Related Experiment Video
Updated: Aug 10, 2026
11:53
Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
Published on: December 9, 2012
Risk- and robustness-based solutions to a multi-objective water distribution system rehabilitation problem under
Z Kapelan1, D A Savic, G A Walters
1Department of Engineering, University of Exeter, Harrison Building, North Park Road, Exeter EX4 4OF, United Kingdom. Z.Kapelan@ex.ac.uk
Summary
This study optimizes water distribution system rehabilitation by minimizing cost and maximizing robustness or minimizing risk under uncertain demands. A novel rNSGAII method achieves significant computational savings.
Area of Science:
- Environmental Engineering
- Operations Research
- Civil Engineering
Background:
- Water distribution systems (WDS) require rehabilitation to ensure reliable service.
- Rehabilitation planning faces uncertainty, primarily from future water consumption.
- Optimizing WDS rehabilitation involves balancing cost, robustness, and risk.
Purpose of the Study:
- To formulate WDS rehabilitation as a multi-objective optimization problem under uncertainty.
- To develop and evaluate a novel optimization method (rNSGAII) for WDS rehabilitation.
- To compare two alternative objective formulations: maximizing robustness versus minimizing risk.
Main Methods:
- Formulating WDS rehabilitation as a multi-objective optimization problem with cost as one objective.
- Modeling uncertain demands using probability density functions (PDFs).
- Employing the Latin Hypercube sampling technique and a modified NSGAII algorithm (rNSGAII) for efficient computation.
Main Results:
- The rNSGAII method significantly reduces computational load compared to full sampling.
- Both proposed methodologies successfully identify robust (near) Pareto optimal fronts.
- The New York tunnels case study validates the effectiveness of the developed approaches.
Conclusions:
- The rNSGAII method offers a computationally efficient approach to WDS rehabilitation optimization.
- Multi-objective optimization effectively balances competing goals in WDS rehabilitation.
- The study provides valuable insights for planning resilient and cost-effective WDS upgrades.
Related Concept Videos
01:17Design Example: Analyzing Capacity Contours for Flood Risk Assessment
Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a vital tool in this process, as they illustrate the potential spread of water at specific levels in a given area. In the context of building a bund across a small valley, these contours play a critical role in evaluating the safety of nearby residential areas.In this example, the bund is intended to store stormwater in the valley. The engineers...
01:27Design Example: Design of an Irrigation Channel
Trapezoidal channels are widely used in irrigation systems due to their cost-effectiveness and efficiency in conveying water. Trapezoidal channels feature a flat bottom and sloping sides, making them stable and easier to construct compared to other shapes. The bottom width and side slope ratio are determined based on the required flow capacity and site conditions. The side slope is kept gentle for unlined channels to prevent soil erosion.Hydraulic parameters in channel design include the flow...
01:21Multiple Pipe Systems
Multipipe systems consist of complex configurations of interconnected pipes designed to transport fluids efficiently across intricate networks. They are essential in engineering applications requiring precise control over flow distribution, pressure, and head loss. They are categorized into series, parallel, loop, and network configurations, each distinguished by unique flow characteristics and applications.
Series Configuration
In a series configuration, fluid flows sequentially from one pipe...
Series Configuration
In a series configuration, fluid flows sequentially from one pipe...
01:28Lagrange Multipliers: Two Constraints
The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
01:18Uniform Depth Channel Flow: Problem Solving
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
01:25Indefinite Integrals
The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...