Optimal Exploitation of Urban Water Supply Networks Based on Pressure Management with the Nondominated Sorting Differential Evolution (NSDE) Algorithm
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Optimization Algorithm
- NSDE exhibits a good balance between convergence (finding solutions close to the true Pareto front) and diversity (exploring different regions of the Pareto front). It has been observed to maintain a diverse set of high-quality solutions throughout the optimization process.
- NSDE is known for its efficiency in terms of computational time and resource utilization. It can effectively handle large-scale optimization problems and converge to near-optimal solutions within a reasonable number of iterations.
- NSDE is robust against noisy or uncertain objective functions. It can handle objective functions with stochastic variations or noise, making it suitable for real-world optimization scenarios where objective values might be subject to variability.
- NSDE tends to produce a well-distributed set of solutions that cover different regions of the Pareto front. This feature allows decision-makers to gain insights into the trade-offs between conflicting objectives and make informed decisions based on their preferences.
- NSDE can be easily adapted and applied to various domains, including water supply network optimization. It can handle different types of decision variables, constraints, and objective functions commonly encountered in such applications.
- Generate the initial population based on constraints and scale of the problem,
- Evaluate the population based on the defined objective functions,
- Apply the non-superior sorting method to categorize the population based on their performance,
- Calculate the control parameter called Crowding Distance for each member in each group, which represents the closeness of the target sample to other members of the population in that group (target group),
- Select the parent population for reproduction,
- Perform jump and intersection.
2.2. The EPANET Model
2.3. Algorithm Implementation and Coding
2.4. Equations and Laws in Water Distribution Networks
- Losses due to friction along the walls of the pipes;
- Losses due to disturbances in the flow caused by equipment and other factors that alter the flow conditions (known as local losses).
2.5. Formulation of the Optimization
2.6. Alternative Techniques
- Alternative optimization techniques offer different search strategies and exploration-exploitation balances. By considering multiple approaches, you can explore different regions of the search space and potentially discover better solutions that may have been missed by a single technique. Each technique has its strengths and weaknesses, so combining them can provide a more comprehensive search.
- Different optimization techniques may have specific adaptations or variations designed for particular problem characteristics. By exploring alternative techniques, you may find an approach that is better suited for the specific problem at hand. For example, some techniques may excel in handling discrete variables or constraints, while others may be more efficient for continuous optimization or multi-objective problems.
- Comparing the performance of different optimization techniques can provide valuable insights into their strengths and limitations. It allows you to assess factors such as convergence speed, solution quality, robustness, and scalability. Comparative analysis helps in selecting the most suitable optimization technique for a given problem and understanding the trade-offs involved.
- By using alternative optimization techniques, you can benchmark and verify the results obtained using NSDE. This process ensures the reliability and accuracy of the optimization outcomes. Verification through different techniques provides confidence that the solutions achieved are robust and not biased due to a particular algorithm’s limitations.
3. Results and Discussion
- The final point can be determined based on a fixed and predetermined number of pressure-relief valves in the system,
- The minimum required pressure reduction in the desired network can be used to determine the final point (in general, the minimum required improvement in the objective function),
- The final point can be determined based on the location on the curve where increasing the number of pressure-relief valves does not significantly decrease the pressure and leakage of the entire system network,
- The maximum approved budget for the pressure management plan can be used to determine the end point.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
NSDE | Nondominated Sorting Differential Evolution |
PSO | Particle swarm optimization |
EPANET | US Environmental Protection Agency’s hydraulic design software |
GA | Genetic algorithm |
NSGA-II | Non-Dominated Sorting Genetic Algorithm II |
CP | Crossover probability |
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Parameter | Population Size | Max Iteration | Crossover Pop. | Scaling Factor |
---|---|---|---|---|
Value | 150 | 100 | 0.70 | 0.50 |
No. | Active Valve Number | Ave. Network Pressure (Water Meters) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
0 | Active valve number | 63.96 | ||||||||
1 | Active valve number | 1 | 52.71 | |||||||
2 | Active valve number | 1 | 25 | 40.86 | ||||||
3 | Active valve number | 1 | 4 | 13 | 36.55 | |||||
4 | Active valve number | 1 | 4 | 6 | 15 | 32.25 | ||||
5 | Active valve number | 1 | 4 | 11 | 13 | 26 | 28.06 | |||
6 | Active valve number | 1 | 4 | 11 | 13 | 26 | 38 | 27.71 | ||
7 | Active valve number | 1 | 4 | 13 | 14 | 26 | 33 | 20 | 27.36 | |
8 | Active valve number | 1 | 4 | 6 | 15 | 26 | 33 | 20 | 13 | 27.05 |
No. | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|
Percentage reduction | 0 | 17.589 | 36.116 | 42.855 | 49.578 | 56.129 | 56.676 | 57.223 | 57.708 |
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Cemiloglu, A.; Licai, Z.; Ugurenver, A.; Nanehkaran, Y.A. Optimal Exploitation of Urban Water Supply Networks Based on Pressure Management with the Nondominated Sorting Differential Evolution (NSDE) Algorithm. Water 2023, 15, 2583. https://doi.org/10.3390/w15142583
Cemiloglu A, Licai Z, Ugurenver A, Nanehkaran YA. Optimal Exploitation of Urban Water Supply Networks Based on Pressure Management with the Nondominated Sorting Differential Evolution (NSDE) Algorithm. Water. 2023; 15(14):2583. https://doi.org/10.3390/w15142583
Chicago/Turabian StyleCemiloglu, Ahmed, Zhu Licai, Abbas Ugurenver, and Yaser A. Nanehkaran. 2023. "Optimal Exploitation of Urban Water Supply Networks Based on Pressure Management with the Nondominated Sorting Differential Evolution (NSDE) Algorithm" Water 15, no. 14: 2583. https://doi.org/10.3390/w15142583