problem that can be solved very quickly. In this work, we extend that framework to real-time and high-speed applications focusing on parametric mixed-integer quadratic optimization. We propose an extremely fast online optimization method consisting of a feedforward neural network evaluation and a linear system solution where the matrix has already been factorized. Therefore, this online approach does not require any solver or iterative algorithm. We show the speed of the proposed method both in terms of total computations required and measured execution time. We estimate the number of floating point operations required to completely recover the optimal solution as a function of the problem dimensions. Compared with state-of-the-art MIO routines, the online running time of our method is very predictable and can be lower than a single matrix factorization time. We benchmark our method against the state-of-the-art solver Gurobi obtaining up to two to three orders of magnitude speedups on examples from fuel cell energy management, sparse portfolio optimization, and motion planning with obstacle avoidance. Summary of Contribution: We propose a technique to approximate the solution of online optimization problems at high speed using machine learning. By exploiting the repetitive nature of online optimization, we learn the mapping between the key problem parameters and an encoding of the optimal solution to greatly speed up the solution time. This allows us to significantly improve the computation time and resources needed to solve online mixed-integer optimization problems. We obtain a simple method with a very low computing time variance, which is crucial in online settings.}
}

@book{schrijverCombinatorialOptimizationPolyhedra2002,
  title = {Combinatorial {{Optimization}}: {{Polyhedra}} and {{Efficiency}}},
  shorttitle = {Combinatorial {{Optimization}}},
  author = {Schrijver, Alexander},
  year = {10 prosince 2002},
  series = {Algorithms and {{Combinatorics}}},
  volume = {24},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  url = {https://link.springer.com/book/9783540443896},
  abstract = {This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented.},
  isbn = {978-3-540-44389-6}
}

@book{bertsimasOptimizationIntegers2005,
  title = {Optimization {{Over Integers}}},
  author = {Bertsimas, Dimitris and Weismantel, Robert},
  year = {2005},
  month = jun,
  publisher = {Dynamic Ideas},
  address = {Belmont},
  url = {https://www.dynamic-ideas.com/books/x0g7bsm2nvnl6j7ebqodcrhsvlgbm7},
  abstract = {The book provides a unified, insightful, and modern treatment of the theory of integer optimization. The book is used in the doctoral level course, "Integer and Combinatorial Optimization" at the Massachusetts Institute of Technology. For solutions to exercises and other instructor resources, please contact Dimitris Bertsimas (dbertsim@mit.edu). The chapters of the book are logically organized in four parts: Part I: Formulations and relaxations includes Chapters 1-5 and discusses how to formulate integer optimization problems, how to enhance the formulations to improve the quality of relaxations, how to obtain ideal formulations, the duality of integer optimization and how to solve the resulting relaxations both practically and theoretically. Part II: Algebra and geometry of integer optimization includes Chapters 6-8 and develops the theory of lattices, oulines ideas from algebraic geometry that have had an impact on integer optimization, and most importantly discusses the geometry of integer optimization, a key feature of the book. These chapters provide the building blocks for developing algorithms. Part III: Algorithms for integer optimization includes Chapters 9-12 and develops cutting plane methods, integral basis methods, enumerative and heuristic methods and approximation algorithms. The key characteristic of our treatment is that our development of the algorithms is naturally based on the algebraic and geometric developments of Part II. Part IV: Extensions of integer optimization includes Chapters 13 and 14, and treats mixed integer optimization and robust discrete optimization. Both areas are practically significant as real world problems have very often both continuous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner. Distinguishing Characteristics Of This Book:* Develops the theory of integer optimization from a new geometric perspective via integral generating sets; * Emphasizes strong formulations, ways to improve them, integral polyhedra, duality, and relaxations; * Discusses applications of lattices and algebraic geometry to integer optimization, including Grobner bases, optimization over polynomials and counting integer points in polyhedra; * Contains a unified geometric treatment of cutting plane and integral basis methods; * Covers enumerative and heuristic methods, including local search over exponential neighborhoods and simulated annealing; * Presents the major methods to construct approximation algorithms: primal-dual, randomized rounding, semidefinite and enumerative methods; * Provides a unified treatment of mixed integer and robust discrete optimization; * Includes a large number of examples and exercises developed through extensive classroom use.},
  isbn = {978-0-9759146-2-5},
  langid = {english}
}