Use of Genetic Algorithm in Optimization of Irrigation Pumping Stations

Energy costs constitute the largest expenditure for nearly all water utilities worldwide and can consume up to 65% of a water utility’s annual operating budget. One of the greatest potential areas for energy cost savings is in the scheduling of pump operations. This paper presents a new management model, WAPIRRA Scheduler, for the optimal design and operation of water distribution systems. The model makes use of the latest advances in genetic algorithm (GA) optimization to automatically determine annually the least cost of pumping stations while satisfying target hydraulic performance requirements. Optimal design and operation refers to selecting pump type, capacity, and number of units as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a given set of demand curves. The optimization process consists of three main steps: (1) generating randomly an initial set of pump combinations to start the optimization process for a given demand-duration curve; (2) minimizing the total annual cost, which consists of operation and maintenance costs and depreciation cost of the initial investment, by changing the set and discharge of pump sets based on the provided model; and (3) achieving the final criterion to stop the optimization process and reporting the optimized results of the model. Computational analysis is based upon one major objective function and solving it by means of a computer program that is developed following the GA approach to find the optimized solution of generated equations. Application of the model to a real-world project shows considerable savings in cost and energy.     

Minimum Cost Irrigation Network Design Using Interactive Fuzzy Integer Programming

Minimum cost irrigation network design has been conventionally based on crisp pressure requirements at the hydrants of the network. In order to incorporate obscure knowledge on these pressure requirements at the design stage, an interactive fuzzy integer programming methodology is proposed. In the integer linear programming, formulation membership functions are adopted for expressing pressure constraints. Also, the interactive character of the proposed methodology enables the designer to select a less demanding range of pressures at some “critical” hydrants. By using the proposed methodology significant economic gains may be achieved reducing the cost of the network, since the energy line is adapted more satisfactorily to the ranging pressure requirements. Finally, an application of the methodology to an irrigation network is presented.     

Probability of Pressure Deficit in On-Demand Branched Networks and Incorporation into Design Decisions

This technical paper presents analytical expressions to estimate the probability function of head losses in any path of an on-demand branched irrigation network. They are developed for estimating the probability of pressure deficit of a given magnitude at any hydrant. They are also useful for examining the probability of a power deficit at a pumping station designed to guarantee service to a hydrant, as well as the head characteristic curve of the distribution system linked to a definite probability. All this quantified information is useful for decision making on network design and performance. The probabilities calculated with the developed expressions can be taken as complementary or alternative concepts to Clément’s classical design flow method, which is taken here as a benchmark for comparisons. Illustrative examples of network designs are presented to validate the proposed expressions. The least cost design solutions using Clément’s design flows are compared with design solutions here obtained to get the same probability of pressure deficit at the most unfavorable hydrants. The new solutions are less expensive because the flow constraint can be avoided.     

Assessing Pressure Changes in an On-Demand Water Distribution System on Drip Irrigation Performance—Case Study in Italy

The hydrant pressure head in an on-demand water distribution system can be subject to high fluctuation depending on the discharge flowing inside the pipes, with consequent impacts on the performance of on-farm irrigation systems. In this work, an Italian water distribution system was analyzed using the AKLA model at upstream discharges of 1,200 and 600?L?s?1 to estimate the range of hydrant pressure variation. A computer model was developed, calibrated, and used to evaluate the performance of a drip irrigation system by relating the on-farm network with the hydrant characteristic curve at a certain operating status. The flow regulator within the hydrant played an important role in stabilizing the performance of the network at hydrant pressures higher than 27 m. At lower hydrant pressures, to apply the same amount of water, irrigation time must be extended by 17 and 95% for pressure heads of 20 and 12 m, respectively. These approaches described have great utility to ensure adequate irrigation management when water is delivered by pressurized on-demand systems.     

Scheduling∕Cost Optimization and Neural Dynamics Model for Construction

A general mathematical formulation is presented for the scheduling of construction projects and is applied to the problem of highway construction scheduling. Repetitive and nonrepetitive tasks, work continuity constraints, multiple-crew strategies, and the effects of varying job conditions on the performance of a crew can be modeled. An optimization formulation is presented for the construction project scheduling problem, with the goal of minimizing the direct construction cost. The nonlinear optimization is then solved by the neural dynamics model developed recently by Adeli and Park. For any given construction duration, the model yields the optimum construction schedule for minimum construction cost automatically. By varying the construction duration, one can solve the cost-duration trade-off problem and obtain the global optimum schedule and the corresponding minimum construction cost. The new construction scheduling model provides the capabilities of both the critical path method (CPM) and linear scheduling method (LSM) approaches. In addition, it provides features desirable for repetitive projects, such as highway construction, and allows schedulers greater flexibility. It is particularly suitable for studying the effects of change order on the construction cost. This research provides the mathematical foundation for development of a new generation of more general, flexible, and accurate construction scheduling systems.     

Layout Design of Irrigation Networks in Highly Parcelled Territories Using Geographical Information System

Traditional irrigation zones in the east of Spain have been denoted by the high level of parcellation. The layout of the irrigation network design in highly parcelled territories presents an important degree of difficulty, the previous experience of the designer in this task being crucial in the final result. In this work, a new heuristic algorithm for layout of the irrigation network design is presented. We start from a classical graph theory algorithm (Dijkstra’s algorithm) used for solving the shortest path spanning tree problem. This algorithm is modified to assign weights to the arcs and plot limits are used as if they were the arcs of a graph. The algorithm is implemented on a geographical information system, thus creating an application that automatically generates the layout of the irrigation network design. The only necessary initial data are the origin of the network (supply point) and the hydrants (delivery points). The advantage of this heuristic is that the subjectivity introduced for the designer is removed. Moreover, it allows for solving complex problems, and therefore it is applicable to highly parcelled zones, where the number of vertices and edges is so high that it would inhibit calculating capacity of any optimization process. A practical example is presented, in which the layout design obtained by applying the heuristic is compared with the original existing layout.     

Set Sprinkler Irrigation and Its Cost

In this study, annual water application costs per unit area (ha) have been analyzed at the level of irrigation subunit in set sprinkler irrigation systems designed with pipes of different materials. In the cost, investment (pumping, pipes, sprinklers, ditches), energy, labor, maintenance, and water costs have been considered. Four systems were studied: one with buried pipes, in a permanent solid-set system, using: (a) polyvinyl chloride with buried pipes (PVCb), and three with pipes on the surface in surface solid-set systems, using (b) polyvinyl chloride pipes, (c) polyethylene pipes, and (d) aluminum pipes. The correct selection of the irrigation subunit size and shape can lead to a significant decrease in cost. The most economic irrigation subunits, among the four systems studied, were those formed by four laterals and a number of sprinklers per lateral of 10, 9, and 6 at 12?m×12?m, 12?m×18?m, and 18?m×18?m spacing, respectively. The most influential factor on the annual water application cost was spacing. Considering total annual cost, water cost was the most important, followed by investment and energy. Among the analyzed systems, the permanent system using PVCb produced the lowest annual water application cost per unit area.     

Water Delivery System Planning Considering Irrigation Simultaneity

Time should be considered in carrying out the design and management of demand irrigation distribution systems. In this paper, a method to characterize the pumping flow in demand pressurized systems throughout the day and irrigation season is presented. This method considers the temporal evolution of water requirements during the irrigation season and water demand concentration in certain periods of the irrigation day due to different electrical energy charges. The model was established based on data from an actual water distribution network of an irrigation district in southern Spain. The results differed significantly from those obtained using approaches based on establishing a uniform working probability for the outlets of the water distribution network at all hours of the irrigation day, which underestimated the circulating flows or system capacity. The most probable pumping flow with uniform probability was 3.1 m3/s, a smaller value than those obtained in the off-peak and average energy tariff times (4 and 3.4 m3/s, respectively). The total energy head required at the booster pumping in each period of the irrigation season was simulated. 10,000 randomly chosen scenarios were simulated for each irrigation day and each energy tariff time. The heterogeneous vertical stratification between 50 and 103 m of the required piezometric head was obtained as a function of the demanded flow for the water distribution system. This paper includes a pump selection algorithm for recommending least cost or optimum pump combinations in the distribution network and to evaluate the system’s energy cost. The pump recommendations show that the optimal solution could have saved 41% of the pumping cost of the Fuente Palmera irrigation district.     

Competent Genetic-Evolutionary Optimization of Water Distribution Systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms—a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms.     

Water Distribution Management in Small West African Canal Systems

The performance and progressive development of irrigation distribution and rotation methods were studied in two government-sponsored systems of Niger, West Africa. Systemwide water distribution was monitored intensively throughout several growing seasons and farmer surveys were conducted at both sites. Characteristics of farmer-managed rotation among tertiary canals and among parcels were examined in relation to farmer response to physical and organizational system constraints. A method for indexing the orderliness of irrigation rotation was developed. Where water deliveries were limited, organizational efforts on behalf of the farmers resulted in functional, orderly rotation and distribution among parcels. Farmers exhibit less incentive to organize efficient and orderly rotation among parcels where access to water is less limited. Several organizational and design factors influence the degree to which farmers are both willing and able to organize functional water distribution among themselves. Also, farmers may circumvent design intentions or management strategies imposed on them by irrigation authorities in order to establish their own more effective water management methods, which tend to better accommodate local labor and production constraints. Technical and organizational considerations related to water distribution and management derived from the study results may serve to facilitate the design and operation of small-holder systems in the Sahel.     

Performance of Model Predictive Control on ASCE Test Canal 1

Model predictive control (MPC) is a popular control algorithm in the process control industry that is particularly suited to the automatic control of irrigation water delivery systems because it explicitly accounts for the long delay times encountered in open-channel flow. In addition, a feedforward routine is easy to implement in MPC and many of the constraints that canal operators face can be directly incorporated into the MPC scheme. The ASCE Task Committee on Canal Automation Algorithms developed a series of test cases to evaluate the performance of canal control algorithms. In this paper, simulation tests were performed on ASCE test canal 1 using a remote downstream control configuration of MPC. The MPC algorithm effectively controls ASCE test canal 1, and its performance was similar to that of other proposed controllers. When there were no minimum gate movement constraints, MPC was fairly robust because the controller performance did not significantly degrade under untuned conditions. In the presence of minimum gate movement constraints, the water levels continually oscillate around the water level setpoint. Using the configuration presented in this paper, the feedforward portion of MPC does not perform as well as other proposed feedforward routines. This underperformance is related to the simplifications made by the underlying process model and not to MPC itself.     

轧钢成品库无人天车与货车调度协同优化

 为了研究轧钢库区货车入库高效调度和无人天车作业合理分配协同优化问题,针对轧钢成品库区产品多品种小批量、出入库频繁等特点,建立了以订单服务时间最小为目标的整数规划模型,然后通过仿真试验对天车分配规则进行学习,并在不同订单规模下对经验规则、遗传算法和自适应遗传算法3种调度方法进行了对比试验。试验结果和现场验证均表明在各个订单规模下自适应遗传算法调度方案能高效准确地找出最优调度方案,从而为钢厂无人仓库天车调度进行指导,有效地优化了仓库物流库存管理。     

Optimal Furrow Design.?II: Explicit Calculation of Design Variables

The furrow irrigation system design problem (at minimum cost) is significantly simplified by analytically solving it. For a specified furrow length, a simple algebraic equation is derived to directly calculate the appropriate inflow rate (and cutoff time) so that the minimum cost of the furrow system is obtained. The proposed equation is independent of the water and labor cost coefficients. Comparison tests indicated that the optimum inflow rate values obtained analytically were in close agreement to the optimum values obtained using the outcome of the zero-inertia numerical model. The method is extended for furrow design considering the furrow length also as a design variable. The optimum number of distribution lines and widthwise furrow sets are easily determined by a simple calculation procedure.     

Multiobjective Linear Programming Model for Scheduling Linear Repetitive Projects

Linear repetitive construction projects require large amounts of resources which are used in a sequential manner and therefore effective resource management is very important both in terms of project cost and duration. Existing methodologies such as the critical path method and the repetitive scheduling method optimize the schedule with respect to a single factor, to achieve minimum duration or minimize resource work breaks, respectively. However real life scheduling decisions are more complicated and project managers must make decisions that address the various cost elements in a holistic way. To respond to this need, new methodologies that can be applied through the use of decision support systems should be developed. This paper introduces a multiobjective linear programming model for scheduling linear repetitive projects, which takes into consideration cost elements regarding the project’s duration, the idle time of resources, and the delivery time of the project’s units. The proposed model can be used to generate alternative schedules based on the relative magnitude and importance of the different cost elements. In this sense, it provides managers with the capability to consider alternative schedules besides those defined by minimum duration or maximizing work continuity of resources. The application of the model to a well known example in the literature demonstrates its use in providing explicatory analysis of the results.     

New Methodology to Evaluate Flow Rates in On-Demand Irrigation Networks

Although Clément methodology is the most commonly used model for obtaining the design flow rate in on-demand irrigation networks, studies have shown that the Clément methodology does not always fit properly. A new stochastic methodology is proposed in this paper [random daily demand curve (RDDC)], in order to achieve a more accurate design flow. Results from Clément and the proposed RDDC methodology are compared to measured flow data in an on-demand irrigation network located in Tarazona de La Mancha (Albacete, Spain). RDDC is shown to have a better fit with the measured data compared to the Clément methodology, which underestimated the design flow by 35%–40%. RDDC methodology avoids the problem of using average opening hydrant probability, resulting in a better estimation of the network behavior.     

Pipe Index Vector: A Method to Improve Genetic-Algorithm-Based Pipe Optimization

This paper proposes a methodology for the optimal design of water distribution systems based on genetic algorithms. The objective of the optimization is to minimize the capital cost, subject to ensuring adequate pressures at all nodes during peak demands. The proposed method is novel in that it involves the use of a pipe index vector to control the genetic algorithm search. The pipe index vector is a measure of the relative importance of pipes in a network in terms of their impact on the hydraulic performance of the network. By using the pipe index vector it is possible to exclude regions of the search space where impractical and infeasible solutions exist. By reducing the search space it is possible to generate feasible solutions more quickly and hence process much healthier populations than would be the case in a standard genetic algorithm. This results in optimal solutions being found in a fewer number of generations resulting in a substantial saving in terms of computational time. The method has been tested on several networks, including networks used for benchmark testing least cost design algorithms, and has been shown to be efficient and robust.     

Pumping Selection and Regulation for Water-Distribution Networks

Because of the increasing importance of on-demand irrigation systems, a support system for general use has been developed to aid in selecting and regulating pumping stations. This innovation will improve the balance between total costs (project and energy) and operation quality. The procedure first determines the maximum and minimum system head curves, followed by the evolution of demand curves to obtain the maximum discharge needed. Once this discharge is determined, it is possible to carry out the dimensioning and regulation of the pumping station. An easy tool to select the number of variable and fixed speed pumps has also been developed Excel and Visual Basic can be used. The results demonstrate the importance of selecting pumps that are best adapted to the system head curve. The minimum total cost solution has been obtained by using one variable-speed pump in conjunction with another operating at fixed speed.     

Minimum-Risk Bedding for Flexible Drain Pipes

The soil bedding for nonpressurized buried flexible pipes is critical for minimum-risk performance. Lack of adequate bedding reduces the strength of the pipes by a factor of 2 or more. To compensate, pipes must have high strength, at increased cost, in order to avoid the risk of failure. Structural performance and performance limits are compared for plastic drainpipes with a variety of beddings. Compared to a flat bedding, the risk of failure is greatly reduced by shaping the bedding. Shaped beddings perform essentially as well as full-contact embedment with select granular soil. Tests and analyses show that a 90° V-groove bedding that supports and aligns the pipe performs nearly as well as a 180° form-fit circular groove or a full-contact embedment of select soil. Comparison of beddings is important in the design and installation of drainpipes in order to assure minimum risk of failure.     

Influence of the Spatial Configuration of the Irrigated Zone on the Irrigation Network Layout Design

The present work aims at taking us closer to the study of the influence of the spatial configuration of the irrigated zone on the unit cost (?ha) of a layout irrigation network design. The layout analyzed in this paper is carried out by means of the algorithm, based on the graph theory which eliminates the skill or experience of the designer, thus giving rise to homogeneous results. These layouts are sized using the method of the modified economic series. Then, the irrigated zone is studied by applying spatial analysis techniques and calculating a series of variables that may have some effects on the cost (?ha) of the network. Finally, we look for the existing relationship between the spatial variables and the cost by using the statistical technique of multiple regression analysis. Variables such as accessibility of supply, location of the network origin, total irrigated area, density of irrigable plots, perimeter, or hydrants spatial point pattern are extremely important in the cost of the network. The statistical model explains more than 99% of the variability found in unit cost. The equation obtained may be very useful before performing a design, in order to find out a suitable location of the network origin, as well as to check if the design of a single network is preferred to the alternative of dividing it into several smaller networks. Moreover, it would also be interesting to verify if the hydrant spatial point pattern as a whole is appropriate.     

OCCASION: New Planning Tool for Optimal Climate Change Adaption Strategies in Irrigation

To sustain productive irrigated agriculture with limited water resources requires a high water use efficiency. This can be achieved by the precise scheduling of deficit irrigation systems taking into account the crops’ response to water stress at different stages of plant growth. Particularly in the light of climate change with rising population numbers and increasing water scarcity, an optimal solution for this task is of paramount importance. We solve the corresponding complex multidimensional and nonlinear optimization problem, i.e., finding the ideal schedule for maximum crop yield with a given water volume by a well tailored approach which offers straightforward application facilities. A global optimization technique allows, together with physically based modeling, for the risk assessment in yield reduction considering different sources of uncertainty (e.g., climate, soil conditions, and management). A new stochastic framework for decision support is developed which aims at optimal climate change adaption strategies in irrigation. It consists of: (1) a weather generator for simulating regional impacts of climate change; (2) a tailor-made evolutionary optimization algorithm for optimal irrigation scheduling with limited water supply; and (3) mechanistic models for rigorously simulating water transport and crop growth. The result, namely, stochastic crop-water production functions, allows to assess the impact of climate variability on potential yield and thus provides a valuable tool for estimating minimum water demands for irrigation in water resources planning and management, assisting furthermore in generating maps of yield uncertainty for specific crops and specific agricultural areas. The tool is successfully applied at an experimental site in southern France. The impacts of predicted climate variability on maize are discussed.