令和3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
2021 Shikoku-Section Joint Convention Record of the Institutes of Electrical and Related Engineers

1-31
Whale Optimization Algorithm with Agents Being Chased by Orcas
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 orca. We compare results of theproposed method and the conventional WOA.

t − tmax /2 2) .
100−→−→−→−→V (t + 1) = w V (t) + X (t) − X (t − 1).

w(t) = rand[0.5, 1.5] exp ({ −→−→ −→−→
D = | C .X ∗ (t) − X (t)|−→−→−→−→−→X (t + 1) = w(t) V (t) + X (t) − A . D .
−→(if | A | ≤ 1, p > 0.5)
{ −→−→−→
D′ = |X ∗ (t) − X (t)|−→−→−→−→→X (t + 1) = −w (t) V (t) + D′ ebl cos (2πl ) + X ∗ (t).
−→(if | A | > 1)
{ −−−→ −−−→ −→Drand = |Xrand − X (t)|−→−→−−−→ −→ −−−→−→X (t + 1) = w (t) V (t) + Xrand − A .Drand .

The possibility that WOA finds local solution is high. We
propose Whale Optimization Algorithm with Orca(WOAO)
to escape from the local solution. In WOAO, when a search
agent approaches an Orca agent, it will perform a diﬀerent
search than usual. Orca chases whales the farthest whales
from optimal solution. Orca moves according to Eqs. (4)or (5).
{ −→−→ −→−→D = | C .Xw (t) − Xe (t)|(4)−→−→−→−→ (if p ≤ 0.5)
Xe (t + 1) = Xe (t) − A . D .

(if p > 0.5) (5)−→−→Where Xe is position of orca and Xw is position of thefarthest whales from the optimal solution. Whales escapefrom orcas under Eq. (6).
−→−→−→−→|Xe (t) − X (t)| < |X ∗ (t) − Xw (t)|/2.

(6)

When escaping from a orca, the whale move in consideration of its previous movement. The chased whale moves
according to Eqs. (7)-(11).

(10)

(11)

We compare WOAO 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

Formulan∑f1∑

i=1nf2xi2√−xi sin(|xi |)RangeOptimal value[-100,100]

0[-500,500]− 418.9829 × n

i=1

Each numerical experiment runs 100 times. In each test
function, we define tmax = 1000, n = 30 and 50. Averagevalues of 100 times are shown in Table 2.

Table 2: Results of WOA and the proposed method.
f1
f2{ −→−→−→
D′ = |X ∗ (t) − Xe (t)|−→−→−→Xe (t + 1) = D′ ebl cos (2πl ) + Xw (t).

(9)

4. Simulation Results⃗ is decreased from 2 to 0 over the course of
Where |A|
iteration.

3. Proposed Method(8)−→(if | A | ≤ 1, p ≤ 0.5)

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 performance⃗ isfor unimodal functions. WOA has some parameters. |A|decreased from 2 to 0 over the course of iteration. WOA
updates position of agents by Eqs. (1), (2) or (3).
−→(if | A | ≤ 1, p ≤ 0.5)
{ −→−→ −→−→
D = | C .X ∗ (t) − X (t)|(1)−→−→−→−→X (t + 1) = X (t) − A . D .
−→(if | A | ≤ 1, p > 0.5)
{ −→−→−→
D′ = |X ∗ (t) − X (t)|(2)−→′ bl−→−→X (t + 1) = D e cos (2πl ) + X ∗ (t).
−→(if | A | > 1)
{ −−−→ −−−→ −→Drand = |Xrand − X (t)|(3)−→−−−→ −→ −−−→X (t + 1) = Xrand − A .Drand .

(7)

WOA

WOAO

30 dimensions

7.07 × 10−43

9.59 × 10−3150 dimensions

8.56 × 10−36

3.86 × 10−27

30 dimensions−6852−8884

50 dimensions−11191−13528WOAO obtains better results than the conventional WOA
in multimodal function. However WOAO obtains inferior
results to the conventional one in unimodal function.

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

–31–