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We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual…

Optimization and Control · Mathematics 2026-02-03 Paulo Michel F. Yamagishi , Marcia Fampa , Jon Lee

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, for checking node fathoming,…

Optimization and Control · Mathematics 2021-12-06 Nathan Adelgren , Akshay Gupte

A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection can affect the size of the resulting search trees by orders of magnitude. A…

Optimization and Control · Mathematics 2020-08-31 Daniel Anderson , Pierre Le Bodic , Kerri Morgan

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

Computational Engineering, Finance, and Science · Computer Science 2024-01-26 Kasia Świrydowicz , Nicholson Koukpaizan , Maksudul Alam , Shaked Regev , Michael Saunders , Slaven Peleš

Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce…

Optimization and Control · Mathematics 2022-08-04 Defeng Liu , Matteo Fischetti , Andrea Lodi

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

Information Theory · Computer Science 2007-07-13 Mohammad H. Taghavi , Paul H. Siegel

Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…

Computer Science and Game Theory · Computer Science 2007-05-23 Rica Gonen , Daniel Lehmann

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

Information Theory · Computer Science 2007-07-13 Mohammad H. Taghavi N. , Paul H. Siegel

In this paper we introduce an evolutionary algorithm for the solution of linear integer programs. The strategy is based on the separation of the variables into the integer subset and the continuous subset; the integer variables are fixed by…

Neural and Evolutionary Computing · Computer Science 2014-07-29 João Pedro Pedroso

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…

Mathematical Software · Computer Science 2024-01-31 Thanh Son Nguyen , Alexey Solovyev , Ganesh Gopalakrishnan

Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on…

Machine Learning · Computer Science 2025-09-25 Connor Lawless , Yingxi Li , Anders Wikum , Madeleine Udell , Ellen Vitercik

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has…

Optimization and Control · Mathematics 2015-01-29 Michael Patriksson , Christoffer Strömberg

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…

Optimization and Control · Mathematics 2025-10-13 Víctor Blanco , Diego Laborda , Miguel Martínez-Antón

We use convex relaxation techniques to produce lower bounds on the optimal value of subset selection problems and generate good approximate solutions. We then explicitly bound the quality of these relaxations by studying the approximation…

Optimization and Control · Mathematics 2010-06-21 Francis Bach , Selin Damla Ahipasaoglu , Alexandre d'Aspremont

In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…

Networking and Internet Architecture · Computer Science 2021-02-05 Wei-Kun Chen , Ya-Feng Liu , Yu-Hong Dai , Zhi-Quan Luo

In many operational applications, it is necessary to routinely find, within a very limited time window, provably good solutions to challenging mixed-integer linear programming (MILP) problems. An example is the Security-Constrained Unit…

Optimization and Control · Mathematics 2022-08-23 Xiaoyi Gu , Santanu S. Dey , Álinson S. Xavier , Feng Qiu

When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for…

Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…

Machine Learning · Computer Science 2025-06-10 Xiaoke Wang , Batuhan Altundas , Zhaoxin Li , Aaron Zhao , Matthew Gombolay

We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…

Data Structures and Algorithms · Computer Science 2018-09-14 Matthias Becker , Nicolas Ginoux , Sebastien Martin , Zsuzsanna Roka

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…

Optimization and Control · Mathematics 2023-03-22 Julia Grübel , Richard Krug , Martin Schmidt , Winnifried Wollner