A nonlinearity interval mapping scheme for efficient waste load allocation simulation‐optimization analysis

Applications using simulation‐optimization approaches are often limited in practice because of the high computational cost associated with executing the simulation‐optimization analysis. This research proposes a nonlinearity interval mapping scheme (NIMS) to overcome the computational barrier of applying the simulation‐optimization approach for a waste load allocation analysis. Unlike the traditional response surface methods that use response surface functions to approximate the functional form of the original simulation model, the NIMS approach involves mapping the nonlinear input‐output response relationship of a simulation model into an interval matrix, thereby converting the original simulation‐optimization model into an interval linear programming model. By using the risk explicit interval linear programming algorithm and an inverse mapping scheme to implicitly resolve nonlinearity in the interval linear programming model, the NIMS approach efficiently obtained near‐optimal solutions of the original simulation‐optimization problem. The NIMS approach was applied to a case study on Wissahickon Creek in Pennsylvania, with the objective of finding optimal carbonaceous biological oxygen demand and ammonia (NH 4 ) point source waste load allocations, subject to daily average and minimum dissolved oxygen compliance constraints at multiple points along the stream. First, a simulation‐optimization model was formulated for this case study. Next, a genetic algorithm was used to solve the problem to produce reference optimal solutions. Finally, the simulation‐optimization model was solved using the proposed NIMS, and the obtained solutions were compared with the reference solutions to demonstrate the superior computational efficiency and solution quality of the NIMS.