Artificial neural networks (ANNs) rely significantly on activation functions for optimal performance. Traditional activation functions such as ReLU and Sigmoid are commonly used. However, they have computational and h...
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This paper presents a Mixed-Integer Programming Model for the urban freight transport planning problem through the estimation of the Origin-Destination Matrix. The Origin-Destination Matrix is used to know the pattern...
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This paper presents a Mixed-Integer Programming Model for the urban freight transport planning problem through the estimation of the Origin-Destination Matrix. The Origin-Destination Matrix is used to know the pattern of travel or vehicle flow between different zones of a city and is estimated from the counting of vehicles on the routes of a road network. For the estimation of the Origin-Destination Matrix, the Entropy Maximization approach is applied. This approach is based on a non-linear optimization model. In order to overcome this difficulty, an optimization model based on the piecewise linear approximation method is proposed. To test the proposed model, an instance was built based on a road network of a real case. The proposed model obtained good results in a reduced computational time, demonstrating its usefulness for the urban freight transport planning.
Considering the increased interactions between power grids and natural gas grids, this study presents a chance-constrained maintenance scheduling model for integrated gas-electric grids with wind energy integration. G...
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Considering the increased interactions between power grids and natural gas grids, this study presents a chance-constrained maintenance scheduling model for integrated gas-electric grids with wind energy integration. Given the uncertainties of wind power, the loss of wind power probability is modelled as a chance constraint, ensuring the high utilisation of wind power. To overcome the adversities caused by the non-linear and non-convex models of natural gas systems, a piecewise linear approximation method is employed to transform the non-linear models into a group of mixed integer linear models. A big-M formulation method is used to construct inequality constraints for lines/pipelines to be under maintenance. In addition, unit commitment is also coordinated to achieve the best maintenance strategies. The proposed chance-constrained stochastic programming model is converted into an equivalent deterministic programming model via a strong extended formulation for the sample average approximation by leveraging the star-inequalities. Several tests on a four-node natural gas system with a six-bus power system and a 20-node natural gas system with a modified IEEE 118-bus power system demonstrate the effectiveness of the proposed model.
The system of interconnected energy hubs (EHs) is a key multi-carrier energy system (MES) model. It is difficult, however, to directly calculate the operational state of the model because of its highly dimensional non...
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The system of interconnected energy hubs (EHs) is a key multi-carrier energy system (MES) model. It is difficult, however, to directly calculate the operational state of the model because of its highly dimensional nonlinear characteristics. To resolve the foregoing problem, a standardised modelling and optimisation method for the system of interconnected EH model is introduced in this paper. In this proposed method, one-dimensional and multi-dimensional piecewise linear approximation methods are adopted to simplify non-convex natural gas transmission functions, generator cost functions, and compressor function. Moreover, a multi-step linearisation method is applied to EHs. The whole system can accordingly be reformulated as a mixed-integer linear programming (MILP) problem. In contrast to the traditional model, the formulated MILP model is effortlessly implemented in the optimisation of the MES with existing advanced optimisation techniques. Finally, the method is verified using a modified three-hub interconnected system. The test results show that the method can save more than 90% computational time with sufficient accuracy. The results also demonstrate that the unified dispatch exploits different energy resources, and the applied energy storage devices can reduce the operational cost from $319,840.267 to $316,382.685.
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