# Meta-heuristic algorithms as tools for hydrological science

- Do Guen Yoo
^{1}and - Joong Hoon Kim
^{2}Email author

**1**:4

https://doi.org/10.1186/2196-4092-1-4

© Yoo and Kim; licensee Springer. 2014

**Received: **3 September 2013

**Accepted: **2 January 2014

**Published: **6 March 2014

## Abstract

In this paper, meta-heuristic optimization techniques are introduced and their applications to water resources engineering, particularly in hydrological science are introduced. In recent years, meta-heuristic optimization techniques have been introduced that can overcome the problems inherent in iterative simulations. These methods are able to find good solutions and require limited computation time and memory use without requiring complex derivatives. Simulation-based meta-heuristic methods such as Genetic algorithms (GAs) and Harmony Search (HS) have powerful searching abilities, which can occasionally overcome the several drawbacks of traditional mathematical methods. For example, HS algorithms can be conceptualized from a musical performance process and used to achieve better harmony; such optimization algorithms seek a near global optimum determined by the value of an objective function, providing a more robust determination of musical performance than can be achieved through typical aesthetic estimation. In this paper, meta-heuristic algorithms and their applications (focus on GAs and HS) in hydrological science are discussed by subject, including a review of existing literature in the field. Then, recent trends in optimization are presented and a relatively new technique such as Smallest Small World Cellular Harmony Search (SSWCHS) is briefly introduced, with a summary of promising results obtained in previous studies. As a result, previous studies have demonstrated that meta-heuristic algorithms are effective tools for the development of hydrological models and the management of water resources.

## Keywords

## Background

Optimization is the process of ensuring that an object or system is as useful or effective as possible; that is, optimization involves finding the best solutions to satisfy specific objectives and conditions. In conventional theoretical problems, traditional mathematical techniques such as linear programming (LP), non-linear programming (NLP), and dynamic programming (DP) can guarantee global optima in simple idealized models. However, in real world problems, factors such as non-linearity and complexity produce obstacles to obtaining global optima.

Heuristic algorithms can be used to overcome such shortcomings of mathematical techniques and produce distinguished outcomes when applied to specific problems; however, they remain inapplicable in a broad range of situations. To address this, meta-heuristic optimization techniques based on iterative simulations have been introduced, allowing appropriate solutions to be found using limited computation time and memory and without requiring any complex derivatives. Many meta-heuristic algorithms that combine rules and randomness mimicking natural phenomena have been developed, including ant colony optimization (ACO), genetic algorithms (GAs), particle swarm optimization (PSO), simulated annealing (SA), and tabu search (TS). Such simulation-based meta-heuristic methods have powerful searching abilities, often allowing them to overcome the several drawbacks of traditional mathematical methods. For example, harmony search (HS) algorithms can be conceptualized based on musical performances (e.g., by a jazz trio or an orchestra) and used to improve harmony. Typically, musical performers aim for a near-optimal state (i.e., fantastic harmony) that is determined by aesthetic estimation; conversely, optimization algorithms seek a best state (i.e., a global optimum, represented by the minimum cost or maximum benefit or efficiency) that can be determined according to the values of objective functions. Aesthetic estimation is achieved by practicing the set of sounds achieved by a combination of instruments, whereas the value of the objective function is evaluated by investigating the set of the values produced by composed variables. Moreover, just as “better” aesthetic sounds can be achieved through practice, the minimization/maximization of the objective function can be achieved by repeated iterations [1, 2].

Here, meta-heuristic optimization techniques are introduced and their applications are discussed with reference to recent trends in water resources engineering, particularly in hydrological science. In Section 2, meta-heuristic algorithms and their applications to hydrological science are discussed by subject, including a review of existing literature in the field. In Section 3, HS algorithms and their application in hydrological science are described. Then, in Section 4, recent trends in optimization are presented and relatively new technique such as Smallest Small World Cellular Harmony Search (SSWCHS) is briefly introduced with a summary of promising results obtained in previous studies. Finally, Section 5 presents concluding remarks.

## Methods

### Meta-heuristic algorithms and their applications in hydrological science

A meta-heuristic is a higher level procedure that can be used to find a near global optimal solution to optimization problems that include incomplete or imperfect information or limited computation capacity. Meta-heuristics often make few assumptions about the optimization problem being solved, which makes them suitable for a wide variety of problems. Moreover, because they can search through large sets of feasible solutions, meta-heuristics can often find good solutions with less computational effort than traditional iterative methods or simple heuristics [3, 4].

### Harmony search algorithms as a tool in hydrological science

As discussed above, HS algorithms can be used to achieve better harmony in the process of musical performance, unlike other meta-heuristic algorithms. Musical performances seek fantastic harmony, which is typically determined by aesthetic estimation, whereas optimization algorithms seek a global optimum that can be determined from the value of an objective function. HS algorithms preserve the history of past vectors and can vary the adaptation rate during computation. Moreover, as with GAs, HS algorithms manage several vectors simultaneously, although HS algorithms are different from GAs in many respects. HS algorithms offer two primary advantages: 1) they produce a new vector after considering all existing vectors, rather than considering only two parent vectors (as in GAs); and 2) they do not require the initial values of decision variables to be specified. Thus, it can be generally said HS algorithms offer more flexibility and better solutions than GAs.

Applications of HS algorithms in hydrological science can be divided by discipline, as with other meta-heuristic algorithms, and the first hydrological applications of the HS technique were described in 2001. HS algorithms were applied to minimize the cost of a pipe network during the design process and to estimate parameters for the non-linear Muskingum routing model [1, 2]. Subsequently, Paik et al. [24] developed a parameter calibration method for rainfall–runoff models and demonstrated how adopting powerful meta-heuristic optimization algorithms such as HS algorithms can enable researchers to focus on aspects of the rainfall–runoff model other than parameter calibration. Ayvaz [25] first introduced HS algorithms to aquifer modeling, using the technique to determine aquifer parameters and the zonal structure of these parameters based on a given set of observations of piezometric head. More recently, Kougias and Theodossiou [26] solved problems related to dam operation using HS techniques; in particular, they investigated the optimum operation of a four-reservoir system over one day, with the aim of maximizing the daily benefits obtained from the reservoir system. The studies cited here represent only a small portion of the existing literature in this field, yet their results demonstrate the potential for use of HS algorithms in solving complex optimization problems successfully and efficiently.

## Results and discussion

### Recent trends in optimization in hydrological science

The latest trends in meta-heuristic optimization in hydrological science can be classified into three primary categories as follows: 1) Hybrid algorithms involve combinations of existing algorithms and are designed to increase the possibility of solving complex problems by adopting the favorable properties of different optimization methods. 2) Recently, an automatic assignment technique has been developed for the setting of algorithm parameters. Existing meta-heuristic algorithms require decision-makers to set some parameters, and the efficiency of many processes can be affected considerably by parameter selection. Moreover, setting parameters often involves time-consuming tasks such as sensitivity analyses. However, in recent years, algorithms have been developed that do not require any parameters to be set; such algorithms can change parameters automatically based on factors such as the value of an objective function or the number of iterations. These algorithms have been shown to achieve similar results to those obtained using more traditional meta-heuristic algorithms and can be very useful tools for decision-makers. 3) A particularly interesting branch of optimization research focuses on the expansion from single-objective to multi-objective optimization. Multi-objective optimization seeks to obtain the Pareto-optimal sets between conflicting objectives, where Pareto-optimal sets comprise the sets of solutions that are better than all other solutions for at least one objective; these sets were referred to as non-dominated or Pareto-optimal solutions by Pareto [27]. Multi-objective optimization is effective for use in real-world problems, particularly because most real practical problems involve many trade-offs between objectives.

## Conclusions

In this paper, meta-heuristic optimization techniques are introduced and recent trends in their application in water resources engineering particularly hydrological science are discussed. The information presented here can be summarized as follows: 1) In hydrological science, GAs is the most widely utilized meta-heuristic algorithm. 2) Several previous studies have shown that meta-heuristic techniques can be used as effective tools for the development of hydrological models and the management of water resources. 3) Some recent trends in optimization in hydrological science (e.g., hybrid algorithms, parameter-free techniques, multi-objective optimization) have the potential to provide efficient solutions to real-world problems. 4) Hybrid type algorithms, the SSWCHS algorithm for example, can produce very competitive solutions with less iteration than other algorithms. It is recommended that meta-heuristic algorithms be utilized as tools for pertinent studies in hydrological science.

## Declarations

### Acknowledgements

This work was supported by the National Research Foundation of Korean (NRF) grant funded by the Korean government (MSIP) (No. 2013R1A2A1A01013886).

## Authors’ Affiliations

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