Elsevier

Advances in Water Resources

Volume 105, July 2017, Pages 188-204
Advances in Water Resources

A novel generic optimization method for irrigation scheduling under multiple objectives and multiple hierarchical layers in a canal network

https://doi.org/10.1016/j.advwatres.2017.04.025Get rights and content

Highlights

  • A generic approach to optimize canal scheduling in a multi-hierarchical canal network, under multiple conflicting objectives.

  • A network-wide solution that is also optimal for lower hierarchical layers.

  • Flexibility for the decision maker to change local priorities based on immediate network priorities.

  • Solvable using available multi-objective evolutionary algorithms.

  • Independent of mathematical modeling of objectives and process modeling of network hydraulics - Lets easy addition of details.

Abstract

This research proposes a novel generic method for irrigation scheduling in a canal network to optimize multiple objectives related to canal scheduling (e.g. maximizing water supply and minimizing imbalance of water distribution) within multiple hierarchical layers (e.g. the layers consisting of the main canal, distributaries) while utilizing traditional canal scheduling methods. It is based on modularizing the optimization process. The method is theoretically capable of optimizing an unlimited number of user-defined objectives within an unlimited number of hierarchical layers and only limited by resource availability (e.g. maximum canal capacity and water limitations) in the network. It allows flexible decision-making through quantification of the mutual effects of optimizing conflicting objectives and is adaptable to available multi-objective evolutionary algorithms. The method’s application is demonstrated using a hypothetical canal network example with six objectives and three hierarchical layers, and a real scenario with four objectives and two layers.

Introduction

In a typical farm, water is supplied to fields by a canal network and there is a hierarchical order of layers within the network. The main canal can be considered the top-most layer, the set of branch canals (distributaries) the second layer and so on, while fields form the bottom-most layer. The operation of an irrigation canal network is of interest to several stakeholders such as the canal management, canal operators, farmers and possibly environmental authorities. The objectives of canal scheduling and their relative importance are different from the perspective of different stakeholders. For example, the operator may be interested in maintaining water level variations within limits, whereas farmers mainly care about timely water supply. The local decisions taken at lower layers have an impact on fulfilling objectives at a higher layer. For example, meeting all water demands in a tertiary area may conflict with network-wide equity objectives. Decisions on high priority objectives are made by different actors depending on the form of system management and the prevailing network conditions, and any optimization method should be sensitive to these concerns. At the same time, it should be aware of practical limitations such as the difficulty in turning a canal outlet ON and OFF intermittently at short intervals and maintaining a high adequacy level during a drought. This highlights the importance of changing the objectives (or rather the importance given to them) in real-time as per the specific situation. The change of priorities should also be backed up by a quantitative analysis of the alternative outcomes. When provided with all the possible options, the decision-maker or the canal management authority can make informed decisions and prepare a suitable schedule.

Before proceeding, let us define some terms for the purpose of consistency throughout the paper. Field-scale is defined as the operational scope within a field and farm-scale as the scope of the operations in the canal system up to field inlets. Network-scale is the collective field-farm-scales (see Fig. 1).

Optimization of operations (in terms of water use and root zone soil moisture deficit (RZSMD)) at field-scale is achieved in Delgoda et al. (2016a) by optimizing irrigation control. This involves utilizing the field water supply through field inlets and changing the time and amount of water application to the field. In this research, we discuss optimization of operations (in terms of various canal scheduling objectives mentioned above) at farm-scale by proposing a generic method to optimize canal scheduling. In other words, this is a systematic procedure to change the amount and time of water delivery to individual field inlets. The method needs to consider multiple conflicting objectives across multiple hierarchical layers in the canal network, while providing flexibility in analyzing the outcomes quantitatively and modifying the priorities in real-time.

Canal irrigation scheduling can be performed while aiming to optimize one or more scheduling objectives. Realizing the scheduling objectives is usually subject to constraints. Constraints are posed by the physical configuration of the canal network, the canal scheduling method and factors such as water availability and cost. Thus, the canal scheduling optimization can generally be expressed as a constrained optimization problem.

Integer programming (Wang et al., 1995), dynamic programming (Sunantara, Ramirez, 1997, Vedula, Mujumdar, 1992, Yaron, Dinar, 1982), linear programming (Mohan, Jothiprakash, 2003, Paudyal, Gupta, 1990) and non-linear programming (Benli, Kodal, 2003, Rydzewski, Rashid, 2007) are proposed to solve the optimization problem of canal scheduling. The optimization typically involves non-linear non-convex problems, therefore, heuristic methods such as evolutionary algorithms are a preferred method to solve them. For single objective optimization, using the genetic algorithm (GA) – a popular evolutionary algorithm – is a well-established practice in the canal scheduling related literature (Haq, Anwar, 2010, Nixon, Dandy, Simpson, 2001, Wardlaw, Bhaktikul, 2004). A summary of these studies is given in Singh (2013). Most of these approaches are efficient and accurate, although the solutions are highly specific for a given scenario. By the time the solutions are applied in reality, the network conditions, the objective set and priorities might have been changed. The optimization solutions need to adapt to these changes.

Also, most of the existing literature is limited to optimization of the objectives belonging to a single hierarchical layer of the canal network. There are few instances where two layers are considered (Peng, Wang, Khan, Rana, Luo, 2012, Wardlaw, Bhaktikul, 2004), however, they are based on very specific site details and a fixed set of objectives. Providing flexibility in customizing the objectives is an important step towards selecting only the relevant objectives and to make compromises between objectives whenever necessary.

Irrigation scheduling often involves multi- (two or more) objectives. The usual approach to solving such optimization problems is through combinatorial multi-objective optimization, where each objective is assigned a weight according to its importance. Without knowing the impact of one objective on other a priori, assigning weights is not practical, especially under changes in the background such as weather and stakeholder preferences. Therefore, using combinatorial multi-objectives may lead to bias in optimization. Using manual sorting methods as in Santhi and Pundarikanthan (2000) is tedious and does not allow constraints to be incorporated into the problem. Methods such as Lexographic ordering used in work such as Lotov et al. (2004), Lotov et al. (2005), Miettinen (1999) also need a priori knowledge on priority levels of objectives, which is not usually available.

When multiple objectives are optimized, the complete set of optimal solutions corresponds to different combinations of objectives (implied by their weights). This solution set is expressed by a Pareto frontier (PF) where each point has one to one mapping with an optimal solution for each distinct objective combination (this concept will be further explained in Section 2). The designer can select any solution out of this solution set based on preference. Work of Peng et al. (2012) built on this concept, utilized multi-objective GA for their bi-objective optimization of irrigation scheduling in a canal network. However, as mentioned above, the solution is limited to a specific network topology with two fixed objectives.

In this paper, we propose an optimization method that addresses all the above concerns: multiple conflicting objectives, changing priorities, multiple hierarchies and implementation issues. The basic concept is to generate a large pool of optimal solutions/strategies at lower hierarchical layers and select the best combinations of solutions from the pool that meet the objectives at higher layers. The solution pool is narrowed down systematically until the best strategy or set of alternative strategies are obtained.

As mentioned above, generating a PF is one way to represent several optimal solutions. There are often more than two objectives involved in our canal scheduling problem. However, generating multi (more than two) dimensional PF using evolutionary algorithms is a rather complex process and the available algorithms are tested for only two or three objectives (Deb, Gupta, 2004, Gil, Márquez, Baños, Montoya, Gómez, 2007, Zitzler, Laumanns, Thiele, 2002). In this paper, we use a simple workaround for this issue in the context of canal scheduling.

Section 2 explains the method and Section 3 demonstrates the use of the method through a hypothetical irrigation network and a classical example from canal scheduling literature. Section 4 summarizes the concluding remarks.

Section snippets

Methodology

As mentioned earlier, having a number of objectives of interest to multiple parties of stakeholders makes the canal scheduling a complex task with vague decision boundaries. Thus, decision-makers who have specialized knowledge about the whole network are needed, in order to make sensible decisions which take the entire network situation into account and prioritize the important scheduling objectives. This could be one of the main reasons why almost any of the innumerable canal scheduling

Simulation results and discussion

We demonstrate the proposed generic optimization method for canal scheduling using two examples: a hypothetical example and a real world scenario. The following assumptions have been used in the example applications for simplicity: (i) the water flows in the canals are assumed to be at steady state; (ii) Seepage and evaporation losses along the canal up to a field inlet are proportional to the distance from the canal head to the inlet; (iii) Rainfall amount over the canal surface and runoff

Conclusion

This paper proposes a generic approach to optimize canal scheduling under multiple (more than two) conflicting objectives in a canal network consisting of multiple hierarchical layers. The optimization process is modularized according to the physical connectivity. It provides network-wide optimal scheduling plans while maintaining the optimality at lower hierarchical layers. PF concept is used to generate optimal scheduling plans.

The method gives an insight into the effects of optimizing

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