Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become mo...
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Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident and multiple works in recent years have focused on this task. In this work, using a unified framework, we show that there exists a polyhedron that simultaneously encodes, in its facial structure, all possible deep neural network training problems that can arise from a given architecture, activation functions, loss function, and sample size. Notably, the size of the polyhedral representation depends only linearly on the sample size, and a better dependency on several other network parameters is unlikely. Using this general result, we compute the size of the polyhedral encoding for commonly used neural network architectures. Our results provide a new perspective on training problems through the lens of polyhedral theory and reveal strong structure arising from these problems. & COPY;2023 Elsevier B.V. All rights reserved.
The goal of this article is to establish a methodology for ordering of single-valued neutrosophic numbers (SVN-numbers) on the basis of values and ambiguities. First of all, the idea of neutrosophic numbers is discuss...
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Land use configuration in any given landscape is the result of a multi-objective optimization process, which takes into account different ecological, economic, and social factors. In this process, coordinating stakeho...
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Land use configuration in any given landscape is the result of a multi-objective optimization process, which takes into account different ecological, economic, and social factors. In this process, coordinating stakeholders is a key factor to successful spatial land use optimization. Stakeholders need to be modeled as players who have the ability to interact with each other towards their best solution, while considering multiple goals and constraints at the same time. Game theory provides a tool for land use planners to model and analyze such interactions. In order to apply the spatial allocation model and address stakeholder conflicts, an integrated model based on linear programming and game theory was designed in this study. For implementing such model, we conducted an optimal land use allocation process through multi-objective land allocation (MOLA) and linear programming methods. Then, two groups of environmental and land development players were considered to implement the optimization model. The game algorithm was used to select the appropriate constraint so that the result would be acceptable to all stakeholders. The results showed that during the third round of the game, the decision-making process and the optimization of land uses reached the desired Nash Equilibrium state and the conflict between stakeholders was resolved. Ultimately, in order to localize the results, a suitable solution was presented in a GIS environment.
This paper presents the impact of uncoordinated and coordinated charging management of electric vehicles (EVs) on the loading capability of major distribution system equipment, voltage quality, and energy loss in a di...
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This paper presents the impact of uncoordinated and coordinated charging management of electric vehicles (EVs) on the loading capability of major distribution system equipment, voltage quality, and energy loss in a distribution system. The main emphasis is given to the overloading of distribution transformers, primary feeders, and a substation transformer. The voltage quality of load points along the feeders and the system energy loss are also underlined. The load profile for uncoordinated EV charging is simulated by a Monte Carlo method with several deterministic and stochastic variables involved. To mitigate the overloading of the system components, a coordinated charging (also known as smart charging) model formulated as a linear programming problem is proposed with the objective of maximizing the total amount of energy consumption by EVs and the sum of all individual final states of charge (SoCs), and minimizing the sum of the absolute deviation of individual SoCs from the overall average SoC. The optimization problem is subject to equipment capability loading and planning criteria constraints with low, medium, and high EV penetration levels. The voltage quality problem and energy loss are also analyzed by an unbalanced three-phased power flow model. A case study of a real and practical 115/22 kV distribution system of the Provincial Electricity Authority (PEA) with a 50 MVA substation transformer, 5 feeders, and 732 distribution transformers shows that the possibility of overloaded system components, voltage drops along the feeders, and the system energy loss can be identified in the uncoordinated charging scenario and offer the readiness for equipment replacement and network reinforcement planning. The proposed smart charging model allows the distribution system to accommodate more EVs by appropriately managing the power and the start times of charging for the individual EVs over the timeslots of a day. The study results confirm no violation of the system comp
Given two stable matchings in a many-to-one matching market with q-responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least ...
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Given two stable matchings in a many-to-one matching market with q-responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.
If excess generation caused by increasing of photovoltaic and wind power generation plants is foreseen in a power system, the generation outputs of those plants are curtailed as a last resort in order to maintain the ...
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Background: Lack of dietary diversity in complementary feeding contributes to nutrient gaps leading to undernutrition. Food-based strategies have been successfully used to enrich the complementary diets of infants and...
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Background: Lack of dietary diversity in complementary feeding contributes to nutrient gaps leading to undernutrition. Food-based strategies have been successfully used to enrich the complementary diets of infants and young children. However, context-specific recommendations based on an objective diet optimization is needed to formulate sound and practical nutritional guidelines. Objectives: The present study aimed to identify problem nutrients in complementary diets and formulate complementary feeding recommendations (CFRs) using linear programming analysis for children aged 6 to 23 months in the rural Philippines. Methods: A cross-sectional survey was conducted in the municipality of Mercedes, Philippines. Dietary intakes of breastfed children 6 to 8, 9 to 11, and 12 to 23 months of age (n = 297) were assessed using a multipass 24-hour recall method with 7-day food consumption frequency. A linear programming tool was used to identify the recommended nutrient intakes that could not be met within the existing local food patterns and develop CFRs that would best fulfil nutrient adequacy for 11 modelled micronutrients. Results: Problem nutrients in the current diets were iron and calcium in any age-group, zinc for 6 to 8 and 9 to 11 months old, and thiamine and folate for 12 to 23 months old children. Adoption of CFRs with 4 to 5 food groups in the diet would ensure the adequacy of 7 to 8 nutrients, depending on the age-group. Conclusion: Within the boundaries of local dietary patterns, adequacy for most nutrients could be achieved by promoting realistic servings of nutrient-dense foods and food groups. The linear programming results provide an evidence-based strategy in designing interventions to improve the quality of Filipino complementary diets.
This paper discusses a model that can optimize plant operation by considering transportation cost and metallurgical assays. All boundary conditions were set using ore samples taken from different locations in the same...
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This paper discusses a model that can optimize plant operation by considering transportation cost and metallurgical assays. All boundary conditions were set using ore samples taken from different locations in the same mine. Transportation from the mine to milling plants, dumping areas, and leaching units is also analyzed. Transportation from the mill to the smelter depends on assay results to ensure market readiness. We hypothesize that the grade of the material varies according to its source because milling plants are built to process different types of ore. Mines and processing units may be far apart, and therefore, it is critical to optimize production. Previous studies have discussed mine production optimization but did not consider metallurgical plants. The proposed model merges all units of a production system to determine the optimal planning solution. linear programming uses network formulations of planning problems to consider a combination of mining and metallurgy operations. This technology is useful for analyzing the combination of two major systems, and hence, the dual theory was used in formulating the problem. The final model was applied to minimize the costs of production and distribution. The study checked the optimality of the solution for accuracy and its use as an indicator for long-term planning.
The hybridization of energy systems is based on the combined integration of both renewable and non-renewable technologies and thermal energy storage. These hybrid installations improve cost effectiveness and energy ef...
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The hybridization of energy systems is based on the combined integration of both renewable and non-renewable technologies and thermal energy storage. These hybrid installations improve cost effectiveness and energy efficiency when they are correctly designed and the operation strategy is suitable. Despite the relevance of achieving the optimal configuration, sizing and control strategy of hybrid thermal systems, there is no simple and generic methodology which allows this type of installations to be optimized in the project phase. In response to this issue, in this work, a mixed integer linear programming-based simple model is carried out with the aim of obtaining the optimal design, sizing and operation of thermal energy systems in residential buildings. To do so, a superstructure is defined that includes the main technologies commercialized for thermal energy systems in buildings. Technical, economic, environmental and legal constraints are determined in the proposed generic model. In order to validate the method, it is applied to a central space heating and domestic hot water installation of a residential building located in a cold climate in Spain. Optimal solutions are obtained considering three different perspectives -economic, environmental and multicriteria- and are compared to the current installation. According to the results, the overall cost of the economic optimal configuration is reduced by 15%, whereas the greenhouse gas emissions decrease by 56% in the environmental optimal solution. It is thus demonstrated that the proposed generic and simple model is a useful tool for determining the optimal hybridization of the plant and for analysing the technical, economic and environmental feasibility of these systems in the project phase.
Optimized allocation of water resources in relatively water-scarce areas is the basis for rational development and utilization of regional water resources and the fundamental guarantee for sus-tainable utilization of ...
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Optimized allocation of water resources in relatively water-scarce areas is the basis for rational development and utilization of regional water resources and the fundamental guarantee for sus-tainable utilization of water resources. In this paper, game theory and linear programming from the aspect of non-engineering measures are used to construct a cooperative game mode (maximizing economic benefits of urban agglomerations in the watershed) and a non-cooperative game mode (maximizing economic benefits of individual cities in the watershed), and it is concluded that the water consumption benefit of the cooperative game mode in the techno garden scenario (ratio-nality of urban agglomerations in the Jiulong River Watershed) is 64.442 billion yuan higher than that of the non-cooperative game (rationality of each city). Moreover, under this scenario, water resource allocation is optimized and the water quality is also significantly improved. Therefore, the cooperative game is the optimum model for the development of urban agglomerations in the watershed, and more attention should be paid to the comprehensive management of water resources, ecological resources, and human activities from the aspect of the river catchment areas given the particularity of water resources.
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