abstract
- © ICIC International 2021.This project aims to model the wastewater regulation problem as a bilevel optimization problem. Due to human activities such as industry, agriculture, and domes-tic use, many bodies of water have been affected by pollution. To remedy the problem of water quality Environmental Protection Agencies use environmental penalty functions. This enforces managers of wastewater treatment plants to find treatment strategies that meet water quality standards before discharging pollution to the environment. In the case of shallow bodies of water, the behavior of the wastewater dispersion is governed by the Navier-Stokes equation; therefore, the objective functions of the decision-makers have a nonlinear behavior relative to a leader-follower dynamic. To find the optimal penalty func-tion we construct the emission concentration system solution and define the wastewater regulation problem as a bilevel optimization problem. The aim of this paper is three-fold: First, it formulates the wastewater regulation problem as a bilevel optimization problem; second, it provides theoretical insight when the problem is reformulated to a single-level formulation using a Karush-Kuhn-Tucker condition approach; third, it devel-ops discretization techniques that allow finding numerical solutions of the location of the wastewater regulation problem.