令和2年度電気・電子・情報関係学会四国支部連合大会 講演論文集 (愛媛大学)
2020 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME UNIV.)

1-15

Whale Optimization Algorithm with Natural Enemy
Hidehiro SUGIOKA, Yoko UWATE and Yoshifumi NISHIO( Tokushima University)
1. Introduction
Swarm intelligence algorithm is optimization algorithm
which simulate behavior of creature. Examples are Ant
Colony Optimization (ACO), Particle Swarm Optimizatio(PSO) and Whale Optimization Algorithm (WOA), etc.
In this study, we propose a new WOA considering thatwhales escape from the natural enemy. We compare resultsof the proposed method and the conventional WOA.

2. Whale Optimization Algorithm
WOA is nature-inspired meta-heuristic optimization algorithm which simulate the feeding behavior of humpback
whales. WOA is characterized by high search performancefor unimodal functions.
WOA has some parameters. ⃗a is linearly decreased from−→
2 to 0 over the course of iteration. A is determined byEq. (1).
−→A = 2⃗a.r⃗1 − ⃗a. (r⃗1 : [0, 1])(1)
WOA updates position of agents by Eqs. (2), (3) or (4).
−→(if | A | ≤ 1, p ≤ 0.5)
{ −→−→ −→−→D = | C .X ∗ (t) − X (t)|(2)−→−→−→−→X (t + 1) = X (t) − A . D .
−→(if | A | ≤ 1, p > 0.5)
{ −→−→−→
D′ = |X ∗ (t) − X (t)|(3)−→′ bl−→−→X (t + 1) = D e cos (2πl ) + X ∗ (t).
−→(if | A | > 1)
{ −−−→ −−−→ −→Drand = |Xrand − X (t)|(4)−→−−−→ −→ −−−→X (t + 1) = Xrand − A .Drand .

by five. There are two types of whales chased by naturalenemies. In the first type, chased whales move randomly
within the search range. In the second type, the chased
whale moves according to Eq. (8).
{ −−−→−−−→ −→Drand = 3|Xrand − X (t)|(8)−→−−−→ −→ −−−→X (t + 1) = Xrand − A .Drand .

4. Simulation Results
We compare WOANE to the conventional WOA withbenchmark functions. Formula, range and the optimal valueof each function are shown in Table 1. The xi denotes idimensional variable in the function.

Table 1: Benchmark functions.
Name{ −→−→−
→D′ = |X ∗ (t) − Xe (t)|−→−→−→Xe (t + 1) = D′ ebl cos (2πl ) + Xw (t).

(if p > 0.5) (6)−→−→Where Xe is position of Natural enemy and Xw is positionof the farthest whales from the optimal solution.
Whales escape from natural enemies under Eq. (7).
−→−
→−
→−→
|Xe (t) − X (t)| < |X ∗ (t) − Xw (t)|.

(7)

In addition, the whale that once escaped from a natural enemy will not escape until the number of iterations increases

Range

Optimal value[-100,100]

0[-500,500]−1.26 × 104[xi 2 − 10 cos(2πxi ) + 10][-5.12,5.12]

01 ∑ 2 ∏xi
xi −cos( )4000i[-600,600]

0n
∑

f1

∑

f2
f3n
∑
i=1

f4xi

2

i=1

n

−xi sin(√|xi |)

i=1

n

n

i=1

i=1

Each numerical experiment runs 100 times. In each test
function, we define tmax = 2000, n = 30. Average value
and standard deviation are shown in Table 2.

Table 2: Results of WOA and the proposed method.
WOAf1

3. Proposed Method
The possibility that WOA finds local solution is high.
We propose Whale Optimization Algorithm with NaturalEnemy (WOANE) to escape from the local solution. In
WOANE, when a search agent approaches a natural enemy
agent, it searches globally. Natural enemy chases whales
the farthest whales from optimal solution. Natural enemy
moves according to Eq. (5) or (6).
{ −→−→ −→−→D = | C .Xw (t) − Xe (t)|(5)−→−→−→−→ (if p ≤ 0.5)
Xe (t + 1) = Xe (t) − A . D .

Formula

f2
f3
f4

WOANE

WOANE(ramdom)(Eq. (8))

ave

9.66 × 10−84

1.06 × 10−78

9.63 × 10−84

std

6.09 × 10−83

1.04 × 10−77

6.09 × 10−83

ave−7.22 × 103−7.23 × 103−7.27 × 103

std

5.83 × 102

5.72 × 102

5.50 × 102

ave

1.20

0.552

0.375

std

3.75

2.48

1.64

ave

9.90 × 10−3

6.53 × 10−3

4.91 × 10−3

std

2.37 × 10−2

1.26 × 10−2

8.94 × 10−2

Both WOANE obtain better results than the conventional
WOA in multimodal function. WOANE, in which whales
escape randomly, obtain inferior results to the conventional
one in unimodal function. One the other hand, WOANE
that the whale escapes according to Eq. (7) obtain the same
result as the conventional WOA in the unimodal function.

5. Conclusion
We proposed the new WOA considering that whales escape from the natural enemy to escape from the local solution. The search performance of the conventional WOA
proposal method is compared by searching the minimum
value of the benchmark function. We confirmed that theproposed method obtains better results than the conventional WOA in multimodal functions.