Publicado

2017-01-01

A numerical solution for the air pollution control problem in 3D1

Una solución numérica del problema de control de contaminación de aire en 3D

Palabras clave:

Semi-infinite programming, stochastic programming, air pollution control, numerical solution, three-dimensional region (3D) (en)
Programación semi-infinita, programación estocástica, control de contaminación del aire, solución numérica, región tridimensional (3D) (es)

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This paper studies the minimization of the cost of an air pollution control problem in a three-dimensional region where there exists several sources of pollution. Since the control area has an infinite set of points, the proposed model was formulated using semi-infinite programming (SIP). The problem was solved by using a version of Volkov–Zavriev’s (1997) stochastic outer approximations method, which consists of an active search for relevant constraints based in quasi-optimal functions. The concentration of the contaminant at each point in the region is obtained from a Gaussian model. Three cases were analyzed taking into account the Colombian standard for sulfur dioxide. The hypothesis that polluting sources should not be established within cities was supported. Lastly, results indicate that solutions that cost the least allow the harmful effects caused by sources in a control area to be estimated.
Este trabajo estudia la minimización del costo del problema de control de contaminación del aire, en una región tridimensional donde existen varias fuentes de contaminación. Dado que el área de control tiene un conjunto infinito de puntos, el modelo propuesto ha sido formulado utilizando programación semi-infinita (SIP). El problema se resolvió utilizando una versión del método estocástico de aproximaciones externas creado por Volkov – Zavriev (1997), que consiste en una búsqueda activa de restricciones relevantes basada en funciones cuasi-óptimas. La concentración del contaminante en cada punto de la región se obtiene de un modelo gaussiano. Se analizaron tres casos teniendo en cuenta la norma colombiana para dióxido de azufre. La hipótesis de que fuentes contaminantes no se establezcan dentro de las ciudades fue apoyada. Por último, los resultados indican que las soluciones de mínimo costo permiten estimar los efectos perjudiciales causados por fuentes en una zona de control.

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