Orthogonal Design-Based NSGA-III for the Optimal Lockage Co-Scheduling Problem

Abstract

Lockage co-scheduling of Three Gorges Dam and Gezhou Dam (LCSTD) is a mixed-integer nonlinear optimization (MINO) problem. This paper establishes a multi-objective MINO model for the LCSTD problem, in which two criteria reflecting the interests of shippers on the one side and owners of the lock on the other side are considered as two parallel optimization objectives. The LCSTD problem is separated into three sub-problems. The first sub-problem concerns the lockage number and lockage direction determination, while the second and third sub-problems refer to lockage time optimization and ship placement, respectively. An orthogonal design-based non-dominated sorting genetic algorithm III (ONSGA-III) is presented, and then, we combine the ONSGA-III with a time-area series assignment method to optimize the LCSTD problem. Meanwhile, a heuristic adjustment strategy is proposed according to the structure of the lockage time optimization sub-problem to enhance the exploration ability of ONSGA-III. Furthermore, a compromise solution is chosen from the achieved non-dominated Pareto solutions by utilizing a membership function. Finally, the method is tested on the instances, which are extracted from historical data at Three Gorges Dam and Gezhouba Dam. The Pareto solutions achieved by the proposed method are compared with those of other methods. The simulation results demonstrate that the proposed method is efficient for solving the LCSTD problem.