Development of Hybrid Inexact Optimization Models for Water Quality Management under Uncertainty

Abstract

Water quality management (WQM) significantly affects water use and ecosystem health, which is helpful for achieving sustainability in environmental and economic aspects. However, the implementation of water quality management is still challenging in practice due to the uncertainty and nonlinearity existing in water systems, as well as the difficulty of the integration of simulation and optimization analyses. Therefore, effective optimization frameworks for handling nonlinearity, various uncertainties, and integrated complex water quality simulation models are highly desired. This dissertation tries to address such challenges by proposing new efficient hybrid inexact optimization models for water quality management under uncertainty through: i) developing an interval quadratic programming (IQP) model for handling both nonlinearity and uncertainty expressed as intervals for water quality management, and solving the developed model by three algorithms to compare and investigate the most effective and straightforward solution algorithm for IQP-WQM problems; ii) developing a simulation-based interval chance-constrained quadratic programming model, which is able to deal with nonlinearity and uncertainties with multiple formats, and implementing a real-world case study of phosphorus control in the central Grand River, Ontario, Canada; iii) proposing a data-driven interval credibility constrained quadratic programming model for water quality management by utilizing a data-driven surrogate model (i.e., inexact linear regression) to incorporate a complex water quality simulation model with the optimization framework to overcome challenges from the integrated simulation-optimization. The performance of the proposed frameworks/models was tested by different case studies and various mathematical techniques (e.g., sensitivity analysis). The results indicate the proposed models are capable of dealing with nonlinearity and various uncertainties, and significantly reducing the computational burden from simulation-optimization analysis. Coupling such efforts in developing efficient hybrid inexact optimization models for water quality management under uncertainty can provide useful tools to solve large-scale complex water quality management problems in a robust manner, and further provide reliable and effective decision supports for water quality planning and management.