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ObstacleAware LongestPath Routing with Parallel MILP Solvers
"... Abstract—Longestpath routing problems, which can arise in the design of highperformance printed circuit boards (PCBs), have been proven to be NPhard. In this article, we propose a mixed integer linear programming (MILP) formulation to gridded longestpath routing problems; each of which may conta ..."
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contain obstacles. After a longestpath routing problem has been transformed into an MILP problem, parallel MILP solvers can be used to find optimal solutions. In addition, suboptimal solutions can be generated in exchange for reduced execution time. The proposed formulation method can also be used
MILP Software
"... This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose ..."
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This article concerns software for solving a general Mixed Integer Linear Program (MILP) in the form min{c T x: Ax ≥ b, x ≥ 0, xj ∈ Z ∀j ∈ I}. (1) The algorithmic approach relies on the iterative solution, through generalpurpose
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 403 (47 self)
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), for which e#cient solvers have been recently developed. Some examples and a simulation case s...
TIGHTER APPROXIMATED MILP FORMULATIONS FOR UNIT COMMITMENT PROBLEMS
"... The shortterm Unit Commitment (UC) problem in hydrothermal power generation is a largescale, MixedInteger NonLinear Program (MINLP), which is difficult to solve efficiently, especially for largescale instances. It is possible to approximate the nonlinear objective function of the problem by mean ..."
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Cited by 17 (7 self)
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by means of piecewiselinear functions, so that UC can be approximated by a MixedInteger Linear Program (MILP); applying the available efficient generalpurpose MILP solvers to the resulting formulations, good quality solutions can be obtained in a relatively short amount of time. We build
An MILP Approach to a Nonlinear Pattern Classification of Data
"... In this paper, we deal with the separation of data by concurrently determined, piecewise nonlinear discriminant functions. Toward the end, we develop a new l1distance norm error metric and cast the problem as a mixed 01 integer and linear programming (MILP) model. Given a finite number of discrimi ..."
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of discriminant functions as an input, the proposed model considers the synergy as well as the individual role of the functions involved and implements a simplest nonlinear decision surface that best separates the data on hand. Hence, exploiting powerful MILP solvers, the model efficiently analyzes any given data
A MILPbased decision procedure for the (Fuzzy) Description Logic ALCB
"... Abstract. To overcome the inability of Description Logics (DLs) to represent vague or imprecise information, several fuzzy extensions have been proposed in the literature. In this context, an important family of reasoning algorithms for fuzzy DLs is based on a combination of tableau algorithms and O ..."
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algorithm is deterministic, in the sense that it defers the inherent nondeterminism in ALCB to a MILP solver. 1
Symmetries in MILP Matrix Symmetry
"... A symmetry of a matrix is a permutation of rows and columns such that the permuted matrix is identical to the original one. ..."
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A symmetry of a matrix is a permutation of rows and columns such that the permuted matrix is identical to the original one.
Algorithms for hybrid MILP/CP models for a class of optimization problems
 INFORMS Journal on Computing
, 2001
"... The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered ..."
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Cited by 96 (12 self)
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The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered
HYBRID LAGRANGIANMILP APPROACHES FOR UNIT . . .
, 2007
"... The shortterm Unit Commitment (UC) problem in hydrothermal power generation is a fundamental problem in shortterm electrical generation scheduling. Historically, Lagrangian techniques have been used to tackle this largescale, difficult MixedInteger NonLinear Program (MINLP); this requires being ..."
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of piecewiselinear functions, so that UC can be approximated by a MixedInteger Linear Program (MILP); in particular, using a recently developed class of valid inequalities for the problem, called “Perspective Cuts”, significant improvements have been obtained in the efficiency and effectiveness
Iterative MILP methods for vehiclecontrol problems
 IEEE Transactions on Robotics
"... Abstract—Mixedinteger linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this paper, we present iterative MILP algorithms that addr ..."
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Cited by 20 (0 self)
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Abstract—Mixedinteger linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this paper, we present iterative MILP algorithms
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