Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization
Abstract
:1. Introduction
2. Methodology
2.1. Evolutionary Algorithms and Their Parameterization
2.2. Case Studies
3. Searching Measure Metrics
3.1. Search Quality Measure Metrics
3.2. Convergence Measure Metrics
4. Case Study Results and Discussion
4.1. Search Quality Results
4.2. Convergence Measure Results
4.3. Solution Comparisons
5. Conclusions
- The three EAs have exhibited significantly different searching behaviours in both the solution space and decision space. Such differences can be related to their underlying model structures and the searching mechanisms. This demonstrates that the proposed run-time metrics are effective in revealing the searching properties of the EAs.
- From the obtained real-time metric results, it can be concluded that the DE has an overall best ability to locate feasible solutions as well as high quality solutions for the WDS design problems. The ACO performed overall the worst in identifying the optimal solutions as observed in this study. This provides a guideline for the selection of the algorithms for WDS design optimization.
- If the computational budget is rather limited, the GA can identify better solutions than the DE as shown in this study. This suggests that the GA is promising for the case when the optimization solution needs to be identified in a short time such as real-time WDS operation and management.
Author Contributions
Funding
Conflicts of Interest
References
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The Algorithm Name | Parameters of Each Algorithm | Parameter Values for Five Different Case Studies | ||||
---|---|---|---|---|---|---|
Hanoi (HP) | Extend Hanoi (EHP) | ZJ | Balerma (BN) | Rural Network (RN) | ||
ACO | 100 | 100 | 500 | 500 | 500 | |
1 | 1 | 1 | 1 | 1 | ||
0.98 | 0.98 | 0.98 | 0.98 | 0.98 | ||
5 | 5 | 5 | 5 | 5 | ||
DE | 100 | 100 | 500 | 1000 | 1000 | |
0.5 | 0.5 | 0.3 | 0.3 | 0.3 | ||
0.5 | 0.5 | 0.5 | 0.5 | 0.5 | ||
GA | 100 | 100 | 500 | 1000 | 1000 | |
0.9 | 0.9 | 0.9 | 0.9 | 0.9 | ||
0.02 | 0.02 | 0.06 | 0.02 | 0.02 |
Case Study | No. of Decision Variables | No. of Diameter Options | Size of Total Search Space | Pressure Head Constraint | Reference |
---|---|---|---|---|---|
Hanoi (HP) | 34 | 6 | [8] | ||
Extend Hanoi (EHP) | 34 | 10 | [34] | ||
ZJ | 164 | 14 | [36] | ||
Balerma (BN) | 454 | 10 | [17] | ||
Rural network (RN) | 476 | 15 | [37] |
Case Studies | Current Best Known Solution | GA | DE | ACO | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Best Solution | Worst Solution | Average Cost | Best Solution | Worst Solution | Average Cost | Best Solution | Worst Solution | Average Cost | ||
Hanoi (HP) ($M) | 6.081 [17] | 6.174 (1.5%) | 6.560 | 6.395 | 6.081 (0%) | 6.329 | 6.155 | 7.198 (18.4%) | 7.761 | 7.440 |
Extend Hanoi (EHP) ($M) | 5.346 [34] | 5.357 (0.2%) | 5.616 | 5.460 | 5.338 (−0.2%) | 5.364 | 5.341 | 5.432 (1.6%) | 5.718 | 5.582 |
ZJ ($M) | 7.082 [36] | 7.248 (2.3%) | 7.509 | 7.345 | 7.125 (0.6%) | 7.176 | 7.140 | 7.579 (7.0%) | 8.0362 | 7.787 |
Balerma (BN) (€M) | 1.923 [36] | 2.045 (6.3%) | 2.152 | 2.103 | 2.002 (4.1%) | 2.075 | 2.040 | 2.332 (21.3%) | 2.846 | 2.618 |
Rural Network (RN) ($M) | 31.220 [37] | 33.010 (5.7%) | 35.821 | 34.332 | 30.989 (−0.7%) | 31.776 | 31.396 | 36.737 (17.7%) | 39.963 | 38.332 |
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Bi, W.; Xu, Y.; Wang, H. Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization. Water 2020, 12, 695. https://doi.org/10.3390/w12030695
Bi W, Xu Y, Wang H. Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization. Water. 2020; 12(3):695. https://doi.org/10.3390/w12030695
Chicago/Turabian StyleBi, Weiwei, Yihui Xu, and Hongyu Wang. 2020. "Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization" Water 12, no. 3: 695. https://doi.org/10.3390/w12030695
APA StyleBi, W., Xu, Y., & Wang, H. (2020). Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization. Water, 12(3), 695. https://doi.org/10.3390/w12030695