An application of interactive multi-criteria optimization to air pollution control

Abstract

In this paper a problem of air pollution control is studied, posing it as a multi-objective control problem of partial differential equations. The original problem, dealing with the optimal management of a set of industrial plants inside a populated area, is formulated by means of the diffusion transport equation, including a linear reaction term and source terms modelled by Dirac deltas. Introducing adjoint state techniques, the problem transforms into a problem of multi-objective optimization in Banach spaces, where the large number of objective functions discourages the complete search of its Pareto front. Therefore, in order to solve the problem, two interactive methods of multi-objective programming are proposed: the VIA and the STEM algorithms. Finally, the paper illustrates how to combine both algorithms to solve in a more effective way a realistic problem posed in the Metropolitan Area of Guadalajara (Mexico).

Keywords:

• interactive multi-objective programming
• multi-objective control of partial differential equations
• optimal control
• air pollution
• numerical simulation

AMS Subject Classifications:

• 90C29
• 90B50
• 49J20

Acknowledgements

This work was supported by Project MTM2012-30842 of M.E.C. (Spain) and FEDER. The second author also thanks the support from Sistema Nacional de Investigadores SNI-52768 and Programa de Mejoramiento del Profesorado PROMEP/103.5/13/6219 (Mexico).