Mixed-Integer Nonlinear Programming for Resilient Water Network Design
Published on 11. May 2022
Book
Paperback/Softback
153 pages
978-3-8439-5048-0 (ISBN)
Description
This dissertation investigates the handling of uncertainty in technical systems. The focus is the formulation of complex technical systems as mixed-integer nonlinear models and their optimization with regards to investment and operational cost.
Uncertainty is introduced by the explicit consideration of component failures. The optimized (resilient) system has to tolerate a given number of these failures. We thus combine mixed-integer nonlinear optimization with a discrete uncertainty set to form a special robust optimization problem. This problem can be understood as a nested optimization game between two antagonists with three levels. The designer plans in the upper level the topology of the system and wants to minimize costs, while an antagonist chooses the worst possible failure for this system in the second level. In a third level the designer can react to these influences, e.g., by controlling pumps in a water network appropriately.
In order to investigate resilient structure in more detail, this dissertation investigates the exemplary optimization of a high-rise water supply system and a solution algorithm is developed. Based on these considerations a general three-level formulation is analyzed and a solution algorithm by means of a nested decomposition is designed. Several applications can be solved with our implementation. However, for the success of our approach it is necessary, that the reaction of the constructor to the disruptions can be quickly computed. Since this is done by solving mixed-integer nonlinear problems, we also consider the relation between so called indicator variables with nonlinear functions. We derive several valid inequalities, which can be added to the problem formulations, in order to improve the solving speed for our main application, the design of resilient water networks.
Uncertainty is introduced by the explicit consideration of component failures. The optimized (resilient) system has to tolerate a given number of these failures. We thus combine mixed-integer nonlinear optimization with a discrete uncertainty set to form a special robust optimization problem. This problem can be understood as a nested optimization game between two antagonists with three levels. The designer plans in the upper level the topology of the system and wants to minimize costs, while an antagonist chooses the worst possible failure for this system in the second level. In a third level the designer can react to these influences, e.g., by controlling pumps in a water network appropriately.
In order to investigate resilient structure in more detail, this dissertation investigates the exemplary optimization of a high-rise water supply system and a solution algorithm is developed. Based on these considerations a general three-level formulation is analyzed and a solution algorithm by means of a nested decomposition is designed. Several applications can be solved with our implementation. However, for the success of our approach it is necessary, that the reaction of the constructor to the disruptions can be quickly computed. Since this is done by solving mixed-integer nonlinear problems, we also consider the relation between so called indicator variables with nonlinear functions. We derive several valid inequalities, which can be added to the problem formulations, in order to improve the solving speed for our main application, the design of resilient water networks.