GOHBA: Improved Honey Badger Algorithm for Global Optimization
Abstract
:1. Introduction
- (1)
- The introduction of the Tent Chaos algorithm for initialization improves the diversity of the population and the quality of the initial population to achieve better optimization results.
- (2)
- The use of a new density factor helps the algorithm to explore more extensively in the whole solution space, especially in the early stage of the algorithm, which can effectively avoid premature convergence to a local optimal solution.
- (3)
- The golden sine strategy is introduced to improve the global search capability, accelerate the convergence speed, and help avoid falling into local optimal solutions.
- (4)
- Test the GOHBA on 23 test functions. Successfully solve two examples of engineering optimization problems as well as a quadruped robot path planning problem.
- Section 2: introduces the honey badger algorithm and proposes an improved GOHBA.
- Section 3: Compares the GOHBA with seven algorithms using 23 test functions. Analyzes performance via statistical tests and convergence analysis.
- Section 4: demonstrates the GOHBA’s application in engineering optimization and quadruped robot path planning.
- Section 5: summarizes experimental results, discusses limitations, and explores future development directions, such as integrating the GOHBA with other techniques.
2. Algorithm Analysis
2.1. The Honey Badger Algorithm
2.2. The Proposed Algorithm
2.2.1. Tent Sequence Initialization Population
2.2.2. Introduction of New Density Factors
2.2.3. Gold Sine Strategy
2.2.4. Algorithm Flow
2.3. Complexity Analysis
2.3.1. Computational Complexity
2.3.2. Space Complexity
2.4. The Path Planning Optimization Problem
3. Experiments
3.1. Experimental Setup and Assessment Criteria
3.2. Test Functions
3.3. Sensitivity Analysis
3.4. Experimental Results
3.5. Friedman Calibration
3.6. Wilcoxon Symbolic Rank Calibration
3.7. Convergence Analysis
3.8. Stability Analysis
4. GOHBA Application
4.1. Application to Engineering Design Problems
4.1.1. Robot Gripper Design Problem
4.1.2. Speed Reducer Design Problem
4.2. Robot Path Planning with GOHBA
Simulation of Robot Path Planning
4.3. GOHBA Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Function | D | R | f (x*) |
---|---|---|---|
30 | [−100,100] | 0 | |
30 | [−10,10] | 0 | |
30 | [−100,100] | 0 | |
30 | [−100,100] | 0 | |
30 | [−30,30] | 0 | |
30 | [−100,100] | 0 | |
30 | [−1.28,1.28] | 0 | |
30 | [−500,500] | −12569.4 | |
30 | [−5.12,5.12] | 0 | |
30 | [−32,32] | 0 | |
30 | [−600,600] | 0 | |
30 | [−50,50] | 0 | |
30 | [−50,50] | 0 | |
2 | [−65,65] | 1 | |
4 | [−5,5] | 0.00003075 | |
2 | [−5,5] | −1.0316285 | |
2 | [−5,5] | 0.398 | |
2 | [−2,2] | 3 | |
3 | [0,1] | −3.86 | |
6 | [0,1] | −3.32 | |
4 | [0,10] | −10 | |
4 | [0.10] | −10 | |
4 | [0,10] | −10 |
Function | Criterion | p/t 60/250 | p/t 30/500 | p/t 15/1000 |
---|---|---|---|---|
F1 | Mean Std Rank | 1.7142 × 10−283 0 2 | 0 0 2 | 0 0 2 |
F2 | Mean Std Rank | 1.5485 × 10−145 8.7921 × 10−145 3 | 1.2544 × 10−273 0 1.5 | 0 0 1.5 |
F3 | Mean Std Rank | 2.5563E−273 0 2 | 0 0 2 | 0 0 2 |
F4 | Mean Std Rank | 2.2952 × 10−143 9.0280 × 10−143 3 | 1.0078 × 10−268 0 1.5 | 0 0 1.5 |
F5 | Mean Std Rank | 2.5151 × 101 4.6295 × 10−1 2 | 2.4791 × 101 5.2181 × 10-1 3 | 2.4916 × 101 3.6635 × 10−1 1 |
F6 | Mean Std Rank | 1.0971 × 10−3 6.6149 × 10−4 3 | 2.3806 × 10−04 1.7511 × 10−04 2 | 9.5836 × 10−5 7.7331 × 10−5 1 |
F7 | Mean | 1.5468 × 10−4 | 1.3085 × 10−4 | 1.6314 × 10−4 |
Std | 1.3565 × 10−4 | 9.6256 × 10−5 | 1.5177 × 10−4 | |
Rank | 2 | 1 | 3 | |
F8 | Mean Std Rank | −1.1565 × 104 8.7136 × 102 3 | −1.1419 × 104 7.5399 × 102 1 | −1.1425 × 104 8.7099 × 102 2 |
F9 | Mean Std Rank | 0 0 2 | 0 0 2 | 0 0 2 |
F10 | Mean Std Rank | 4.4409 × 10−16 0 2 | 4.4409 × 10−16 0 2 | 4.4409 × 10−16 0 2 |
F11 | Mean Std Rank | 0 0 2 | 0 0 2 | 0 0 2 |
F12 | Mean Std Rank | 1.3269 × 10−4 7.5080 × 10−5 3 | 3.1881E × 10−5 2.6201 × 10−5 1 | 1.9846 × 10−5 3.1180 × 10−5 2 |
F13 | Mean Std Rank | 5.7978 × 10−3 6.7686 × 10−3 1 | 9.7015 × 10−3 2.0111 × 10−2 2 | 1.5350 × 10−2 2.1065 × 10−2 3 |
F14 | Mean Std Rank | 2.3088 3.1913 1 | 2.9375 3.5261 2 | 4.0693 4.2901 3 |
F15 | Mean Std Rank | 3.0756 × 10−4 1.3235 × 10−7 1 | 3.0780 × 10−4 8.7970 × 10−7 2 | 4.6868 × 10−4 1.1350 × 10−3 3 |
F16 | Mean Std Rank | −1.0316 3.7532 × 10−16 3 | −1.0316 3.5037 × 10−16 2 | −1.0316 3.4164 × 10−16 1 |
F17 | Mean Std Rank | 3.9789 × 10−1 0 2 | 3.9789 × 10−1 0 2 | 3.9789 × 10−1 0 2 |
F18 | Mean Std Rank | 3.0000 2.6773 × 10−15 1 | 3.5400 3.8184 2 | 6.7800 13.373 3 |
F19 | Mean Std Rank | −3.8622 2.1599 × 10−3 2 | −3.8626 1.1146 × 10−03 1 | −3.8620 2.3885 × 10−03 3 |
F20 | Mean Std Rank | −3.2282 6.3648 × 10−02 1 | −3.2142 8.4419 × 10−2 2 | −3.2353 8.9149 × 10−2 3 |
F21 | Mean Std Rank | −10.153 2.3119 × 10−15 3 | −10.153 1.1061 × 10−15 1 | −10.153 1.6833 × 10−15 2 |
F22 | Mean Std Rank | −10.403 1.4355 × 10−15 1 | −10.403 2.1682 × 10−15 2 | −10.250 1.0800 3 |
F23 | Mean | −10.536 | −10.536 | −10.536 |
Std | 2.2697 × 10−15 | 2.2555 × 10−15 | 2.4864 × 10−15 | |
Rank | 2 | 1 | 3 | |
Rank-Count Ave-Rank Overall-Rank | 47.00 2.04 2 | 40.00 1.74 1 | 51.00 2.22 3 |
Function | Algorithm | Mean | Std | Function | Algorithm | Mean | Std |
---|---|---|---|---|---|---|---|
F1 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 9.5334 × 10−136 1.8327 × 10−147 0 0 1.7665 × 10−73 4.7616 × 10−43 6.6684 × 10−2 4.8704 × 10−280 | 3.1770 × 10−135 8.6713 × 10−147 0 0 1.2490 × 10−72 3.2749 × 10−42 2.2264 × 10−02 0 | F13 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 0.50283 0.54545 6.3470 × 10−3 1.0836 × 10−2 1.8507 0.29398 4.9868 × 10−2 2.4079 | 0.35069 0.33952 1.0825 × 10-2 2.3800 × 10-2 0.48175 0.81989 2.7722 × 10-2 0.42596 |
F2 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.1649 × 10−72 3.1952 × 10−77 5.1704 × 10−242 7.3796 × 10−275 1.5914 × 10−36 1.0658 × 10−25 2.9972 × 103 2.3919 × 10−141 | 2.5286 × 10−72 1.0432 × 10−76 0 0 1.1253 × 10−35 5.3651 × 10−25 1.9594 × 1004 1.2551 × 10−140 | F14 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.9601 1.4506 3.7002 3.3275 1.0179 1.3150 10.788 3.6973 | 2.4640 1.6106 3.9934 3.8655 0.14058 0.88036 5.9670 4.1621 |
F3 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.8839 × 10−95 1.1811 × 10E−121 0 0 6.2076 × 10−82 5.0568 × 10−52 1.0715 × 102 1.7675 × 10−262 | 9.4665 × 10−95 6.3943 × 10−121 0 0 3.1551 × 10−81 2.4078 × 10−51 67.106 0 | F15 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 4.9888 × 10−3 5.8892 × 10−3 3.0749 × 10−4 3.0782 × 10−4 2.0645 × 10−3 1.4895E × 10−3 7.6863 × 10−3 4.0657 × 10−3 | 8.6964 × 10-3 1.1639 × 10-2 1.0135 × 10-10 1.3621 × 10-6 5.6323 × 10-3 3.9106 × 10-3 1.7056 × 10-2 7.7180 × 10-3 |
F4 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.3975 × 10−57 1.5153 × 10−65 5.6896 × 10−239 3.7000 × 10−268 1.9947 × 10−44 7.0883 × 1024 24.065 1.1857 × 10−138 | 3.5954E−57 3.5655E−65 0 0 1.0643 × 10−43 4.5737 × 10−23 6.4515 7.2777 × 10−138 | F16 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 −1.0316 | 3.0917 × 10-16 3.2349 × 10-16 3.2812 × 10-16 3.5888 × 10-16 3.7532 × 10-16 3.5110 × 10-10 2.7862 × 10-7 3.9746 × 10-16 |
F5 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 24.006 25.336 23.477 24.851 27.655 27.430 338.14 27.824 | 0.71976 0.70241 0.47340 0.53801 0.94309 0.47233 5.5200 × 102 0.75809 | F17 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 0.39789 0.39789 0.39789 0.39789 0.39789 0.39789 0.39789 0.39789 | 3.0917 × 10-16 3.2349 × 10-16 3.2812 × 10-16 3.5888 × 10-16 3.7532 × 10-16 3.5110 × 10-10 2.7862 × 10-7 3.9746 × 10-16 |
F6 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 2.4071 × 10−2 0.11606 5.4509 × 10−6 2.4749 × 10−4 2.2955 5.9312 × 10−3 5.8685 × 10−2 2.9545 | 7.2801 × 10−2 0.15916 7.5596 × 10−6 1.3729 × 10−4 1.5747 6.8283 × 10−3 2.1420 × 10−2 0.43331 | F18 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 3.0000 5.7000 3.0000 4.6200 3.0000 3.0000 4.6200 3.0000 | 1.8485 × 10-15 12.499 1.7690 × 10-15 6.4772 1.8485 × 10-15 7.5191 × 10-14 11.455 3.3020 × 10-15 |
F7 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 3.4028 × 10−4 3.8793 × 10−4 1.4679 × 10−4 1.2001 × 10−4 3.6102 × 10−4 2.6341 × 10-4 0.28906 2.9395 × 10−4 | 2.6880 × 10−4 2.7480 × 10−4 1.0950 × 10−4 1.1524 × 10−4 3.0664 × 10−4 2.2036 × 10−4 0.12683 2.5676 × 10−04 | F19 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −3.8618 −3.8612 −3.8623 −3.8623 −3.8628 −3.8628 −3.8627 −3.8628 | 2.5872 × 10-3 3.1846 × 10-3 1.8908 × 10-03 1.8908 × 10-03 1.0031 × 10-15 2.7858 × 10-12 4.2399 × 10-05 1.0327 × 10-15 |
F8 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −8.8728 × 103 −8.8750 × 103 −1.1355 × 104 −1.1591 × 104 −8.6730 × 103 −1.1312 × 104 −7.0389 × 103 −4.8415 × 103 | 9.6921 × 102 9.2706 × 102 9.7941 × 102 7.0580 × 102 1.7590 × 103 7.9397 × 102 5.8050 × 102 7.0982 × 102 | F20 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −3.2660 −3.2475 −3.2341 −3.2325 −3.2951 −3.2483 −3.1988 −3.2342 | 7.4959 × 10-2 0.10054 7.7610 × 10-2 7.8819 × 10-2 5.3324 × 10-2 5.8297 × 10-2 3.3200 × 10-2 8.3160 × 10-2 |
F9 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 0 0 0 0 0 0 1.5466 × 102 0 | 0 0 0 0 0 0 37.430 0 | F21 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −8.8796 −9.3659 −10.153 −10.1531 −10.003 −9.4977 −4.9875 −8.7948 | 2.9636 2.3962 3.5436 × 10-15 3.7725 × 10-15 1.0639 2.0217 2.9565 2.2724 |
F10 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.1944 1.0086 × 10−10 4.4409 × 10−16 0 4.4409 × 10−16 4.4409 × 10−16 16.703 4.4409 × 10−16 | 4.7756 6.2654 × 10−10 0 0 0 0 5.8009 0 | F22 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −9.6398 −9.2391 −10.403 −10.403 −10.117 −9.3778 −6.9863 −9.1301 | 2.3204 2.7069 2.0142 × 10-15 1.1349 × 10-15 1.4202 2.4018 3.5595 2.1995 |
F1 F11 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 0 0 0 0 0 0 2.0920 × 102 0 | 0 0 0 0 0 0 37.885 0 | F23 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | −9.0399 −9.2326 −10.536 −10.536 −10.400 −8.0526 −5.8102 −8.7555 | 3.0454 2.8235 2.4074 × 10-15 2.6250 × 10-15 0.94744 3.5864 3.7933 2.6778 |
F12 | HBA HBA1 HBA2 GOHBA BKA ECO GOOSE NRBO | 1.4532 × 10−4 4.5309 × 10−3 1.0044 × 10−6 3.0860 × 10−5 0.13958 2.7357 × 10−4 5.5369 0.26140 | 9.4521 × 10−4 1.5462 × 10-2 1.0240 × 10−6 2.1128 × 10−5 0.21776 7.7691 × 10−4 1.9790 8.2184 × 10−2 |
Functions | HBA | HBA1 | HBA2 | GOHBA | |
---|---|---|---|---|---|
F3 | Mean Std Rank | 1.1649 × 10−72 2.5286 × 10−72 5 | 3.1952 × 10−77 1.0423 × 10−76 4 | 5.1704 × 10−242 0 2 | 7.3796 × 10−275 0 1 |
F4 | Mean Std Rank | 1.3975 × 10−57 3.5954 × 10−57 5 | 1.5153 × 10−65 3.5655 × 10−65 4 | 5.6896 × 10−239 0 2 | 3.7007 × 10−268 0 1 |
F7 | Mean Std Rank | 3.4028 × 10−4 2.6880 × 10−4 5 | 3.8793 × 10−4 2.7480 × 10−4 7 | 1.4679 × 10−4 1.0950 × 10−4 2 | 1.2001 × 10−4 1.1524 × 10−4 1 |
F10 | Mean Std Rank | 1.1944 4.77567 7 | 1.0086 × 10−10 6.2654 × 10−10 6 | 4.4409 × 10−16 0 3 | 4.4409 × 10−16 0 3 |
F11 | Mean Std Rank | 0 0 4 | 0 0 4 | 0 0 4 | 0 0 4 |
F13 | Mean Std Rank | 0.50283 0.35069 5 | 0.54545 0.33952 6 | 6.3470 × 10−3 1.0825 × 10−2 1 | 1.0836 × 10−2 2.3835 × 10−2 2 |
F17 | Mean Std Rank | 0.39789 0 3 | 0.39789 0 3 | 0.39789 0 3 | 0.39789 0 3 |
F21 | Mean Std Rank | −8.8796 2.9636 6 | −9.3659 2.3962 5 | −10.153 3.5436 × 10−15 1 | −10.153 3.7725 × 10−15 2 |
F22 | Mean Std Rank | −9.6398 2.3204 4 | −9.2391 2.7069 6 | −10.403 2.0142 × 10−15 2 | −10.403 1.1349 × 10−15 1 |
F23 | Mean Std Rank | −9.0399 3.0454 5 | −9.2326 2.8235 4 | −10.536 2.4074 × 10−15 1 | −10.536 2.6250 × 10−15 2 |
Rank-Count | 49 | 49 | 21 | 20 | |
Ave-Rank | 4.9 | 4.9 | 2.1 | 2.0 | |
Overall-Rank | 5.5 | 5.5 | 2 | 1 | |
Functions | BKA | ECO | GOOSE | NRBO | |
F2 | Mean Std Rank | 1.5914 × 10−36 1.1253 × 10−35 6 | 1.0658 × 10−25 5.3651 × 10−25 7 | 2.9972 × 103 1.9594 × 104 8 | 2.3919 × 10−141 1.2551 × 10−140 3 |
F4 | Mean Std Rank | 1.9947 × 10−44 1.0643 × 10−43 6 | 7.0883 × 10−24 4.5737 × 10−23 7 | 24.065 6.4515 8 | 1.1857 × 10−138 7.2777 × 10−138 3 |
F7 | Mean Std Rank | 3.6102 × 10−4 3.0664 × 10−4 6 | 2.6341 × 10−4 2.2036 × 10−4 3 | 0.28906 0.12683 8 | 2.9395 × 10−4 2.5676 × 10−4 4 |
F10 | Mean Std Rank | 4.4409 × 10−16 0 3 | 4.4409 × 10−16 0 3 | 16.703 5.8009 × 100 8 | 4.4409 × 10⁻¹⁶ 0.0000 × 10⁰ 3 |
F11 | Mean Std Rank | 0 0 4 | 0 0 4 | 2.0920 × 102 37.885 8 | 0 0 4 |
F13 | Mean Std Rank | 1.8507 0.48175 7 | 0.29398 0.81989 4 | 4.9868 × 10−2 2.7722 × 10−2 3 | 2.4079 0.42596 8 |
F17 | Mean Std Rank | 3.6102 × 10−4 3.0664 × 10−4 6 | 0.39789 1.8099 × 10−7 8 | 0.39789 9.2929 × 10−8 7 | 0.39789 0 3 |
F21 | Mean Std Rank | −10.003 1.0639 3 | −9.4977 2.0217 4 | −4.9875 2.9565 8 | −8.7948 2.2724 7 |
F22 | Mean Std Rank | −10.117 1.4202 3 | −9.3778 2.40180 5 | −6.9863 3.5595 8 | −9.1301 2.1995 7 |
F23 | Mean Std Rank | −10.400 0.94744 3 | −8.0526 3.5864 7 | −5.8102 3.7933 8 | −8.7555 2.6778 6 |
Rank-Count | 47 | 52 | 74 | 48 | |
Ave-Rank | 4.7 | 5.2 | 7.4 | 4.8 | |
Overall-Rank | 3 | 7 | 8 | 4 |
Functions | HBA vs. GOHBA | HBA1 vs. GOHBA | HBA2 vs. GOHBA | BKA vs. GOHBA | ||||
---|---|---|---|---|---|---|---|---|
p | h | p | h | p | h | p | h | |
F1 | 3.3110 × 10−20 | 1 | 3.3110 × 10−20 | 1 | NaN | 0 | 3.3110 × 10−20 | 1 |
F2 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 |
F3 | 3.3110 × 10−20 | 1 | 3.3110 × 10−20 | 1 | NaN | 0 | 3.3110 × 10−20 | 1 |
F4 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 |
F5 | 3.1180 × 10−9 | 1 | 4.0380 × 10−5 | 1 | 9.5300 × 10−17 | 1 | 1.9520 × 10−17 | 1 |
F6 | 5.2790 × 10−6 | 1 | 9.5400 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 |
F7 | 1.5240 × 10−7 | 1 | 4.5400 × 10−9 | 1 | 0.10900 | 0 | 3.6920 × 10−7 | 1 |
F8 | 4.2060 × 10−17 | 1 | 1.5390 × 10−17 | 1 | 0.31580 | 0 | 8.8640 × 10−16 | 1 |
F9 | NaN | 0 | NaN | 0 | NaN | 0 | NaN | 0 |
F10 | 8.2230 × 10−2 | 0 | 0.15940 | 0 | NaN | 0 | NaN | 0 |
F11 | NaN | 0 | NaN | 0 | NaN | 0 | NaN | 0 |
F12 | 3.2870 × 10−8 | 1 | 2.7840 × 10−17 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 |
F13 | 5.0380 × 10−16 | 1 | 9.5400 × 10−18 | 1 | 2.4160 × 10−5 | 1 | 7.0660 × 10−18 | 1 |
F14 | 0.14290 | 0 | 1.2920 × 10−2 | 1 | 0.51920 | 0 | 6.3950 × 10−4 | 1 |
F15 | 0.49270 | 0 | 1.8870 × 10−5 | 1 | 1.5440 × 10−10 | 1 | 0.45030 | 0 |
F16 | 2.6330 × 10−2 | 1 | 0.10970 | 0 | 0..6270 | 0 | 0.42500 | 0 |
F17 | NaN | 0 | NaN | 0 | NaN | 0 | 0.15940 | 0 |
F18 | 0.64770 | 0 | 0.98320 | 0 | 0.76590 | 0 | 0.26960 | 0 |
F19 | 0.71350 | 0 | 3.1040 × 10−2 | 1 | 0.94920 | 0 | 2.6060 × 10−3 | 1 |
F20 | 1.3870 × 10−2 | 1 | 0.30880 | 0 | 0.34250 | 0 | 0.47070 | 0 |
F21 | 1.8480 × 10−2 | 1 | 7.0320 × 10−7 | 1 | 0.91390 | 0 | 3.8370 × 10−18 | 1 |
F22 | 9.2660 × 10−2 | 0 | 2.9130 × 10−5 | 1 | 7.0470 × 10−2 | 0 | 1.5940 × 10−18 | 1 |
F23 | 2.0950 × 10−6 | 1 | 5.3930 × 10−8 | 1 | 0.36810 | 0 | 3.6880 × 10−18 | 1 |
Functions | ECO vs. GOHBA | GOOSE vs. GOHBA | NRBO vs. GOHBA | |||||
p | h | p | h | p | h | |||
F1 | 3.3110 × 10−20 | 1 | 3.3110 × 10−20 | 1 | 3.3110 × 10-20 | 1 | ||
F2 | 7.0660 × 10-18 | 1 | 7.0660 × 10-18 | 1 | 7.0660 × 10-18 | 1 | ||
F3 | 3.3110 × 10-20 | 1 | 3.3110 × 10-20 | 0 | 3.3110 × 10-20 | 1 | ||
F4 | 7.0660 × 10-18 | 1 | 7.0660 × 10-18 | 1 | 7.0660 × 10-18 | 1 | ||
F5 | 1.0750 × 10-17 | 1 | 7.0660 × 10−18 | 1 | 8.4620 × 10−18 | 1 | ||
F6 | 6.3190 × 10−16 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | ||
F7 | 1.4760 × 10−4 | 1 | 7.0660 × 10−18 | 1 | 3.2740 × 10−5 | 1 | ||
F8 | 0.11360 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | ||
F9 | NaN | 0 | 3.3110 × 10−20 | 1 | NaN | 0 | ||
F10 | NaN | 0 | 3.3110 × 10−20 | 1 | NaN | 0 | ||
F11 | NaN | 0 | 3.3110 × 10−20 | 1 | NaN | 0 | ||
F12 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | 7.0660 × 10−18 | 1 | ||
F13 | 7.0660 × 10−18 | 1 | 2.7980 × 10−14 | 1 | 7.0660 × 10−18 | 1 | ||
F14 | 6.3950 × 10−4 | 0 | 1.6950 × 10−11 | 1 | 0.11500 | 0 | ||
F15 | 0.45030 | 1 | 7.0660 × 10−18 | 1 | 2.7920 × 10−11 | 1 | ||
F16 | 0.42500 | 1 | 2.0940 × 10−18 | 1 | 8.6570 × 10−2 | 0 | ||
F17 | 0.15940 | 1 | 3.3110 × 10−20 | 1 | NaN | 0 | ||
F18 | 0.26960 | 1 | 2.6330 × 10−14 | 1 | 3.4860 × 10−2 | 1 | ||
F19 | 2.6060 × 10−3 | 1 | 1.3570 × 10−14 | 1 | 1.0770 × 10−2 | 1 | ||
F20 | 0.47070 | 0 | 6.4630 × 10−6 | 1 | 6.3850 × 10−2 | 0 | ||
F21 | 3.8370 × 10−18 | 1 | 2.7650 × 10−18 | 1 | 2.7650 × 10−18 | 1 | ||
F22 | 1.5940 × 10−18 | 1 | 1.5940 × 10−18 | 1 | 1.6440 × 10−18 | 1 | ||
F23 | 3.6880 × 10−18 | 1 | 3.0830 × 10−18 | 1 | 3.0830 × 10−18 | 1 |
Algorithm | Best-Pos | Best-Score | ||||||
---|---|---|---|---|---|---|---|---|
a | b | c | e | f | l | δ | ||
HBA | 1.5000 × 102 | 1.5000 × 102 | 2.0000 × 102 | 0 | 10.000 | 1.0000 × 102 | 1.5978 | 4.2893 |
HBA1 | 1.5000 × 102 | 95.763 | 2.0000 × 102 | 50.000 | 1.5000 × 102 | 1.5059 × 102 | 3.1399 | 4.1529 |
HBA2 | 1.0238 × 102 | 10.000 | 1.7590 × 102 | 0 | 10.000 | 1.0000 × 102 | 1.0000 | 7.4389 × 10−16 |
GOHBA | 1.0000 × 102 | 38.197 | 2.0000 × 102 | 0 | 10.000 | 1.0000 × 102 | 1.5610 | 7.2741 × 10−17 |
BKA | 99.870 | 38.066 | 1.7466 × 102 | 0 | 32.737 | 1.0000 × 102 | 1.5215 | 8.4241 × 10−17 |
ECO | 1.5000 × 102 | 1.0825 × 102 | 1.5296 × 102 | 34.726 | 1.3030 × 102 | 1.6653 × 102 | 3.1400 | 5.4861 |
GOOSE | 1.2231 × 102 | 1.1863 × 102 | 1.9356 × 102 | 16.159 | 58.996 | 1.7274 × 102 | 2.4542 | 80.715 |
NRBO | 1.4884 × 102 | 1.4454 × 102 | 1.8424 × 102 | 0.56062 | 12.874 | 1.6113 × 102 | 1.7935 | 3.8083 |
Algorithm | Best-Pos | Best-Score | ||||||
---|---|---|---|---|---|---|---|---|
b | m | p | l1 | l2 | d1 | d2 | ||
HBA | 3.50000 | 0.70000 | 17.000 | 7.3000 | 7.7153 | 3.3502 | 5.2867 | 2.9945 × 103 |
HBA1 | 3.5047 | 0.70000 | 17.000 | 7.3000 | 7.7153 | 3.3502 | 5.2867 | 2.9963 × 103 |
HBA2 | 3.5000 | 0.70000 | 17.000 | 7.3000 | 7.7155 | 3.3502 | 5.2867 | 2.9945 × 103 |
GOHBA | 3.5000 | 0.70000 | 17.000 | 7.3000 | 7.7154 | 3.3502 | 5.2867 | 2.9945 × 103 |
BKA | 3.5000 | 0.70000 | 17.000 | 7.9660 | 7.9278 | 3.3515 | 5.2868 | 3.0054 × 103 |
ECO | 3.5026 | 0.70000 | 17.000 | 8.1823 | 7.7605 | 3.3549 | 5.2867 | 3.0059 × 103 |
GOOSE | 3.5030 | 0.70000 | 17.000 | 7.4587 | 8.3000 | 3.3553 | 5.2874 | 3.0117 × 103 |
NRBO | 3.5000 | 0.70000 | 17.000 | 7.3000 | 8.2906 | 3.3502 | 5.4968 | 3.1419 × 103 |
Algorithm | Map | |||
---|---|---|---|---|
MAP1 | MAP2 | MAP3 | ||
BKA | Mean | 32.142 | 47.456 | 65.6981 |
Std | 7.2900 × 10−15 | 2.1870 × 10−14 | 0 | |
ECO | Mean | 32.084 | 47.456 | 65.698 |
Std | 0.26197 | 2.1870 × 10−14 | 0 | |
GOHBA | Mean | 32.025 | 47.456 | 65.698 |
Std | 0.30645 | 2.1870 × 10−14 | 0 | |
GOOSE | Mean | 32.084 | 47.56 | 65.6981 |
Std | 0.18030 | 2.1870 × 10−14 | 0 | |
HBA | Mean | 32.142 | 47.456 | 65.698 |
Std | 7.2900 × 10−15 | 2.1870 × 10−14 | 0 | |
HBA1 | Mean | 32.054 | 47.456 | 65.698 |
Std | 0.28666 | 2.1870 × 10−14 | 0 | |
HBA2 | Mean | 32.084 | 47.456 | 65.6981 |
Std | 0.18030 | 2.1870 × 10−14 | 0 | |
NRBO | Mean | 32.142 | 47.456 | 65.698 |
Std | 7.2900 × 10−15 | 2.1870 × 10−14 | 0 |
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Huang, Y.; Lu, S.; Liu, Q.; Han, T.; Li, T. GOHBA: Improved Honey Badger Algorithm for Global Optimization. Biomimetics 2025, 10, 92. https://doi.org/10.3390/biomimetics10020092
Huang Y, Lu S, Liu Q, Han T, Li T. GOHBA: Improved Honey Badger Algorithm for Global Optimization. Biomimetics. 2025; 10(2):92. https://doi.org/10.3390/biomimetics10020092
Chicago/Turabian StyleHuang, Yourui, Sen Lu, Quanzeng Liu, Tao Han, and Tingting Li. 2025. "GOHBA: Improved Honey Badger Algorithm for Global Optimization" Biomimetics 10, no. 2: 92. https://doi.org/10.3390/biomimetics10020092
APA StyleHuang, Y., Lu, S., Liu, Q., Han, T., & Li, T. (2025). GOHBA: Improved Honey Badger Algorithm for Global Optimization. Biomimetics, 10(2), 92. https://doi.org/10.3390/biomimetics10020092