Optimization model and algorithm of rotation irrigation group for drip irrigation

Abstract: A rotation irrigation is normally implemented in water-shortage regions, such as Xinjiang area of western China with widespread drip irrigation. Nevertheless, the conventional rotation irrigation group is generally divided into the fixed districts in the manual calculation. A better solution is thus highly demanding in this inefficient calculation. The rotation irrigation group is also representing the prominent regional and hydraulic characteristics in recent years. Therefore, it is necessary to clarify how to divide the rotation irrigation group in practice. Furthermore, the operation of the irrigation system needs to gradually complete the whole plot irrigation under the turn-on and turn-off valve sequence of several branch pipes in a rotation irrigation group. Correspondingly, there is a relatively high labor intensity in the operational mode, but with low investment cost, simple maintenance, and wide popularization, compared with the automatic operation of drip irrigation. In this study, a hybrid mathematical model was proposed to explore a better solution using the flow balance and structural constraints in the technical standards and division principles. Neighborhood characteristics were determined from the spatial distribution of branch pipes in the rotation irrigation group. The neighborhood search strategy and the repair of infeasible solution were given in the radius threshold range, further to find the critical path of the maximum extent. Four algorithms were selected to solve the model separately, including the Genetic Algorithm (GA), Greedy-GA, Tyson polygon-GA (Voronoi-GA), and Grid GA. The GA adopted the branch pipe model of actual number coding. The chromosome coding indicated that the branch pipe was opened in that group. The initial population was constructed using the Random, Greedy, Voronoi polygon, and Grid. The spatial distribution of branch pipe was applied in the neighborhood search strategy, further to serve as the structural feature in the rotation irrigation group. A uniform crossover strategy was adopted for the crossover and mutation of the offspring population. A competitive and elite retention strategy was adopted for the selection mechanism. Furthermore, the neighborhood structure represented the use of characteristic information. In the case of the rotation irrigation group, the spatial distribution of branch pipes presented critical structural characteristics. The specific search procedure was: first to establish the adjacency matrix of branch pipe, then to generate the reachable matrix using the Warshall, finally to calculate the critical path set for each valve, thereby converting the code. In a matrix form, the fundamental and non-key matrix was generated using a reachable matrix. Then the temporary path set was calculated and sorted to compare the valves in the non-critical matrix row for the standard deviation index. Feasible solutions were selected to update the matrix using four indicators from standard deviation, path length, connectivity, and running time. Furthermore, an optimal combination was achieved, where the mean flow rate in the rotation irrigation group was 260.06 m3/h, the standard deviation was 10.9 m3/h, the path length was 7 342.6 m, the mean path length was 8 105.2m, the mean path length within the group was 386.4 m, and the mean connectivity was 22. The neighborhood search strategy of the critical path was adopted to balance the distribution of branch pipes under the condition of objective function, suitable for daily management and maintenance. The Grid-GA and repair presented an excellent performance on the rotation operating group in a grip irrigation, particularly without the dimensional disaster in the multi-dimensional combination. Consequently, the hybrid optimal model and algorithm here can meet the hydraulic calculation and engineering requirements in modern agriculture.