Minimizing the cost of a curved corner trapezoidal canal section

Abstract

Designing a curved corner trapezoidal channel section with a minimal cost, which is the study's objective function, encloses minimizing the channel lining and excavation costs. The discharge, as the prime constraint, and the permissible velocities, as subsidiary constraints were considered to solve the problem. Mathematical optimization was used to obtain the optimum canal dimensions. The results were represented in charts form, to facilitate easy design of the optimal channel dimensions with minimum cost. To demonstrate the practicability of the proposed method, a design example has been included. A comparison between the parameters and the cost of the proposed section with the conventional trapezoidal section revealed that, the proposed section is more economic, and more suitable from a maintenance point of view. At last, sensitivity analysis was derived to show the effect of changing the canal dimensions on the cost.

Design of subsurface drainage network with minimum overall cost using Lagrange multiplier optimization

“…As a result, the Lagrange multiplier method is frequently employed to resolve difficult constrained optimization problems. The Karush-Kuhn-Tucker conditions, which can additionally take into consideration inequality constraints of the form h x ð Þ ≤ c for a given constant c, further broaden the method of Lagrange multipliers (Fattouh & Saad, 2021). The design charts are valid for the old lands of the Nile delta and are suitable for any other region with similar agrosystems in terms of soil characteristics, irrigation methods, crop patterns, climate regimes, etc.…”