We present optimization methods for predictive maintenance scheduling of building heating, ventilation, and air conditioning (HVAC) systems via mixed-integer programming. The optimization framework we introduce is com...
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We present optimization methods for predictive maintenance scheduling of building heating, ventilation, and air conditioning (HVAC) systems via mixed-integer programming. The optimization framework we introduce is composed of optimization models and parameter generation methods. Optimization models with time discretized into daily time periods are developed to enable the consideration of slow operation-dependent degradation during long horizons while maintaining computational efficiency. To improve the quality of the obtained maintenance schedules, system operation is simultaneously optimized. Parameter generation methods are introduced to provide parameters for constructing operation-related constraints. The proposed optimization framework can account for various HVAC systems with complex configurations. We show the quality of the generated operation-related parameters, and we provide medium-horizon case studies of central plants to show the model performance. (C) 2020 Elsevier B.V. All rights reserved.
Boolean quadratic optimization problems occur in a number of applications. Their mixedinteger-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxation...
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Boolean quadratic optimization problems occur in a number of applications. Their mixedinteger-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR’s) are proposed in the literature to approximate the solution, which recasts the problem into convex optimization. Nevertheless, SDR’s do not guarantee the extraction of the correct binary minimizer. In this paper, we present a novel approach to enhance the binary solution recovery. The key of the proposed method is the exploitation of known information on the eigenvalues of the desired solution. As the proposed approach yields a non-convex program, we develop and analyze an iterative descent strategy, whose practical effectiveness is shown via numerical results.
The problem of locating telephone exchanges in urban area is a basic problem in the telecommunication system planning. Usually, the mathematical models applied fail in representing the realistic aspects of such proble...
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The problem of locating telephone exchanges in urban area is a basic problem in the telecommunication system planning. Usually, the mathematical models applied fail in representing the realistic aspects of such problem and heuristic techniques should be used to solve it. The classical representation of the urban telephone network is done by dividing the urban area in squares which occasionally causes errors in regions of great and small subscribers density. In our paper, the telephone network is represented through an oriented graph which allows us to formulate the location problem as a mixed (real and zero-one variables) mathematical programming problem. With this approach the problem can be solved by an exact optimization technique. The optimization method used is the Benders' decomposition which divides the mixed problem and works with the real-variable and zero-one problems separately. The program provides the optimal locations of the new switching centers and its subscriber capacities, in the same way that it determines the possible expansions of the existent buildings. The serving areas of each exchange is also provided by the program. A procedure is presented which provides the construction chronogram of the exchanges during the planning period. The computer program is applied to a 700000 inhabitants brazilian city and results are discussed.
Designing stable embedded control systems presents challenges when limited communication and computation resources are involved. This document provides an approach to codesign a scheduler and a resilient controller fo...
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Designing stable embedded control systems presents challenges when limited communication and computation resources are involved. This document provides an approach to codesign a scheduler and a resilient controller for a given set of linear mixed-critical embedded control systems sharing a number of computation resources. Precisely, we are interested in optimizing control inputs and resource allocation in order to ensure control performance, resilience, and faster feedback control response for more critical tasks. The approach is based on a formulation of the problem in the form of a mixed-integer MPC problem. The latter is solved online and provide controllers with new updates, while the latest previous inputs are held constant otherwise. We demonstrate the validity of our approach on an illustrative example.
This paper presents an optimization based mathematical modelling approach for a single source single destination crude oil facility location transshipment problem. We began by formulating a mixed-integer nonlinear pro...
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This paper presents an optimization based mathematical modelling approach for a single source single destination crude oil facility location transshipment problem. We began by formulating a mixed-integer nonlinear programming model and use a rolling horizon heuristic to find an optimal location fora storage facility within a restricted continuous region. We next design a hybrid two-stage algorithm that combines judicious facility locations resulting from the proposed model into a previously developed column generation approach. The results indicate that improved overall operational costs can be achieved by strategically determining cost-effective locations of the transshipment facility.
We use model predictive control (MPC) for the optimal energy distribution in non-residential buildings. Our approach is special in that it treats thermal and electrical energy flows simultaneously. Our sample applicat...
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We use model predictive control (MPC) for the optimal energy distribution in non-residential buildings. Our approach is special in that it treats thermal and electrical energy flows simultaneously. Our sample application is a real office building, where components such as heat pumps and heating rods introduce discrete variables. This implies the optimal control problem that must be solved for MPC is a mixed-integer quadratic programming (MIQP) problem. Because both continuous and integer variables are involved, the computation times may become prohibitive for use in real-time. We explore a computationally efficient approximation that replaces integer variables by continuous variables for later time steps along the horizon. The performance of MPC using this method is investigated in simulations and the results are compared to those for the original MIQP problem and solution. Our method significantly reduces computational time while achieving a nearly optimal solution.
One of the key aspects of the Physical Internet (PI) is the use of standardized, modular containers that enable the coordination of shipments across the supply chain. However, a key open question is how will limiting ...
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One of the key aspects of the Physical Internet (PI) is the use of standardized, modular containers that enable the coordination of shipments across the supply chain. However, a key open question is how will limiting the choice of containers impact the amount of volume that is shipped? We present a mathematical model to determine that impact and report our results for data sets that are based on data from a consumer packaged goods company.
Since the farm financial crisis of the 1980s, Farm Credit System banks continue to merge and consolidate to enhance competitiveness. Two mixed-integer programming models of AgChoice Agricultural Credit Association (AC...
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Since the farm financial crisis of the 1980s, Farm Credit System banks continue to merge and consolidate to enhance competitiveness. Two mixed-integer programming models of AgChoice Agricultural Credit Association (ACA), a recently merged ACA in Pennsylvania, were developed to determine the optimal number, location, and territory of branches. The approach suggests useful information can be determined regarding the reconfiguration process after bank mergers, especially given the fact that the current AgChoice ACA configuration is available for comparison purposes.
Cyclic scheduling is of vital importance in a repetitive discrete manufacturing environment. We investigate scheduling in the context of general cyclic job shops with blocking where there are no intermediate buffers b...
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Cyclic scheduling is of vital importance in a repetitive discrete manufacturing environment. We investigate scheduling in the context of general cyclic job shops with blocking where there are no intermediate buffers between the machines. We also consider sequence-dependent setups (anticipatory and nonanticipatory), which commonly appear in different manufacturing environments. The choice of blocking condition, that is whether the sequence-dependent setups are anticipatory or not, significantly impacts the optimal schedules. We provide a novel mixed-integer programming (MIP) model for the above problem, namely blocking cyclic job-shop scheduling. Furthermore, we study the impact of sequence-dependent setups in this research. The problem is analysed in detail with respect to anticipatory and nonanticipatory setups and the efficiency of the proposed model is investigated via a computational study that is conducted on a set of randomly generated problem instances. The proposed MIP models are capable of solving small-to-medium-sized problems. Moreover, the analysis presented demonstrates that anticipatory setups directly affect blocking conditions, since intermediate buffers between the machines are not present. Hence, in systems with anticipatory setups, cycle times increase to a greater extent compared to systems with nonanticipatory setups.
The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real -world applications. Tree ensemble methods, such as Random Forests or XgBoost,...
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The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real -world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools for classification tasks. However, while combining multiple trees may provide higher prediction quality than a single one, it sacrifices the interpretability property resulting in "black -box" models. In light of this, we aim to develop an interpretable representation of a tree -ensemble model that can provide valuable insights into its behavior. First, given a target tree -ensemble model, we develop a hierarchical visualization tool based on a heatmap representation of the forest's feature use, considering the frequency of a feature and the level at which it is selected as an indicator of importance. Next, we propose a mixed -integer linear programming (MILP) formulation for constructing a single optimal multivariate tree that accurately mimics the target model predictions. The goal is to provide an interpretable surrogate model based on oblique hyperplane splits, which uses only the most relevant features according to the defined forest's importance indicators. The MILP model includes a penalty on feature selection based on their frequency in the forest to further induce sparsity of the splits. The natural formulation has been strengthened to improve the computational performance of mixed -integer software. Computational experience is carried out on benchmark datasets from the UCI repository using a state-of-the-art off -the -shelf solver. Results show that the proposed model is effective in yielding a shallow interpretable tree approximating the treeensemble decision function.
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