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基于火鹰优化算法的论文
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Fire Hawk Optimizer on Open Source Package
Adel REMADI, Aiza AVILA CA
˜
NIVE, Michele Natacha ELA ESSOLA,
Vanshika SHARMA, Xingshan HE and Hamza LAMSAOUB
December 2022
Contents
1 Introduction 2
1.1 Selection of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Metahuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Fire Hawks Optimization 2
2.1 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Implementation of the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Results and performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Evaluation on a Sphere function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Evaluation on the Exponential function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Evaluation on the Ackley 1 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.4 Evaluation on the Becker-lago . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.5 Evaluation on Bird function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Contributions of each member 13
1
1 Introduction
1.1 Selection of the problem
For the project presented here, we decided to collaborate with the open-source package MealPy, which is a package that
develops nature-inspired meta-heuristic algorithms in order to implement them on applications such as Deep Learning.
The objective of our deliverable was to create a class in MealPy that would be able to implement the algorithm
proposed by the paper ”Fire Hawk Optimizer: a novel metaheuristic algorithm”[1]. There are several reasons that got
us interested into doing this project. First of all, the opportunity to make an open-source contribution was new to all
the members of the group and an exciting experience. Second, among all the proposed algorithms by MealPy’s founder,
FHO was the one that was published in Springer, a renown a global publisher that serves and supports the research
community, notably in Data Science. In addition, although the initial article on FHO had a recent publication date
(2022), it has already been cited several times in subsequent publications (despite being recent). Moreover, based on
the Authors’ extensive description, it seemed to outperform other meta-heuristic algorithms, which made it seem like
a meaningful project to us. The Authors of the FHO article are also references in the Data Science field with high
h-index, several publications and awards. The last reason of our choice was the intriguing fact that these Hawks ex-
ist in nature, in Australia’s Northern Territory, and their most common way of hunting is by scaring the preys using fire.
The following report aims to explain what the algorithm is about, the implementation that was carried out in Python
and finally a description of how the algorithm was tested on 5 functions in dimensions 2 and 25.
It is to be noted that the code produced by our group was submitted to the MealPy project. Our pull request was ac-
cepted, as the owner of the project was satisfied of our contribution: https://github.com/thieu1995/metaheuristics/
pull/8.
1.2 Metahuristic Algorithms
First we will solve the question: what are metaheuristic algorithms? These are approximate general purpose search and
optimization algorithms. They are iterative procedures that guide a subordinate heuristic by intelligently combining
different concepts to adequately explore and exploit the search space. The metahuristic is born after having an opti-
mization problem, which in first instance can be solved by two techniques: the exact and the approximate. The exact
ones lead us to the optimal solution, which is not always viable (due to computational cost, amount of data, etc.). On
the other hand, the approximate techniques do not guarantee reaching the best solution but do provide a solution close
to the actual one.
Within this last approach, we have Ad-hoc Heuristics (approximate techniques that are developed specifically for a
problem) and Metaheuristics (which are more general techniques that can be applied to different optimization prob-
lems). The latter are divided into trajectory-based ( which rely on a single candidate solution per iteration) and
population-based techniques, which consider multiple candidate solutions at the same time, and therefore allow differ-
ent strategies to be applied. These strategies have been classified into three categories: “Evolutionary Algorithms”,
“Swarm Intelligence”, and “Physics-Inspired Algorithms”.
The algorithm of interest in this report is considered a ”Swarm Based” algorithm.
2 Fire Hawks Optimization
2.1 Mathematical model
The algorithm that is implemented (FHO) tries to imitate the behavior of the birds in which it takes inspiration.
Initially, a number of candidate solutions (X) are determined, these are the position vectors of the hawks and preys,
followed by a random initialization process to identify the initial positions of these vectors on the search space.
2
X =
X
1
X
2
.
.
.
X
i
.
.
.
X
N
=
x
1
1
x
2
1
· · · x
j
1
· · · x
d
1
x
1
2
x
2
2
· · · x
j
2
· · · x
d
2
.
.
. :
.
.
.
.
.
.
.
.
.
x
1
i
x
2
i
· · · x
j
i
· · · x
d
i
.
.
. :
.
.
.
.
.
.
.
.
.
x
1
N
x
2
N
· · · x
j
N
· · · x
d
N
,
i = 1, 2, . . . , N.
j = 1, 2, . . . , d.
(1)
x
j
i
(0) = x
j
i,min
+ rand .
x
j
i,max
− x
j
i,min
,
i = 1, 2, . . . , N.
j = 1, 2, . . . , d.
(2)
Where: X
i
: represents the ith candidate solution in the search space. d: represents the dimension of the considered
problem N :the total number of solution candidates x
j
i
: the jth decision variable of the ith solution candidate x
j
i
(0): the
initial position of the solution candidates x
j
i,min
and x
j
i,max
: the minimum and maximum bounds of the jth decision
variable for the ith solution candidate rand: a uniformly distributed random number in the range of [0,1].
To determine the locations of the hawks in the search space, the evaluation of the objective function considers some
solutions as the hawks (the best solutions), while the rest are considered as ”preys”. While the best global solution is
supposed to be the main ”fire” that hawks use to hunt in the search space. This in mathematical representation would
look like:
PR =
PR
1
PR
2
.
.
.
PR
k
.
.
.
PR
m
, k = 1, 2 . . . , m. (3)
FH =
FH
1
FH
2
.
.
.
FH
l
.
.
.
FH
n
, l = 1, 2 . . . , n. (4)
where: P R
k
: is the kth prey in the search space regarding the total number of m preys F H
l
: is the lth fire hawk
considering a total number of n fire hawks in the search space.
Next, the distance between the hawks and the prey is calculated by:
D
l
k
=
p
(x
2
− x
1
)
2
+ (y
2
− y
1
)
2
,
l = 1, 2, . . . , n.
k = 1, 2, . . . , m.
(5)
3
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