Shuffled Frog-Leaping Algorithm for Optimal Design of Open Channels

Abstract

Open channels are important water structures for irrigation, water supply, power generation, and drainage. The primary concern of designing a channel is to determine optimum dimensions while minimizing construction costs. In this paper, a memetic metaheuristic algorithms called “shuffled frog-leaping algorithm” (SFLA) is used to optimize sampling design variables of composite open channels. The results of optimization using SFLA and a generic language for interactive general optimization (LINGO) software are compared with other metaheuristic algorithms, such as genetic algorithm (GA), simulated annealing (SA), Lagrange multiplier method (LMM), ant colony optimization (ACO), improved ant colony optimization (IACO), and particle swarm optimization (PSO). Four common nonlinear models in open-channel designing are considered in this study: (1) model I (M1), which applies an equivalent roughness coefficient without any sectional division following the Manning equation; (2) model II (M2), which considers a variation of horizontal velocity over the cross section; (3) model III (M3), which determines minimum construction costs that is constrained on maximum permissible velocities corresponding to different lining materials of the composite channel cross section; and (4) model IV (M4), which imposes additional side-slope constraints over model II. Optimization results using SFLA and LINGO clearly show improvements in objective function in all the studied models. SFLA and LINGO show 14.93 and 12.64% improvement, respectively, in M1 compared to the LMM, GA, ACO, and IACO; 23.43 and 19.03% in M2 compared to GA, ACO, and IACO; 1.34 and 0.63% in M3 compared to GA and ACO; and 26.14 and 21.88% in M4 compared to GA and PSO. An improvement in the objective function is also obtained in SFLA over LINGO by 2.28, 4.40, 0.71, and 4.26%, respectively, in models M1 through M4. This result evidently demonstrates the efficiency of SFLA in optimizing composite open-channel design for increasing economic benefit.