nonlinear programming

The objective of this research was to save water resources, using nonlinear programming model to optimize the crop pattern under full and deficit irrigation techniques in eight observation fields for eleven predominant irrigated crops, including winter wheat, barley, rapeseed, autumn sugar beet, corn, sorghum, tomato, onion and potatoes, bean and autumn watermelon in the downstream lands of Doyraj Dehloran reservoir located in the southwest of Iran. The yield reduction and net income of each crop were calculated for 50, 60, 70, 80, 90 and 100% of water requirements during the growing season. The objective function for maximizing net profit with different constraints including constant cultivated area was determined for the existing cropping pattern, the policies of the Ministry of Agriculture Jihad and the proposed pattern. In the case of full irrigation, the results showed that the net profit of the Ministry of Agriculture Jihad cropping pattern was increased 1.33, 1.19 and 1.05% for 100, 90 and 80% of water requirement, respectively. Under deficit irrigation conditions (90 and 80%), water resources are saved 18 and 34%, respectively. The proposed cropping pattern, including four crops of wheat, canola, autumn sugar beet and grain corn increased the net profit of 60, 70, 80 and 90% of the crop water requirement treatments by 14.4, 33.6, 54 and 74.7%, respectively, as compared to the existing cropping pattern. In the proposed deficit irrigation treatments, the water resources were saved 60%, 49%, 35% and 19%, respectively. The results of nonlinear programing model showed that the optimization of cropping pattern with deficit irrigation technique, not only increases the net profits, but also it can be effective in conserving surface and ground water resources.

Earth dams as controlling structures of surface flows and floods, must can store the water and prevent of water infiltration from their bodies and resist against forces. Important problem in designing earth dams that constructed with available materials, is determination of design that have expected performance with adequate safety and minimum cost. Because investigating and analyzing all possible options for determination best design requires to spend many of time and cost, designing the earth dams can be formulated as optimization problem. In this study, nonlinear programming model has been presented for designing earth dams optimally with the aim of minimizing the section area of dam (volume of materials that consumed in the dam length unit). Optimization was performed by applying constraints that ensure the safety of slopes that mathematical equations for approximation the values of factors of safety of slopes are defined as the new regression equations. . In order to find the optimal solution, shuffled complex evolution (SCE) algorithm was developed by programming. In addition to previous optimization, design variables were optimized using LINGO software. Then initial design of Barzok earth dam has been presented and performance of the proposed model in optimal designing of earth dams has been studied. Result showed that optimization methods used in this study present same estimation of optimal solution and obtained results from running the SCE optimization model and LINGO model showed that these two optimization methods in the optimization of dam section have same performance. The value of minimum objective function that's mean area of Barzok dam section was determined equal to 2725.3 m2 that in primary design, area of dam section is equal to 4400.7 m2. Therefore dam volume %38 has been reduced that is significant value.

Seydan-Farough plain is one of the Marvdasht ''s plains. The area of the considered plain is 369 kilometer on square that 204kilometer on squareof that consist of height and 165 kilometer on squareplain. In this study، nonlinear mathematical programming approach was applied for determination of optimal depth of agricultural wells with objectives of decreasing excavation and pumping costs determination optimal depth of wells. To determine the optimum depth of excavation wells it was assumed thatfarmers to achieve the first discharge In the absence of the aquifer water balance allow re-drilling wells and withdrawal of water. Bottom of the wells to break tackles. Data was collected from 1640 agricultural wells in Seydan-Farough plain. and was analized with GAMS software. The results showed that lifting water from wells is justified with excavation of wells to the altitude 138 meters. Well discharge and pump altitude was quantified respectively 9/81 liter on second and 112/32 meters with excavation of well to until depth of 138 meters. However، optimal cultivation under area determinate for each crop with objective attaining to water required in agricultural due excavation of present wells. At the end optimized consumption management and illegal well exploitation preventing is suggested

Development of precise and simple methods in flood simulation has greatly reduced financial damage and life loss. Various methods and procedures have been implemented based on Saint-Venant''s one-dimensional equation governing unsteady flows. To simplify the solution for these flows، analytical and numerical methods have been used. In the present study، a new method that provides the optimal outcome is introduced using non-linear programming. Penalty function has also been used to convert nonlinear programming (NLP) constrained problems into unconstrained optimal issues. To verify the accuracy of decision variables، the study covered 60 cross-sections of Gharasu River and 25-year flood hydrographs. After determining the model correctness، the 50 and 100-year flood hydrograph were routed in 18 Kilometers. The results were statistically compared with hydraulic and Muskingum hydrological methods. To sum up; the routed hydrographs introduced by NLP method were very close to the hydrographs produced by dynamic wave method. The R2 of calculated discharge of routed hydrograph by NLP and dynamic wave method were 0. 948، 0. 990، and 0. 989، respectively، with the return period of 25، 50 and 100-year flood being 0. 989. It can be concluded that NLP method is more accurate than Muskingum method، especially when predicting the peak discharge of flood hydrograph.

Pumps are among the early instruments invented by humans to be taken advantage of in the use of water utilities. Design and operation problem of pumping stations is a type of mixed integer non linear programming, in which gradient based optimization methods are not efficient for solving complex problems of this type. In this regard, such evolutionary optimization algorithms as genetic algorithm (GA) have been employed in many scientific fields of application and specially design-operation of pumping stations as a search and optimization tool. Apart from all the capabilities and advantags of such algorithms, they need a large amount of execution time as well as converging to the near optimal solutions, which are considered as some of these method's disadvantages. This paper addresses the optimal design and operation of a pumping station system using a hybrid method for optimization consists of nonlinear programming (NLP) method and GA (NLP-GA). After evaluating the developed hybrid model in a test example mathematical problem, it has been applied and examined in a real world design-operation optimization problem. Then, the results of the NLP-GA algorithm are compared with those of three other methods for the same problem, such as GA, honey-bee mating optimization (HBMO) algorithm, NLP and the Lagrange multipliers (LM) method. The results show that the hybrid NLP-GA performers better results and faster convergence in terms of number of function evaluations toward the optimal solution than those of other methods.