Nonlinear optimization of air pollution monitoring networks: Algorithmic considerations and computational results

For most of the history of environmental systems analysis, the ability to formulate large-scale environmental management models has generally outrun the ability to solve them. The authors refer here for the most part to nonlinear nonconvex and nondifferentiable models. The situation, however, seems to be changing rapidly. There now exists an impressive variety of general purpose nonlinear solvers and the computing hardware to make solution of such models practical. In that context then, the authors present a mathematical programming application involving the optimization of an air pollution monitoring network. The monitoring network model is nonlinear, nonconvex and nondifferentiable and requires in each objective function evaluation, the execution of a model to simulate pollutant concentrations in space; a routine to perform optimal interpolation (kriging) and interpolation error estimation; and adaptive quadrature procedures to integrate interpolation errors over space. The Hooke and Jeeves Discrete Step optimization algorithm is used to solve this model and was selected based upon three tests (involving a suite of trial problems) to evaluate its performance relative to seven line search and two other discrete step methods.