Assessment of evolutionary algorithms for optimal operating rules design in real Water Resource Systems

https://doi.org/10.1016/j.envsoft.2014.09.024Get rights and content

Highlights

  • SCE-UA and Scatter Search are assessed in order to design optimal operating rules.

  • An analysis of the parameters is carried out to determinate the best stop criteria.

  • The analysis carried out shows the most influential parameters.

  • SCE-UA algorithm, applied in real cases, seems to be the most efficient algorithm.

  • A way to transmit results is presented in order to make the decision-making easier.

Abstract

Two evolutionary algorithms (EAs) are assessed in this paper to design optimal operating rules (ORs) for Water Resource Systems (WRS). The assessment is established through a parameter analysis of both algorithms in a theoretical case, and the methodology described in this paper is applied to a complex, real case. These two applications allow us to analyse an algorithm's properties and performance by defining ORs, how an algorithm's termination/convergence criteria affect the results and the importance of decision-makers participating in the optimisation process. The former analysis reflects the need for correctly defining the important algorithm parameters to ensure an optimal result and how the greater number of termination conditions makes the algorithm an efficient tool for obtaining optimal ORs in less time. Finally, in the complex real case application, we discuss the participation value of decision-makers toward correctly defining the objectives and making decisions in the post-process.

Introduction

Over the last two decades, Evolutionary algorithms (EAs) have been applied extensively to a number of areas of water resources, such as water distribution systems (Goldberg and Kuo, 1987, Savic and Walters, 1997), urban drainage and sewage systems (Guo et al., 2008), water supply and sewage treatment systems (Murthy and Vengal, 2006), hydrologic and fluvial models (Muleta and Nicklow, 2005) and subterranean systems (Dougherty and Marryott, 1991), as highlighted in a review by Nicklow et al. (2009). However, while EAs have been applied successfully to many academic problems, additional research is required to enable them to be applied in real-life context (Maier et al., 2014). For example, there is a need to determine which searching mechanisms and termination/convergence criteria are best for real-life problems and the best way to convey the results of the optimisation process to decision makers (Maier et al., 2014). Consequently, these issues are the focus of this paper.

Simulation models are the most commonly used tool to analyse the integrated planning and management of WRS. These models allow for more detailed representations of the systems than do the optimisation models (Loucks and Sigvaldason, 1982). Moreover, the applicability of optimisation models to system management for most real reservoirs is limited due to the “high level of abstraction” needed for the efficient implementation of optimisation techniques (Akter and Simonovic, 2004, Moeini et al., 2010).

Normally, simulations of water management systems use operating rules (ORs) to model the efficient management of water resources. Designing and obtaining ORs for multi-reservoir systems is a complex task and has been widely developed during the scientific history of water resource studies (Young, 1967, Bhaskar et al., 1980, Lund and Ferreira, 1996). On the other side, ORs must be implementable in real applications and therefore need to be robust as well as simple to be defined by a set of indicators and parameters.

A common technique used to design ORs is based upon iterative simulations of water management models. In this case, the goal is to find an OR that optimises system management. Therefore, the iterative process to find such an OR can be controlled by an optimisation algorithm that is responsible for varying the OR parameters based upon the results obtained from the simulation. EAs afford several benefits compared with classical optimisation techniques because they can be implemented without heavy a-priori model requirements, and thanks to their ability to manage discrete variables, EA optimisation procedures can directly address alternatives when applied to OR optimisation. To this end, EAs present effective an optimisation algorithm for searching for optimal rules in WRSs. For example, Oliviera and Loucks (1997), and later Ahmed and Sarma (2005), presented an approach for the optimisation of ORs in multi-reservoir systems using EAs. Other cases are reported by Cai et al. (2001) to solve nonlinear models of water management using a combination of an EA and linear programming; by Momtahen and Dariane (2007), who used a direct search approach to optimize the parameters of reservoir operating policies with a EA as an optimization method; or by Elferchichi et al. (2009), who applied an EA to optimise reservoir operations in the Sinistra Ofanto (Foggia, Italy) irrigation system. Furthermore, in the literature were used another metaheuristic approaches such as Guo et al. (2013), who incorporated a multi-population mechanism into a non-dominated sorting particle swarm optimization to obtain optimal rules for a water-supply reservoir; or as in Hossain and El-Shafie (2014) where a nonlinear reservoir release optimization problem was resolved by comparing evolutionary methods and swarm intelligences.

The main purpose of this paper is to test EAs and scattered search approaches to design ORs that optimise WRS management. The EAs used are the SCE-UA (Duan et al. 1992) and the Scatter Search (Glover, 1997), which are combined with the SIMGES network flow simulation model to design optimal ORs. In addition, an analysis of the parameters of both algorithms is carried out, which allows us to determine which termination/convergence criteria are most appropriate for realistic problems, apart from showing the most influential parameters that affect the optimisation process. On the other hand, the previous analysis and the use of one of these EAs in a real complex case demonstrate which of the two studied algorithms is the best for solving this type of problem. Finally, a method of transmitting the optimisation results is presented to make the decision-making easier. To analyse the parameters, a simple theoretical model representing a fictitious WRS is used. In the application for a real complex WRS, the Tirso-Flumendosa-Campidano system located on Sardinia Island (Italy) is used.

Section snippets

Materials and methods

We propose a connection between EAs (SCE-UA or Scatter Search) and a traditional water allocation model (SIMGES) in the water resources field to design optimal ORs for real WRSs. The approach developed is detailed in Fig. 1. Decision variables, OR parameters, are defined by the user and are sought by the EA to design optimal ORs for the WRS to which it is applied. Moreover, some algorithm-specific parameters, such as population size, the number of subgroups or the maximum number of iterations

Parameter analysis

In this section, an analysis of the aforementioned EA is carried out. This analysis studies the influence of the SCE-UA and the Scatter Search parameters when used as a tool to design optimal ORs in WRS. According to Duan et al. (1994), the effectiveness and efficiency of an algorithm are influenced by the choice of the algorithmic parameters. Typically, these algorithms have a higher or lower number of parameters and provide a certain flexibility, i.e., these parameters determine the algorithm

Application real case: Tirso–Flumendosa–Campidano

This section has three objectives: first, to demonstrate the usefulness of both EAs analysed in designing ORs for real WRSs; second, to determine which algorithm is better; and finally, to analyse the influence of decision-makers upon the optimisation pre-process and post-process (using an analysis of the results).

The proposed methodology in Section 2 is applied to the Tirso–Flumendosa–Campidano system located on the island of Sardinia (Italy). The system has a Mediterranean climate and is

Conclusions

In this paper, two EAs have been assessed as optimisation tools to design optimal ORs in a WRS. Several aspects have been considered through analysis of each algorithm's parameters and a real case. The discussed aspects are aimed at a particular study of EAs: which is the best in real case applications, the convergence/termination criteria, and the influence of decision-makers in the optimisation process.

The parameter analysis allows us to better understand the behaviour of the SCE-UA and

Acknowledgements

The authors wish to thank the University of Cagliari (Sardinia) and the Basin Agency of Sardinia for the data provided in the development of this study, as well as the Autonomous Region of Sardinia for funding the research project CRP 2_716. Thanks are also due to the Spanish Ministry of Science and Innovation (Comisión Interministerial de Ciencia y Tecnología, CICYT) for funding the projects NUTEGES (VI Plan Nacional de I+D+i 2008–2011, CGL2012-34978) and SCARCE (program Consolider-Ingenio

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