Abstract
Whale optimization algorithm (WOA) has been developed based on the hunting behavior of humpback whales. Though it has a considerable convergence speed, WOA suffers from diversity in the solution due to the low exploration of search space. As a result, it tends to trap in local optima and suffer from low solution accuracy. This study proposes a novel improved WOA method (ImWOA) with increased diversity in the solution to avoid the aforesaid gaps. The random solution selection process in the search prey phase is altered to increase exploration. The whale's cooperative hunting strategy is also incorporated in the algorithm's exploitation phase to balance the exploration and exploitation phase of WOA. Also, the total iterations are divided into two halves explicitly for exploration and exploitation purposes. The modifications facilitate WOA to jump out of local optima, increase solution accuracy, and increase convergence speed. The experiments were carried out evaluating IEEE CEC 2017 functions in dimensions 10, 30, 50, and 100. The performances were compared with basic algorithms as well as recent WOA variants. Three engineering design problems have also been solved to check its problem-solving ability and compared with a wide range of algorithms. Moreover, the image segmentation problem with multiple thresholding approaches has been solved by using the proposed ImWOA. Comparing results with state-of-the-art algorithms and modified WOAs, statistical analysis, diversity analysis, and convergence analysis validate that ImWOA is superior or competitive.
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Appendix
Appendix
Function type | Function no | Function name | Range | Optimal value |
|---|---|---|---|---|
Unimodal | 1 | Shifted and rotated bent Cigar function | [− 100, 100] | 100 |
2 | Shifted and rotated Zakharov function | [− 100, 100] | 200 | |
Simple multimodal | 3 | Shifted and rotated Rosenbrock’s Function | [− 100, 100] | 300 |
4 | Shifted and rotated Rastrigin’s function | [− 100, 100] | 400 | |
5 | Shifted and rotated expanded Scaffer’s F6 Function | [− 100, 100] | 500 | |
6 | Shifted and rotated Lunacek Bi_Rastrigin function | [− 100, 100] | 600 | |
7 | Shifted and rotated Non-Continuous Rastrigin’s function | [− 100, 100] | 700 | |
8 | Shifted and rotated Levy Function | [− 100, 100] | 800 | |
9 | Shifted and rotated Schwefel’s function | [− 100, 100] | 900 | |
Hybrid | 10 | Hybrid function 1 (N = 3) | [− 100, 100] | 1000 |
11 | Hybrid function 2 (N = 3) | [− 100, 100] | 1100 | |
12 | Hybrid function 3 (N = 3) | [− 100, 100] | 1200 | |
13 | Hybrid function 4 (N = 4) | [− 100, 100] | 1300 | |
14 | Hybrid function 5 (N = 4) | [− 100, 100] | 1400 | |
15 | Hybrid function 6 (N = 4) | [− 100, 100] | 1500 | |
16 | Hybrid function 7 (N = 5) | [− 100, 100] | 1600 | |
17 | Hybrid function 8 (N = 5) | [− 100, 100] | 1700 | |
18 | Hybrid function 9 (N = 5) | [− 100, 100] | 1800 | |
19 | Hybrid function 10 (N = 6) | [− 100, 100] | 1900 | |
Composite | 20 | Composite function 1 (N = 3) | [− 100, 100] | 2000 |
21 | Composite function 2 (N = 3) | [− 100, 100] | 2100 | |
22 | Composite function 3 (N = 4) | [− 100, 100] | 2200 | |
23 | Composite function 4 (N = 4) | [− 100, 100] | 2300 | |
24 | Composite function 5 (N = 5) | [− 100, 100] | 2400 | |
25 | Composite function 6 (N = 5) | [− 100, 100] | 2500 | |
26 | Composite function 7 (N = 6) | [− 100, 100] | 2600 | |
27 | Composite function 8 (N = 6) | [− 100, 100] | 2700 | |
28 | Composite function 9 (N = 6) | [− 100, 100] | 2800 | |
29 | Composite function 10 (N = 3) | [− 100, 100] | 2900 | |
30 | Composite function 11 (N = 3) | [− 100, 100] | 3000 |
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Chakraborty, S., Sharma, S., Saha, A.K. et al. A novel improved whale optimization algorithm to solve numerical optimization and real-world applications. Artif Intell Rev 55, 4605–4716 (2022). https://doi.org/10.1007/s10462-021-10114-z
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DOI: https://doi.org/10.1007/s10462-021-10114-z