Gotowe bibliografie tematyczne / Mixed-Integer Linear Programs

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Gotowa bibliografia na temat „Mixed-Integer Linear Programs”

Autor: Grafiati
Data publikacji: 6 września 2023

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Artykuły w czasopismach na temat "Mixed-Integer Linear Programs"

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Guieu, Olivier, and John W. Chinneck. "Analyzing Infeasible Mixed-Integer and Integer Linear Programs." INFORMS Journal on Computing 11, no. 1 (1999): 63–77. http://dx.doi.org/10.1287/ijoc.11.1.63.

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Cornuéjols, Gérard. "Valid inequalities for mixed integer linear programs." Mathematical Programming 112, no. 1 (2007): 3–44. http://dx.doi.org/10.1007/s10107-006-0086-0.

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Berthold, Timo, and Gregor Hendel. "Learning To Scale Mixed-Integer Programs." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (2021): 3661–68. http://dx.doi.org/10.1609/aaai.v35i5.16482.

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Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes the difference whether these problems can be solved correctly or not. In this paper, we investigate the use of machine learning to choose at the beginning of the solution process between two common scaling methods: Standard scaling and Curtis-Reid scaling. The latter often, but not always, leads to a more robust solution process, but may suffer from longer solution times. Rather than training for overall solution time, we propose to use the attention level of a MIP solution process as a learning label. We evaluate the predictive power of a random forest approach and a linear regressor that learns the (square-root of the) difference in attention level. It turns out that the resulting classification not only reduces various types of numerical errors by large margins, but it also improves the performance of the dual simplex algorithm. The learned model has been implemented within the FICO Xpress MIP solver and it is used by default since release 8.9, May 2020, to determine the scaling algorithm Xpress applies before solving an LP or a MIP.
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Laporte, Gilbert, and Frédéric Semet. "An optimality cut for mixed integer linear programs." European Journal of Operational Research 119, no. 3 (1999): 671–77. http://dx.doi.org/10.1016/s0377-2217(98)00357-9.

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Proll, L. G. "Stronger formulations of mixed integer linear programs: an example." International Journal of Mathematical Education in Science and Technology 28, no. 5 (1997): 707–12. http://dx.doi.org/10.1080/0020739970280507.

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Klotz, Ed, and Alexandra M. Newman. "Practical guidelines for solving difficult mixed integer linear programs." Surveys in Operations Research and Management Science 18, no. 1-2 (2013): 18–32. http://dx.doi.org/10.1016/j.sorms.2012.12.001.

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Bonami, Pierre, Gérard Cornuéjols, Sanjeeb Dash, Matteo Fischetti, and Andrea Lodi. "Projected Chvátal–Gomory cuts for mixed integer linear programs." Mathematical Programming 113, no. 2 (2006): 241–57. http://dx.doi.org/10.1007/s10107-006-0051-y.

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Pryor, Jennifer, and John W. Chinneck. "Faster integer-feasibility in mixed-integer linear programs by branching to force change." Computers & Operations Research 38, no. 8 (2011): 1143–52. http://dx.doi.org/10.1016/j.cor.2010.10.025.

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Chen, Binyuan, Simge Küçükyavuz, and Suvrajeet Sen. "Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs." Operations Research 59, no. 1 (2011): 202–10. http://dx.doi.org/10.1287/opre.1100.0882.

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Li, Xiaobo, Karthik Natarajan, Chung-Piaw Teo, and Zhichao Zheng. "Distributionally robust mixed integer linear programs: Persistency models with applications." European Journal of Operational Research 233, no. 3 (2014): 459–73. http://dx.doi.org/10.1016/j.ejor.2013.07.009.

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Rozprawy doktorskie na temat "Mixed-Integer Linear Programs"

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Guieu, Olivier Carleton University Dissertation Engineering Systems and Computer. "Analyzing infeasible mixed-integer and integer linear programs." Ottawa, 1995.

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Yildiz, Sercan. "Valid Inequalities for Mixed-Integer Linear and Mixed-Integer Conic Programs." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/777.

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Mixed-integer programming provides a natural framework for modeling optimization problems which require discrete decisions. Valid inequalities, used as cutting-planes and cuttingsurfaces in integer programming solvers, are an essential part of today’s integer programming technology. They enable the solution of mixed-integer programs of greater scale and complexity by providing tighter mathematical descriptions of the feasible solution set. This dissertation presents new structural results on general-purpose valid inequalities for mixedinteger linear and mixed-integer conic programs. Cut-generating functions are a priori formulas for generating a cutting-plane from the data of a mixed-integer linear program. This concept has its roots in the work of Balas, Gomory, and Johnson from the 1970s. It has received renewed attention in the past few years. Gomory and Johnson studied cut-generating functions for the corner relaxation of a mixedinteger linear program, which ignores the nonnegativity constraints on the basic variables in a tableau formulation. We consider models where these constraints are not ignored. In our first contribution, we generalize a classical result of Gomory and Johnson characterizing minimal cut-generating functions in terms of subadditivity, symmetry, and periodicity. Our analysis also exposes shortcomings in the usual definition of minimality in our general setting. To remedy this, we consider stronger notions of minimality and show that these impose additional structure on cut-generating functions. A stronger notion than the minimality of a cut-generating function is its extremality. While extreme cut-generating functions produce powerful cutting-planes, their structure can be very complicated. For the corner relaxation of a one-row integer linear program, Gomory and Johnson identified continuous, piecewise linear, minimal cut-generating functions with only two distinct slope values as a “simple” class of extreme cut-generating functions. In our second contribution, we establish a similar result for a one-row problem which takes the nonnegativity constraint on the basic variable into account. In our third contribution, we consider a multi-row model where only continuous nonbasic variables are present. Conforti, Cornuéjols, Daniilidis, Lemaréchal, and Malick recently showed that not all cutting-planes can be obtained from cut-generating functions in this framework. They also conjectured a natural condition under which cut-generating functions might be sufficient. In our third contribution, we prove that this conjecture is true. This justifies the recent research interest in cut-generating functions for this model. Despite the power of mixed-integer linear programming, many optimization problems of practical and theoretical interest cannot be modeled using a linear objective function and constraints alone. Next, we turn to a natural generalization of mixed-integer linear programming which allows nonlinear convex constraints: mixed-integer conic programming. Disjunctive inequalities, introduced by Balas in the context of mixed-integer linear programming in the 1970s, have been a principal ingredient in the practical success of mixed-integer programming in the last two decades. In order to extend our understanding of disjunctive inequalities to mixed-integer conic programming, we pursue a principled study of two-term disjunctions on conic sets. In our fourth contribution, we consider two-term disjunctions on a general regular cone. A result of Kılınç-Karzan indicates that conic minimal valid linear inequalities are all that is needed for a closed convex hull description of such sets. First we characterize the structure of conic minimal and tight valid linear inequalities for the disjunction. Then we develop structured nonlinear valid inequalities for the disjunction by grouping subsets of valid linear inequalities. We analyze the structure of these inequalities and identify conditions which guarantee that a single such inequality characterizes the closed convex hull of the disjunction. In our fifth and sixth contributions, we extend our earlier results to the cases where the regular cone under consideration is a direct product of second order cones and nonnegative rays and where it is the positive semidefinite cone. Disjunctions on these cones deserve special attention because they provide fundamental relaxations for mixed-integer second-order cone and mixed-integer semidefinite programs. We identify conditions under which our valid convex inequalities can be expressed in computationally tractable forms and present techniques to generate low-complexity relaxations when these conditions are not satisfied. In our final contribution, we provide closed convex hull descriptions for homogeneous two-term disjunctions on the second-order cone and general two-term disjunctions on affine cross-sections of the second-order cone. Our results yield strong convex disjunctive inequalities which can be used as cutting-surfaces in generic mixed-integer conic programming solvers.
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Nwana, Vincent Lebga. "Parallel algorithms for solving mixed integer linear programs." Thesis, Brunel University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368540.

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Salvagnin, Domenico. "Constraint Programming Techniques for Mixed Integer Linear Programs." Doctoral thesis, Università degli studi di Padova, 2009. http://hdl.handle.net/11577/3425690.

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Many decision problems in industry, logistics, and telecommunications can be viewed as satisfiability or optimization problems. Two paradigms have reached a high degree of sophistication from the point of view of both theory and implementation: Constraint Programming (CP) and Mixed Integer Programming (MIP). The CP and MIP paradigms have strengths and weaknesses that complement each other. On the one hand, CP, through the use of sophisticated propagation techniques, privileges primal inference. On the other hand, MIP, through the techniques of relaxation and strengthening through cutting planes, privileges dual inference. This thesis presents several studies in Mixed Integer Programming, with emphasis on computational aspects and integration with the Constraint Programming paradigm. In particular, CP concepts and techniques, such as nogoods, minimal infeasiblity and constraint propagation, are used to improve different MIP solving components, namely, dominance detection, Benders cuts selection strategy and primal heuristics. This cross-fertilization of techniques and ideas has proven very effective. Finally, an appendix is given covering a MIP application to robust railway timetabling.<br>Molti problemi decisionali nell'industria, nella logistica e nelle telecomunicazioni possono essere formulati come problemi di soddisfacibilita' o di ottimizzazione. Due paradigmi per la modellazione e la risoluzione di tali problemi hanno raggiunto un elevato grado di sviluppo, sia dal punto di vista teorico che implementativo: la Programmazione a Vincoli (Constraint Programming, CP) e la Programmazione Lineare Intera Mista (Mixed Integer Programming, MIP). I paradigmi CP e MIP hanno vantaggi e debolezze complementari. Da una parte, la CP privilegia l'inferenza primale, attraverso sofisticate tecniche di propagazione. Dall'altra, la MIP privilegia l'inferenza duale, attraverso i rilassamenti e il loro rafforzamento mediante piani di taglio. Questa tesi presenta alcuni studi in Programmazione Lineare Intera Mista, con enfasi sugli aspetti computazionali e sull'integrazione col paradigma della Programmazione a Vincoli. In particolare, concetti e tecniche CP, quali nogood, insoddisfacibilita' minimale e propagazione, sono usati per migliorare varie componenti risolutive per la MIP, quali procedure di dominanza, strategia di selezione dei tagli di Benders e euristiche primali. Questo scambio di idee e tecniche si e' dimostrato molto efficace. Infine, un'applicazione MIP alla generazione di orari robusti in ambito ferroviario e' presentata in appendice.
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Köppe, Matthias [Verfasser]. "Exact Primal Algorithms for General Integer and Mixed-Integer Linear Programs / Matthias Köppe." Aachen : Shaker, 2003. http://d-nb.info/1179032292/34.

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Chen, Binyuan. "FINITE DISJUNCTIVE PROGRAMMING METHODS FOR GENERAL MIXED INTEGER LINEAR PROGRAMS." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145120.

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In this dissertation, a finitely convergent disjunctive programming procedure, the Convex Hull Tree (CHT) algorithm, is proposed to obtain the convex hull of a general mixed–integer linear program with bounded integer variables. The CHT algorithm constructs a linear program that has the same optimal solution as the associated mixed-integer linear program. The standard notion of sequential cutting planes is then combined with ideasunderlying the CHT algorithm to help guide the choice of disjunctions to use within a new cutting plane method, the Cutting Plane Tree (CPT) algorithm. We show that the CPT algorithm converges to an integer optimal solution of the general mixed-integer linear program with bounded integer variables in finitely many steps. We also enhance the CPT algorithm with several techniques including a “round-of-cuts” approach and an iterative method for solving the cut generation linear program (CGLP). Two normalization constraints are discussed in detail for solving the CGLP. For moderately sized instances, our study shows that the CPT algorithm provides significant gap closures with a pure cutting plane method.
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Smith, Edmund. "Parallel solution of linear programs." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8833.

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The factors limiting the performance of computer software periodically undergo sudden shifts, resulting from technological progress, and these shifts can have profound implications for the design of high performance codes. At the present time, the speed with which hardware can execute a single stream of instructions has reached a plateau. It is now the number of instruction streams that may be executed concurrently which underpins estimates of compute power, and with this change, a critical limitation on the performance of software has come to be the degree to which it can be parallelised. The research in this thesis is concerned with the means by which codes for linear programming may be adapted to this new hardware. For the most part, it is codes implementing the simplex method which will be discussed, though these have typically lower performance for single solves than those implementing interior point methods. However, the ability of the simplex method to rapidly re-solve a problem makes it at present indispensable as a subroutine for mixed integer programming. The long history of the simplex method as a practical technique, with applications in many industries and government, has led to such codes reaching a great level of sophistication. It would be unexpected in a research project such as this one to match the performance of top commercial codes with many years of development behind them. The simplex codes described in this thesis are, however, able to solve real problems of small to moderate size, rather than being confined to random or otherwise artificially generated instances. The remainder of this thesis is structured as follows. The rest of this chapter gives a brief overview of the essential elements of modern parallel hardware and of the linear programming problem. Both the simplex method and interior point methods are discussed, along with some of the key algorithmic enhancements required for such systems to solve real-world problems. Some background on the parallelisation of both types of code is given. The next chapter describes two standard simplex codes designed to exploit the current generation of hardware. i6 is a parallel standard simplex solver capable of being applied to a range of real problems, and showing exceptional performance for dense, square programs. i8 is also a parallel, standard simplex solver, but now implemented for graphics processing units (GPUs).
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Ramakrishnan, V. S., and Jeremy F. 1939 Shapiro. "Analyzing Multi-Objective Linear and Mixed Integer Programs by Lagrange Multipliers." Massachusetts Institute of Technology, Operations Research Center, 1991. http://hdl.handle.net/1721.1/5322.

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A new method for multi-objective optimization of linear and mixed programs based on Lagrange multiplier methods is developed. The method resembles, but is distinct from, objective function weighting and goal programming methods. A subgradient optimization algorithm for selecting the multipliers is presented and analyzed. The method is illustrated by its application to a model for determining the weekly re-distribution of railroad cars from excess supply areas to excess demand areas, and to a model for balancing cost minimization against order completion requirements for a dynamic lot size model.
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Adams, Warren Philip. "The mixed-integer bilinear programming problem with extensions to zero-one quadratic programs." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/74711.

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This research effort is concerned with a class of mathematical programming problems referred to as Mixed-Integer Bilinear Programming Problems. This class of problems, which arises in production, location-allocation, and distribution-application contexts, may be considered as a discrete version of the well-known Bilinear Programming Problem in that one set of decision variables is restricted to be binary valued. The structure of this problem is studied, and special cases wherein it is readily solvable are identified. For the more general case, a new linearization technique is introduced and demonstrated to lead to a tighter linear programming relaxation than obtained through available linearization methods. Based on this linearization, a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm is developed. Extensive computational experience is provided to test the efficiency of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm. The solution strategy developed for the Mixed-Integer Bilinear Programming Problem may be applied, with suitable modifications,. to other classes of mathematical programming problems: in particular, to the Zero-One Quadratic Programming Problem. In what may be considered as an extension to the work performed on the Mixed-Integer Bilinear Programming Problem, a solution strategy based on an equivalent linear reformulation is developed for the Zero-One Quadratic Programming Problem. The strategy is essentially an implicit enumeration algorithm which employs Lagrangian relaxation, Benders' cutting planes, and local explorations. Computational experience for this problem class is provided to justify the worth of the proposed linear reformulation and algorithm.<br>Ph. D.
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Gayen, Neela. "Automatic parallelization of stream programs for resource efficient embedded processors." Thesis, Queensland University of Technology, 2021. https://eprints.qut.edu.au/213058/1/Neela_Gayen_Thesis.pdf.

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This thesis considers how to exploit the specific characteristics of data streaming functions and multi-core processors to increase throughput through appropriate software process mappings. The hypothesis is that large numbers of low-power processors can achieve high throughput for streaming applications if a good mapping is provided. The innovation is to use compilation principles to guide the mapping, rather than heuristics. Three increasingly complex approaches are developed that focus on computational bottlenecks, then adds communication overheads, and lastly adds the costs of splitting and merging operations. Using this approach demonstrates that the successively more complex models can achieve correspondingly greater throughput.
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Części książek na temat "Mixed-Integer Linear Programs"

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Qualizza, Andrea, Pietro Belotti, and François Margot. "Linear Programming Relaxations of Quadratically Constrained Quadratic Programs." In Mixed Integer Nonlinear Programming. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1927-3_14.

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Niu, Yi-Shuai, and Tao Pham Dinh. "A DC Programming Approach for Mixed-Integer Linear Programs." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-87477-5_27.

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Johnson, Ellis L. "Modeling and Strong Linear Programs for Mixed Integer Programming." In Algorithms and Model Formulations in Mathematical Programming. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83724-1_1.

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Walter, Matthias. "Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs." In Integer Programming and Combinatorial Optimization. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73879-2_28.

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Gomory, Ralph E. "Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem." In 50 Years of Integer Programming 1958-2008. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-68279-0_4.

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Jeong, Jihwan, Scott Sanner, and Akshat Kumar. "A Mixed-Integer Linear Programming Reduction of Disjoint Bilinear Programs via Symbolic Variable Elimination." In Integration of Constraint Programming, Artificial Intelligence, and Operations Research. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33271-5_6.

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Güney, Evren. "A Mixed Integer Linear Program for Election Campaign Optimization Under D’Hondt Rule." In Operations Research Proceedings. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89920-6_11.

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Mouret, Sylvain, Ignacio E. Grossmann, and Pierre Pestiaux. "Tightening the Linear Relaxation of a Mixed Integer Nonlinear Program Using Constraint Programming." In Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01929-6_16.

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Frisch, Sarah, Philipp Hungerländer, Anna Jellen, and Dominic Weinberger. "A Mixed Integer Linear Program for Optimizing the Utilization of Locomotives with Maintenance Constraints." In Operations Research Proceedings. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18500-8_14.

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Westerlund, J., and L. G. Papageorgiou. "Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems." In Progress in Industrial Mathematics at ECMI 2004. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/3-540-28073-1_48.

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Streszczenia konferencji na temat "Mixed-Integer Linear Programs"

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Chin, Tat-Jun, Yang Heng Kee, Anders Eriksson, and Frank Neumann. "Guaranteed Outlier Removal with Mixed Integer Linear Programs." In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2016. http://dx.doi.org/10.1109/cvpr.2016.631.

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Gupta, Vijay, and Ignacio E. Grossmann. "Computational Strategies for Multistage Mixed-Integer Linear Stochastic Programs with Endogenous Uncertainty." In A Special Workshop of the Stochatic Programming Community and the European Association of Operational Research Societies (EURO) on "Stochastic Programming for Implementation and Advanced Applications". The Association of Lithuanian Serials, 2012. http://dx.doi.org/10.5200/stoprog.2012.06.

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Sadat, Sayed A., and Lingling Fan. "Mixed integer linear programming formulation for chance constrained mathematical programs with equilibrium constraints." In 2017 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2017. http://dx.doi.org/10.1109/pesgm.2017.8273875.

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Butter, Thomas, Franz Rothlauf, Jörn Grahl, Tobias Hildenbrand, and Jens Arndt. "Genetic algorithms and mixed integer linear programs for optimal strategies in a student's "sports" activity." In the 8th annual conference. ACM Press, 2006. http://dx.doi.org/10.1145/1143997.1144296.

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Kouider, Ahmed, Hacene Ait Haddadene, Samia Ourari, and Ammar Oulamara. "Mixed integer linear programs and tabu search approach to solve mixed graph coloring for unit-time job shop scheduling." In 2015 IEEE International Conference on Automation Science and Engineering (CASE). IEEE, 2015. http://dx.doi.org/10.1109/coase.2015.7294257.

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Akintunde, Michael E., Elena Botoeva, Panagiotis Kouvaros, and Alessio Lomuscio. "Verifying Strategic Abilities of Neural-symbolic Multi-agent Systems." In 17th International Conference on Principles of Knowledge Representation and Reasoning {KR-2020}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/kr.2020/3.

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We investigate the problem of verifying the strategic properties of multi-agent systems equipped with machine learning-based perception units. We introduce a novel model of agents comprising both a perception system implemented via feed-forward neural networks and an action selection mechanism implemented via traditional control logic. We define the verification problem for these systems against a bounded fragment of alternating-time temporal logic. We translate the verification problem on bounded traces into the feasibility problem of mixed integer linear programs and show the soundness and completeness of the translation. We show that the lower bound of the verification problem is PSPACE and the upper bound is coNEXPTIME. We present a tool implementing the compilation and evaluate the experimental results obtained on a complex scenario of multiple aircraft operating a recently proposed prototype for air-traffic collision avoidance.
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Iranmanesh, Ehsan, and Ramesh Krishnamurti. "Mixed Integer Program Heuristic for Linear Ordering Problem." In 5th International Conference on Operations Research and Enterprise Systems. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0005710701520156.

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Shao, Yufen, Jizhou Li, Ming–Jung Seow, et al. "Integrated Concept Analytics and Development Optimization Under Uncertainties." In ADIPEC. SPE, 2022. http://dx.doi.org/10.2118/211442-ms.

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Abstract Decision-making complexity in the oil and gas industry has risen dramatically in recent years, especially in consideration of uncertainties related to geopolitics, policies, marketing, subsurface resources etc. To enable decision making with the best quality opportunities and projects, we are developing an integrated suite of machine augmented mathematical technologies to recommend holistic decisions for concept selection and development planning under uncertainties. Our ongoing technology development is progressing a set of prototypes and use cases including: 1) AI-based uncertainty handling technologies aiming to detect uncertainties, quantify impacts, and translate to influence factors for decision-making (e.g., IRR, cost); 2) Decision-driven surrogate reservoir models approximating subsurface dynamics to enable rapid concept screening; 3) a set of mathematical optimization-based decision models in the form of mixed-integer linear programs (MILP) to provide solution alternatives to address different business challenges under uncertainties. We demonstrate that the use of systematic technical applications combined with human interaction can improve the decision quality significantly by considering all influence factors, searching through the entire decision space, and recommending a range of alternatives for business users to consider with minimal bias. These technologies have been designed to plug into existing processes and platforms to accelerate technology adoption and usage.
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Guirguis, David, David A. Romero, and Cristina H. Amon. "Efficient Wind Turbine Micrositing in Large-Scale Wind Farms." In ASME 2016 10th International Conference on Energy Sustainability collocated with the ASME 2016 Power Conference and the ASME 2016 14th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/es2016-59594.

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As wind energy is established as a sustainable alternative source of electricity, very large-scale wind farms with hundreds of turbines are becoming increasingly common. For the optimal design of wind farm layouts, the number of decision variables is at least twice the number of turbines (e.g., the Cartesian coordinates of each turbine). As the number of turbines increases, the computational cost incurred by the optimization solver to converge to a satisfactory solution increases as well. This issue represents a serious limitation in the computer-aided design of large wind farms. Moreover, the wind farm domains are typically highly constrained including land-availability and proximity constraints. These non-linear constraints increase the complexity of the optimization problem and decrease the likelihood of obtaining even a feasible solution. Several approaches have been proposed for micrositing of wind turbines, including random searches, mixed-integer programs, and metaheuristics. Each of these methods has its own trade-off between the quality of optimized layouts and the computational cost of obtaining the solution. In this paper, we demonstrate the capability of non-linear mathematical programming for optimizing very large-scale wind farms by leveraging explicit, analytical derivatives for the objective and constraint functions, thus overcoming the aforementioned limitations while also providing convergence and local optimality guarantees. For that purpose, two large farms with hundreds of turbines and significant land-use constraints are solved on a standard personal computer.
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Bae, Su W., Jong Park, and John-Paul Clarke. "Modified Mixed Integer Linear Program for Airport Departure Scheduling." In AIAA Guidance, Navigation, and Control (GNC) Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-4885.

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