Integer and Combinatorial Optimization

By Karla L. Hoffman, T. Ralphs. 2013

2,096 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Industrial and Manufacturing Engineering, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Industrial and Manufacturing Engineering

In Optimization & Training

Citations in the corpus

Learning to learn by gradient descent by gradient descent (2016, background): “Note, however that these earlier works do not directly address the transfer of a learned training procedure to novel problem instances and instead focus on adaptivity in the online setting.”
Learning to Branch in Mixed Integer Programming (2016, background): “Branch-and-Bound (Nemhauser and Wolsey 1988) keeps a list of search nodes, each with a corresponding LP problem, obtained by relaxing the integrality requirements on the variables in I that have not been fixed to an integer value at an ancestor node.”
Sub-Channel Assignment, Power Allocation, and User Scheduling for Non-Orthogonal Multiple Access Networks (2016, background): “Note that this is a non-convex optimization problem due to the binary constraint in (6d) and the existence of the interference term in the objective function [24].”
Hybrid metaheuristics in combinatorial optimization: A survey (2011, background): “For many combinatorial optimization problems the ﬁeld of mathematical programming and (mixed) integer linear programming (MIP) in particular provides powerful tools; for comprehensive introductions into this area see e.g. [99, 100].”
Algorithms and Software for Convex Mixed Integer Nonlinear Programs (2012, background): “…kilinc@wisc.edu ‡Department of Industrial and Systems Engineering, University of WisconsinMadison, 1513 University Ave., Madison, WI, 53706, linderoth@wisc.edu, The work of the second and third authors is supported by the US Department of Energy under grants DE-FG02-08ER25861 and…”
Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning (2016, neutral): “An early overview of the core B&B algorithm was provided by Lawler and Wood [2]; the solution procedure is also covered in the excellent texts by Nemhauser and Wolsey [3], Bertsimas and Tsitsiklis [4], and Papadimitriou and Steiglitz [5].”
Mixed-integer nonlinear optimization*† (2013, methodology): “In most presentations of the convex combination model (Dantzig, 1960, 1963; Jeroslow and Lowe, 1985; Nemhauser and Wolsey, 1988b; Wilson, 1998; Lee and Wilson, 2001; Vielma et al., 2010; Geissler et al., 2012) this condition is instead formulated by using the following constraints: λ0 ≤ z1, λd ≤ zd,”
Learning to segment under various forms of weak supervision (2015, background): “[3] A (0,+1,−1) matrix A is totally unimodular if it contains no more than one +1 and no more than one −1 in each column.”
Predictive Control for Linear and Hybrid Systems (2017, result): “We highlight the main techniques of the translation process, by generalizing several results that appeared in the literature [126, 244, 287, 213, 83, 42, 81, 277, 286, 219].”
A Model Predictive Control Approach to Microgrid Operation Optimization (2014, background): “It is well known that MILP problems are NP complete and their computational complexity mainly depends on the number of integer variables [39], [50].”
Cloud task scheduling based on ant colony optimization (2013, background): “Local search algorithms start from some initial solution and iteratively try to replace the current solution by a better solution in an appropriately defined neighborhood of the current solution [11].”
Recommender Systems (2016, neutral): “A discussion of the submodularity property may be found in [452].”
Stochastic dual dynamic integer programming (2018, neutral): “Then, we have the following equalities: where (4.5) follows from Theorem 1 in [32] (also c.f. Theorem 6.2 in [59]).”
Guiding Combinatorial Optimization with UCT (2012, background): “…of depthfirst traversal work best in the context of propositional satisfiability (SAT), while best-first, fastest descent, and various heuristic combinations of the above work better in other contexts such as state space search and mixed-integer programming or MIP optimization [cf. 8, 12].”
Towards Total Recall in Industrial Anomaly Detection (2021, methodology): “Because PatchCore uses nearest neighbour computations (next Section), we use a minimax facility location coreset selection, see e.g., [48] and [49], to ensure approximately similar coverage of the M -coreset M C in patch-level feature space as compared to the original memory bank M M ∗ C = arg min T”
Assortment Planning Under the Multinomial Logit Model with Totally Unimodular Constraint Structures (2013, background): “Such matrices are known to be totally unimodular; see Proposition 2.6 in Chapter III.1 of Nemhauser and Wolsey (1988), along with Heller (1957) and Heller and Hoffman (1962).”
Mixed Integer Linear Programming Formulation Techniques (2015, methodology): “For more details on basic branch-and-bound and state-of-the-art solvers, we refer the reader to [22, 36, 131, 166] and [1, 2, 25, 23, 92, 112, 24], respectively.”
Stochastic model predictive control for economic/environmental operation management of microgrids: An experimental case study (2016, methodology): “It is well known that MILP problems are NP-complete and their computational complexity mainly depends on the number of integer variables [56,53].”