The natural gas supply chain involves three main agents: producers, transportation companies, and local distribution companies (LDCs). We present a MIP model that is the basis for a decision support system developed f...
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The natural gas supply chain involves three main agents: producers, transportation companies, and local distribution companies (LDCs). We present a MIP model that is the basis for a decision support system developed for a Chilean LDC. This model takes into account many of the complexities of the purchasing and transportation contracts to help optimize daily purchase and transportation decisions in the absence of local storage facilities. The model was solved to optimality within a reasonable time. We show how the model handles several contractual issues and give some insights for the case when demand scenarios are used to deal with uncertainty.
The branch-and-bound optimization algorithm for mixed-integer model predictive control (MI-MPC) solves several convex quadratic program relaxations, but often the solutions are discarded based on already known integer...
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The branch-and-bound optimization algorithm for mixed-integer model predictive control (MI-MPC) solves several convex quadratic program relaxations, but often the solutions are discarded based on already known integer feasible solutions. This letter presents a projection and early termination strategy for infeasible interior point methods to reduce the computational effort of finding a globally optimal solution for MI-MPC. The method is shown to be also effective for infeasibility detection of the convex relaxations. We present numerical simulation results with a reduction of the total number of solver iterations by 42% for an MI-MPC example of decision making for automated driving with obstacle avoidance constraints.
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks...
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We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. We present a generic framework, which may be of independent interest, that provides a way to construct sharp or ideal formulations for the maximum of d affine functions over arbitrary polyhedral input domains. We apply this result to derive MIP formulations for a number of the most popular nonlinear operations (e.g. ReLU and max pooling) that are strictly stronger than other approaches from the literature. We corroborate this computationally, showing that our formulations are able to offer substantial improvements in solve time on verification tasks for image classification networks.
We investigate the NP-hard problem of computing the spark of a matrix (i.e., the smallest number of linearly dependent columns), a key parameter in compressed sensing and sparse signal recovery. To that end, we identi...
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We investigate the NP-hard problem of computing the spark of a matrix (i.e., the smallest number of linearly dependent columns), a key parameter in compressed sensing and sparse signal recovery. To that end, we identify polynomially solvable special cases, gather upper and lower bounding procedures, and propose several exact (mixed-)integerprogramming models and linear programming heuristics. In particular, we develop a branch and cut scheme to determine the girth of a matroid, focussing on the vector matroid case, for which the girth is precisely the spark of the representation matrix. Extensive numerical experiments demonstrate the effectiveness of our specialized algorithms compared to general-purpose black-box solvers applied to several mixed-integer programming models.
We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their p...
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We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved-and in the process, we identify a new state-of-the-art UC formulation.
It is well known that mixed-integer formulations can be used tomodel important classes of nonconvex functions, such as fixed-charge functions and linear economy-of-scale cost functions. The purpose of this paper is to...
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It is well known that mixed-integer formulations can be used tomodel important classes of nonconvex functions, such as fixed-charge functions and linear economy-of-scale cost functions. The purpose of this paper is to formulate a rigorous definition of a mixed-integer model of a given function and to study the properties of the functions that can be so modelled. An interesting byproduct of this approach is the identification of a simple class of functions that cannot be modelled by computer-representable mixed-integer formulations, even though mixed-integer models based on the use of a single arbitrary irrational constant are available for this class.
This study considers the optimal-trajectory generation problem in which a drone recognizes a wheelchair with an onboard camera while avoiding collision with obstacles. The optimal-trajectory generation was developed a...
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This study considers the optimal-trajectory generation problem in which a drone recognizes a wheelchair with an onboard camera while avoiding collision with obstacles. The optimal-trajectory generation was developed as a mixed-integer programming problem. The same method was used to recognize the wheelchair. In this regard, the optimal-trajectory generation problem was solved at each time step using model predictive control, and the first element of the optimal input was applied. The MATLAB optimization toolbox was used to solve this problem. As a result, the drone could avoid obstacles while recognizing the wheelchair that moved to the target trajectory considering the signals transmitted by the drone.
We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent...
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We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts, and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality and a sufficient condition for the global validity of classical cuts after branching has occurred are derived.
The paper presents a new approach for planning high voltage transmission networks. The developed simulation model takes into account the capital investment cost in its discrete form as well as the cost of transmission...
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The paper presents a new approach for planning high voltage transmission networks. The developed simulation model takes into account the capital investment cost in its discrete form as well as the cost of transmission losses. The constraint equations include the DC load flow equations and line loading constraints. The voltage loop equations are written in a modified form, such that a closed-loop equation will be ineffective if any line of this loop is deleted. The simulation model utilises the mixed-integer linear programming technique to obtain the least-cost network satisfying line loading constraints. Verification of the method is made through a test example.
A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programmi...
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A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programming method combined with an expert system is proposed to achieve these requirements. The proposed expert system helps the system planning engineers to allocate an appropriate initial feasible solution, and to decide the position of transformer tap settings as well as the number of capacitor units. From three solution stages using the linear programming approach, the expert system approach, and the mixed-integer programming approach, the discrete VAR optimization problem is promptly solved. Numerical simulations of a small-scale system and a practical system are demonstrated with significant results. The results demonstrate the effectiveness and improvement of the proposed method to solve the VAR optimization problem in a power distribution system.
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