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Network optimization model approach to the volume-to-point heat conduction problem
Network optimization model approach to the volume-to-point... R. P. M. Ferreira et al.
This paper gives the classical volume-to-point heat conduction optimization problem a fresh model and formulation. The new volume-to-point problem model is a minimization problem, whereas the original model is a minimax problem. We establish that both problems have the same solution. The new formulation optimizes the volume and distribution of high-conductive materials while solving the heat flow equations and respecting a maximum temperature constraint. It was inspired by direct methods in optimal control problems. The problem is formulated as a mathematical programming problem, a network optimization problem, and it can be solved using off-the-shelf nonlinear optimization solvers. The new network design formulation is versatile and efficient as it can solve different problems fast and with good results. Numerical experiments show that the obtained solutions with the new formulation are competitive with state-of-the-art literature solutions, which were obtained using heuristics or computationally expensive methods.
Network optimization model approach to the volume-to-point heat conduction problem
Network optimization model approach to the volume-to-point... R. P. M. Ferreira et al.
This paper gives the classical volume-to-point heat conduction optimization problem a fresh model and formulation. The new volume-to-point problem model is a minimization problem, whereas the original model is a minimax problem. We establish that both problems have the same solution. The new formulation optimizes the volume and distribution of high-conductive materials while solving the heat flow equations and respecting a maximum temperature constraint. It was inspired by direct methods in optimal control problems. The problem is formulated as a mathematical programming problem, a network optimization problem, and it can be solved using off-the-shelf nonlinear optimization solvers. The new network design formulation is versatile and efficient as it can solve different problems fast and with good results. Numerical experiments show that the obtained solutions with the new formulation are competitive with state-of-the-art literature solutions, which were obtained using heuristics or computationally expensive methods.
Network optimization model approach to the volume-to-point heat conduction problem
Network optimization model approach to the volume-to-point... R. P. M. Ferreira et al.
Optim Eng
Ferreira, Ricardo Poley Martins (author) / de Freitas Pinto, Ricardo Luiz Utsch (author) / Mahey, Philippe (author)
Optimization and Engineering ; 26 ; 229-251
2025-03-01
23 pages
Article (Journal)
Electronic Resource
English
Network flow optimization , Volume-to-point problem , Heat transfer , Minimization problem Mathematical Sciences , Applied Mathematics , Numerical and Computational Mathematics , Mathematics , Optimization , Engineering, general , Systems Theory, Control , Environmental Management , Operations Research/Decision Theory , Financial Engineering , Mathematics and Statistics
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