Non-probabilistic robust optimization approach for flood control system design

Flood risk management in floodplain systems is a long-standing problem in water resources management. Soft strategies such as land cover change are used to mitigate damages due to flooding. In this approach one chooses the best combination of land covers such that flood damage and the investment costs are minimized. Because of the uncertain nature of the problem, former studies addressed this problem by stochastic programming models which are found to be computationally expensive. In this work, a novel non-probabilistic robust counterpart approach is proposed in which the uncertainty of the rainfall events requires a new formulation and solution algorithms. Non-probabilistic methods, developed in the field of robust optimization were shown to have advantages over classical stochastic methods in several aspects such as: tractability, non-necessity of full probabilistic information, and the ability to integrate correlation of uncertain variables without adding complexity. However, unlike former studies in the field of robust optimization, the resulting optimization model in the flood risk management problem is nonlinear and discontinuous and leads to an intractable robust counterpart model. In this work, a novel iterative linearization scheme is proposed to effectively solve nonlinear robust counterpart models. This work demonstrates the tractability and applicability of non-probabilistic robust optimization to nonlinear problems similar to the flood risk management problem. The results show considerable promise of the robust counterpart approach in terms of showing the tradeoff between flood risk and cost in an efficient manner.