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Discussions and Closures
Discussion of “Application of the Firefly
Algorithm to Optimal Operation of Reservoirs
with the Purpose of Irrigation Supply
and Hydropower Production” by
Irene Garousi-Nejad, Omid Bozorg-Haddad,
Hugo A. Loáiciga, and Miguel A. Mariño
Downloaded from ascelibrary.org by 80.82.77.83 on 10/27/17. Copyright ASCE. For personal use only; all rights reserved.
DOI: 10.1061/(ASCE)IR.1943-4774.0001064
Mojtaba Moravej 1
1
Academic Elite Soldier, National Elite Foundation, 1438833171
Tehran, Iran. ORCID: https://orcid.org/0000-0003-0347-7317. E-mail:
Mojtaba.Moravej@gmail.com
In the original paper, the authors made an effort to show the application of the firefly algorithm (FA) and its superiority to solve different reservoir operation problems in comparison with the genetic
algorithm (GA). Although the paper seems interesting, the discusser would like to mention following points for future studies.
The authors claimed that the FA has not been applied for the
optimal operation of reservoir systems before. On the one hand,
Hosseini-Moghari and Banihabib (2014) applied the FA to optimize the operation of the Bazoft Reservoir. Furthermore, there
are numerous different kinds of lifeform throughout the world; this
cannot mean that researchers should develop, modify, and apply
almost infinite different algorithms based on insects, fish, mammals, and plants. Over the last decade, there has been an explosion
in the development of new so-called metaheuristic optimization
algorithms based on natural metaphors. These algorithms have
attracted criticism globally (Weyland 2010, 2015; Lones 2014;
Sörensen 2015; Swan et al. 2015). It has been argued that these
algorithms just proliferate existing methods by using different terminology in order to hide their lack of novelty (Weyland 2010,
2015; Lones 2014; Sörensen 2015).
The best-known algorithm that lacks novelty is harmony search.
Weyland (2010) provided compelling evidence that the harmony
search algorithm is nothing but a special case of (μ þ 1) of the
evolution strategies, which was proposed by Rechenberg (1973).
Another example of such algorithms is the FA. The difference between glowworm swarm-based optimization (Krishnanand and
Ghose 2006), FA, fly optimization algorithm (Zainal Abidin et al.
2010), fruit-fly optimization algorithm (Pan 2012), multiswarm
fruit-fly optimization algorithm (Yuan et al. 2014), and well-known
particle-swarm optimization (PSO) (Eberhart and Kennedy 1995)
seem negligible (Weyland 2015). The differences between these
various social insect algorithms proved marginal at best (Sörensen
2015). It has been proven that the FA is sensitive to its parameter
selection, converges slowly, and gets trapped in local optimum
points (Yang 2012; Gandomi et al. 2013; Garousi-Nejad et al.
2016). Accordingly, many studies have focused on overcoming
these limitations (Yang 2012; Gandomi et al. 2013; Kazem et al.
2013; Wang et al. 2016; Garousi-Nejad et al. 2016), which shows
that the FA’s performance was insufficient.
Therefore, just because an algorithm has not been applied to an
optimization problem, it is not a praiseworthy work to use it. It is
not clear how an application of such algorithms contributes in the
reservoirs operation field, especially when more powerful tools
have already been developed (Wardlaw and Sharif 1999; Jalali
et al. 2007; Afshar 2013; Moravej and Hosseini-Moghari 2016).
To support this idea, some empirical evidence is provided in this
discussion.
A comparison among the GA, PSO, and reported results in the
original paper is made in Table 1. A two-dimensional Rosenbrock
function is considered and solved using the mentioned algorithms.
The GA is highly sensitive to its parameter selection. This means
that if careful tuning of the GA parameters is neglected, it leads to
unacceptable results. Table 1 demonstrates that this is the case in
the reported results in Table 4 of the original paper. The GA results
reported in Table 1 are calculated using a population of 50 individuals, 500 generations, 2 elites, and a 0.9 crossover probability. The
stochastic uniform is chosen as selection function, and a heuristic
crossover function with a ratio equal to 1.2 is assumed. Adaptive
feasible mutation is selected for the mutation function. All of these
functions are implemented in the global optimization toolbox of
MATLAB. Therefore, they are readily available for researchers to
solve their optimization problems.
The PSO parameters were selected to equal to 0.78, 1.6, and 1.6
for ω, c1 , and c2 , respectively. The method and parameters definitions of the PSO have been given by Kennedy (2011). The GA and
the PSO were executed until 25,000 function evaluations were
reached (same as in the original paper). Table 1 indicates that
the GA results are better than those of the FA. The same conclusion
was made by Garousi-Nejad et al. (2016). They investigated the
performance of the FA and modified firefly algorithm (MFA) to
solve the continuous 10-reservoir operation benchmark problem.
Their results indicated that both FA and MFA fall behind the
GA results reported by Wardlaw and Sharif (1999). It is anomalous
that how the GA can outperform the FA in the complex continuous
10-reservoir operation problem (Garousi-Nejad et al. 2016), but it
cannot solve a simple two-dimensional Rosenbrock function (original paper). The only reasonable conclusion is that the GA in the
original paper is not well tuned. The results in Table 1 support this
conclusion.
Table 1. GA and the PSO Calculated Objective Function of the Rosenvrock Function
Run
1
2
3
4
5
Best (minimum)
Average
Worst (maximum)
© ASCE
GA
PSO
−29
1.75 × 10
9.39 × 10−27
1.85 × 10−27
1.66 × 10−27
1.18 × 10−28
1.75 × 10−29
2.61 × 10−27
9.39 × 10−27
GA (reported in original paper)
FA (reported in original paper)
0.0044
0.0046
0.0041
0.5313
0.5000
0.0041
0.2089
0.5313
1.03 × 10−13
1.69 × 10−13
1.63 × 10−13
1.65 × 10−14
3.77 × 10−14
1.65 × 10−14
9.78 × 10−14
1.69 × 10−13
−26
1.53 × 10
4.76 × 10−22
9.59 × 10−22
2.85 × 10−25
4.80 × 10−27
4.80 × 10−27
2.87 × 10−22
9.59 × 10−22
07017019-1
J. Irrig. Drain Eng., 2018, 144(1): 07017019
J. Irrig. Drain. Eng.
The authors did not consider a constraint on maximum allowable change in storage for each time step. According to Fig. 6 in the
original paper, the reservoir storage fluctuates highly, which might
detrimentally affect dam stability. Therefore, the following constraint is suggested for future studies in order to take into account
dam stability:
Downloaded from ascelibrary.org by 80.82.77.83 on 10/27/17. Copyright ASCE. For personal use only; all rights reserved.
jStþ1 − St j < SC
ð1Þ
where Stþ1 = reservoir storage at t þ 1 time step; St = reservoir
storage at t time step; and SC = maximum allowable change in
storage within each month considering dam stability and safety
conditions.
The authors successfully solved the Aydoghmoush and Karun-4
reservoir operation problems using an exact method (i.e., nonlinear
programming). When an exact method can solve a particular problem, it is not clear that why one should use heuristic methods like
the GA or FA. Heuristic methods generally return solutions that are
worse than optimal (Sörensen 2015). Exact methods guarantee
finding the optimal solution. In order to do that, they not only have
to locate this solution in the solution space but also have to prove
that they are optimal. This process is exhaustively repetitive because the exact methods have to examine every single solution
in the solution space. In some real-world optimization problems,
this repetitive calculation is time-consuming and costly. Heuristic
methods are best second alternatives in such problems. But, in a
one-reservoir operation problem, exact methods perform sufficiently because the numbers of decision variables and constraints
are limited. Researchers could perform novel studies on matheuristics instead of focusing on the application of different heuristic
algorithms. The idea behind the matheuristics is to combine exact
algorithms with a local search via heuristics. This idea leads to
more computationally efficient exact methods.
The authors assert that a sensitivity analysis was made for GA
and FA parameters. But it is not transparent how it took place, and
the results of the sensitivity analysis were not given. The main purpose of a sensitivity analysis is to show how parameter selection
affects the final results’ accuracy. Therefore, the results of a sensitivity analysis should be the output uncertainty under different
given assumptions. The authors could present the sensitivity analysis with box-plots to support and quantify their statements such as
“the best solutions from the GA and FA strongly depend on the best
settings of algorithmic parameters” of the GA and FA. Also, the
way that the sensitivity analysis was carried out is vague throughout the original paper. If the authors had provided details on how
the sensitivity analysis was performed, the discusser would be able
to compare the results of Table 1 with the results of Table 4 in the
original paper.
The authors stated that “the process of producing an initial population in the GA and the FA is random. Therefore, the final value
of the objective function differs each time the algorithm is run.”
Thus, they performed five different runs for each algorithm. Considering the main goal, which is comparing the GA and FA, it is
more convenient to exclude the effects of the initial random solutions. When the effects of the initial random solution are excluded,
the underlying mathematic mechanism of the algorithm would be
the only source that makes a difference in performance. Chaotic
maps and fixed pseudorandom seeds can be applied to eliminate
the initial random solution’s impacts. Different chaotic maps
such as cubic (Xing et al. 2015), logistic (Ma 2012), and Lorenz
(Ebrahimzadeh and Jampour 2013) have been used in metaheuristic
algorithm so far. Also, the authors could simply use fixed pseudorandom seeds for both the GA and FA. It is highly recommended for
future studies that researchers report the pseudorandom seeds when
© ASCE
they work with a random-based method. Reporting such information helps other researchers to reproduce exact outputs; it will
standardize the methodology and help to make comparisons among
different methods easier.
Figures like Fig. 3 in the original paper and conclusions such as
“it is concluded from Fig. 3 that the FA converges faster than GA”
are redundant because it is obvious that with the same number of
function evaluations, the algorithm that has produced a better answer has a steeper convergence slope (in other words, it converges
faster). These same redundant conclusions are numerous in the literature (Bozorg-Haddad et al. 2014; Haddad et al. 2014; Asgari
et al. 2015; Azizipour et al. 2016).
Numerous published papers are engaged in playing the “up-thewall game” (Burke et al. 2009). The only aim in this game is to get
higher up the wall (i.e., obtain better results) than previous studies
or other methods. This game comes with no rules, just getting
higher up the wall for the sake of publication. Science, however,
is not a game. True innovation in metaheuristics research, therefore,
does not come from yet another method that performs better than
its competitors (Sörensen 2015). For example, the authors show in
the original paper that the GA is unable to solve a simple twodimensional Rosenbrock function, but the FA can. Then, GarousiNejad et al. (2016) show that the GA performs better than the FA in
the complex continuous 10-reservoir problem. Empirical evidence
provided in this discussion supports that the GA used in the original
paper had not been tuned well in favor of getting the FA higher up
the wall. Publications that play the up-the-wall game are too many
to list. Papers by Asgari et al. (2015), Azizipour et al. (2016),
and Hamedi et al. (2016), the original paper, and Garousi-Nejad
et al. (2016) are some recent examples of research that plays the
up-the-wall game without bringing any contribution to water resources engineering. The water resources community is invited
to drop and ban this detrimental direction of research.
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