2024-07-12 –, While Loop (4.2)
A multi-objective stochastic optimization approach for sizing the storage of a rainwater harvesting system is presented, considering climate and demand uncertainty. The aim is to maximize system efficiency and minimize cost while satisfying all flow equations, besides incorporating a risk measure to hedge against dry years and high demand. Julia's JuMP and MultiObjectiveAlgorithms packages are used for modeling and solving the problem. The model is verified by data from a garden in Amsterdam.
The optimal design of rainwater harvesting systems requires sizing storage and catchment areas to optimize cost, self-sufficiency, and water quality indicators under climate and demand uncertainty.
In this work, we formulate and solve a multi-objective stochastic optimization problem that allows for explicit trade-off under uncertainty, maximizing system efficiency and minimizing deployment cost, which includes required materials and construction. For this, we use the yield after spillage (YAS) concept to incorporate the physical and operational constraints and the big-M method to reformulate the nonlinear min\max rules of this approach as a mixed-integer linear programming (MILP) problem.
After that, two sources of uncertainty, including water demand and amount of rainfall, are considered, and the problem is formulated as a stochastic programming. In addition, utilization of the conditional value at risk measure allows for the consideration of risk. It guarantees the designer against the highest demand and driest weather conditions. The problem optimizes the efficiency and cost over demand and rainfall scenarios. The JuMP package is used for modeling the resulting stochastic multi-objective quadratic constraint MILP problem. Also, the Gurobi solver and the MultiObjectiveAlgorithms package are utilized to solve this problem. The results are verified with historical data from a botanical garden as a case study in Amsterdam.
