Study on an Adaptive Co-Evolutionary ACO Algorithm for Complex Optimization Problems
Abstract
:1. Introduction
2. Related Works
3. Basic Method
3.1. The CEA
3.2. The ACO Algorithm
3.3. Adaptive ACO Algorithm
4. Adaptive Co-Evolutionary ACO (SCEACO) Algorithm
4.1. The Idea of the SCEACO Algorithm
4.2. The Model of the SCEACO Algorithm
4.3. The Steps of the SCEACO Algorithm
- Step 1.
- The ant colony is divided into multiple sub-populations in a common search space, each sub-population performs the search activity and pheromone updating strategy. The multi-objective optimization problem is divided into several sub-optimization problems, then each sub optimization problem corresponds to one sub-population.
- Step 2.
- Initialize the parameters of the SCEACO algorithm. These parameters include the control parameters and , ant size , the pheromone trial evaporation rate , the maximum iteration times , and the iteration algebraic counter . For the initialized number of ants, each ant stores these parameters in the form of .
- Step 3.
- Calculate the fitness value of each individual in each sub-population, determine whether the result meets the end condition. If the result meets the end condition, then the result is output. Otherwise go to Step 4.
- Step 4.
- The pheromone is updated for each individual according to the improved pheromone updating Equations (3)–(6).
- Step 5.
- In each sub-population, the elitist strategy is used to retain some elitist individuals. The other ants are evolved to generate a new population.
- Step 6.
- Each sub-population selects the current optimal individual, which is used to form a complete solution with the individual of different sub-population in order to complete the information interaction among these sub-populations.
- Step 7.
- The min-max ant strategy is used to set pheromone concentration for each path
- Step 8.
- Determine whether the maximum number of iterations is reached. If the number of iterations is reached, then the result is output. Otherwise go to Step 3.
5. Application of the SCEACO Algorithm in Gate Assignment
5.1. Construct the Optimization Model of Gate Assignment
5.2. Gate Assignment Method by Using the SCEACO Algorithm
6. Case Analysis
6.1. Data Source and Experimental Environment
6.2. Experimental Result
6.3. Comparison and Analysis of the Experimental Results
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Gate | Type | Walking Distance (m) | Gate | Type | Walking Distance (m) |
---|---|---|---|---|---|
G1 | M | 190 | G16 | L | 115 |
G2 | M | 975 | G17 | M | 215 |
G3 | L | 400 | G18 | S | 535 |
G4 | M | 333 | G19 | M | 1050 |
G5 | L | 260 | G20 | M | 170 |
G6 | S | 135 | G21 | L | 585 |
G7 | M | 1100 | G22 | M | 1250 |
G8 | M | 150 | G23 | L | 500 |
G9 | L | 384 | G24 | L | 920 |
G10 | M | 960 | G25 | L | 270 |
G11 | S | 1000 | G26 | M | 230 |
G12 | L | 235 | G27 | L | 265 |
G13 | S | 1200 | G28 | L | 450 |
G14 | M | 580 | G29 | M | 1300 |
G15 | M | 440 | G30 | L | 426 |
Flight | Arrival Time | Departure Time | Walking Distance (m) | Type |
---|---|---|---|---|
F1 | 26 July 2015 0:05:00 | 26 July 2015 1:15:00 | 482 | M |
F2 | 26 July 2015 0:05:00 | 26 July 2015 1:45:00 | 273 | S |
F3 | 26 July 2015 0:10:00 | 26 July 2015 1:30:00 | 261 | S |
F4 | 26 July 2015 0:15:00 | 26 July 2015 1:30:00 | 116 | S |
F5 | 26 July 2015 0:15:00 | 26 July 2015 3:15:00 | 244 | S |
F6 | 26 July 2015 0:20:00 | 26 July 2015 1:30:00 | 312 | M |
F7 | 26 July 2015 0:25:00 | 26 July 2015 2:40:00 | 340 | M |
F8 | 26 July 2015 0:30:00 | 26 July 2015 1:00:00 | 198 | S |
F9 | 26 July 2015 0:35:00 | 26 July 2015 8:10:00 | 184 | S |
F10 | 26 July 2015 0:35:00 | 26 July 2015 10:55:00 | 494 | M |
F11 | 26 July 2015 0:40:00 | 26 July 2015 7:00:00 | 19 | L |
F12 | 26 July 2015 0:45:00 | 26 July 2015 6:40:00 | 443 | L |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
F200 | 26 July 2015 19:30:00 | 26 July 2015 20:25:00 | 252 | S |
F201 | 26 July 2015 19:35:00 | 26 July 2015 20:25:00 | 378 | M |
Gate | Flights | Total | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
G1 | F38 | F59 | F78 | F96 | F140 | F172 | 6 | ||||
G2 | F36 | F116 | F135 | F159 | 4 | ||||||
G3 | F34 | F74 | F95 | F107 | F134 | F148 | 6 | ||||
G4 | F8 | F32 | F101 | F110 | F147 | F173 | 6 | ||||
G5 | F15 | F41 | F56 | F71 | F94 | F100 | F113 | F129 | F157 | 9 | |
G6 | F31 | F51 | F126 | F141 | F169 | 5 | |||||
G7 | F17 | F65 | F89 | F124 | F179 | 5 | |||||
G8 | F1 | F30 | F46 | F60 | F164 | 5 | |||||
G9 | F10 | F29 | F40 | F58 | F70 | F88 | F139 | F146 | F156 | 9 | |
G10 | F16 | F48 | F90 | F161 | 4 | ||||||
G11 | F13 | F37 | F53 | F145 | F171 | 5 | |||||
G12 | F14 | F61 | F72 | F92 | F106 | F115 | F131 | F144 | F155 | F193 | 10 |
G13 | F3 | F133 | F151 | F160 | F189 | 5 | |||||
G14 | F28 | F39 | F50 | F132 | F152 | F163 | F198 | 7 | |||
G15 | F18 | F44 | F68 | F166 | F185 | F192 | 6 | ||||
G16 | F26 | F42 | F108 | F119 | F123 | F162 | F184 | 7 | |||
G17 | F6 | F45 | F55 | F67 | F109 | F150 | F195 | 7 | |||
G18 | F25 | F82 | F86 | F167 | F199 | 5 | |||||
G19 | F4 | F112 | F197 | 3 | |||||||
G20 | F24 | F43 | F57 | F69 | F187 | 5 | |||||
G21 | FF23 | F87 | F105 | F118 | F125 | F158 | F188 | 7 | |||
G22 | F22 | F177 | F183 | 3 | |||||||
G23 | F9 | F21 | F33 | F47 | F52 | F64 | F73 | F168 | F181 | F191 | 10 |
G24 | F2 | F99 | F111 | F122 | F130 | F149 | F170 | F190 | 8 | ||
G25 | F11 | F35 | F54 | F63 | F83 | F194 | 6 | ||||
G26 | F12 | F27 | F117 | F128 | F138 | F176 | F182 | 7 | |||
G27 | F20 | F49 | F62 | F80 | F85 | F153 | F196 | 7 | |||
G28 | F7 | F75 | F91 | F104 | F120 | F127 | F137 | F201 | 8 | ||
G29 | F19 | F66 | F154 | F200 | 4 | ||||||
G30 | F5 | F93 | F114 | F121 | F136 | F165 | F186 | 7 | |||
Total | 186 |
Algorithms | ACO Algorithm | SACO Algorithm | SCEACO Algorithm | ||||||
---|---|---|---|---|---|---|---|---|---|
Times | Iterations | Optimal Value | Flights | Iterations | Optimal Value | Flights | Iterations | Optimal Value | Flights |
1 | 103 | 0.4010 | 155 | 32 | 0.3665 | 165 | 76 | 0.3216 | 181 |
2 | 126 | 0.3941 | 158 | 93 | 0.3686 | 161 | 83 | 0.3243 | 174 |
3 | 115 | 0.3962 | 153 | 98 | 0.3553 | 156 | 60 | 0.3269 | 171 |
4 | 58 | 0.3755 | 162 | 85 | 0.3662 | 151 | 21 | 0.322 | 177 |
5 | 64 | 0.3847 | 166 | 79 | 0.3689 | 170 | 58 | 0.3182 | 182 |
6 | 149 | 0.4070 | 155 | 61 | 0.3658 | 168 | 33 | 0.3266 | 173 |
7 | 121 | 0.3998 | 157 | 82 | 0.3764 | 162 | 64 | 0.3160 | 186 |
8 | 158 | 0.3938 | 166 | 114 | 0.3689 | 180 | 88 | 0.3225 | 175 |
9 | 74 | 0.3855 | 163 | 77 | 0.3613 | 162 | 18 | 0.3246 | 173 |
10 | 143 | 0.3987 | 167 | 83 | 0.3648 | 153 | 96 | 0.3185 | 183 |
11 | 69 | 0.3891 | 162 | 105 | 0.3565 | 167 | 10 | 0.3165 | 181 |
12 | 79 | 0.3973 | 154 | 100 | 0.3698 | 162 | 20 | 0.3227 | 180 |
13 | 156 | 0.3826 | 159 | 39 | 0.3471 | 167 | 37 | 0.3168 | 175 |
14 | 37 | 0.3990 | 163 | 74 | 0.3609 | 164 | 43 | 0.3169 | 176 |
15 | 103 | 0.3805 | 163 | 168 | 0.3742 | 164 | 88 | 0.3198 | 177 |
16 | 138 | 0.4016 | 155 | 41 | 0.3676 | 155 | 80 | 0.3207 | 183 |
17 | 65 | 0.3984 | 161 | 80 | 0.3556 | 163 | 76 | 0.3244 | 182 |
18 | 97 | 0.3988 | 157 | 73 | 0.3718 | 158 | 34 | 0.3217 | 183 |
19 | 141 | 0.3793 | 166 | 11 | 0.3632 | 155 | 28 | 0.3200 | 183 |
20 | 109 | 0.3974 | 158 | 73 | 0.3689 | 167 | 44 | 0.3244 | 173 |
Average | 105.5 | 0.3930 | 160 | 78.4 | 0.3649 | 162.5 | 52.85 | 0.3213 | 178.4 |
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Zhao, H.; Gao, W.; Deng, W.; Sun, M. Study on an Adaptive Co-Evolutionary ACO Algorithm for Complex Optimization Problems. Symmetry 2018, 10, 104. https://doi.org/10.3390/sym10040104
Zhao H, Gao W, Deng W, Sun M. Study on an Adaptive Co-Evolutionary ACO Algorithm for Complex Optimization Problems. Symmetry. 2018; 10(4):104. https://doi.org/10.3390/sym10040104
Chicago/Turabian StyleZhao, Huimin, Weitong Gao, Wu Deng, and Meng Sun. 2018. "Study on an Adaptive Co-Evolutionary ACO Algorithm for Complex Optimization Problems" Symmetry 10, no. 4: 104. https://doi.org/10.3390/sym10040104
APA StyleZhao, H., Gao, W., Deng, W., & Sun, M. (2018). Study on an Adaptive Co-Evolutionary ACO Algorithm for Complex Optimization Problems. Symmetry, 10(4), 104. https://doi.org/10.3390/sym10040104