Memetic Optimization of Wastewater Pumping Systems for Energy Efficiency: AI Optimization in a Simulation-Based Framework for Sustainable Operations Management
Abstract
1. Introduction
2. Materials and Methods
2.1. System Overview
2.1.1. Equal Flow Distribution Method
- : Total required flow rate (e.g., in m3/h)
- N: Number of available pumps
- : Minimum and maximum flow rate of pump iii, for
- : Shaft power curve function for pump i, mapping flow rate Q to power consumption P
- : Total unoptimized shaft power
Algorithm 1: |
|
2.1.2. Power Optimization Model
- Input—the current population and a tournament size k (e.g., k = 3).
- Draw competitors—to pick one parent, draw k distinct individuals from P without replacement; every member of P has the same chance of being chosen for this mini-contest.
- Evaluate—compute the fitness F(g) for each of the k competitors.
- Select the winner—keep the individual with the highest fitness (break ties at random). This winner becomes a parent and is pushed into the mating pool.
- Repeat—return the sampled competitors to the main population (sampling with replacement at the tournament level) and repeat Steps 2–4 until the mating pool reaches the desired size (typically the same as the population size).
- A flow vector or (one gene per pump).
- A mutation-strength vector (one self-adaptive σ per gene).
- The mean is 0.5, on average, and the offspring inherits equal weights from each parent.
- The standard deviation shrinks linearly from an initial value at generation g = 0 to 0 at the final generation g = G.
- ○
- Early in the run is large and ⇒ α can wander well away from 0.5, encouraging exploration.
- ○
- Late in the run is tiny and ⇒ α stays near 0.5, promoting fine-grained exploitation.
- If α = 0.75, the offspring’s i-th flow sits three-quarters of the way from parent 2 toward parent 1.
- Because flows are real numbers (not bits), this arithmetic mix creates intermediate solutions that may lie outside the parents’ discrete choices—useful for searching continuous design spaces.
- A simple average is enough: it keeps inside the range spanned by the parents, preserving self-adaptation information without biasing toward one line.
- These σ values will mutate again later, continuing to tune the search radii gene-by-gene.
- Bounds check—after mutation:
- Flow–balance adjustment—compute the delivery error:
- ○
- If , choose I with and
- ○
- If , choose I with and ,
- After hydraulic repair, draw a small random subset S
- Define a step size :
- Iterative hill climb (up to L rounds).
- ○
- For each with
- ○
- repair each trial vector to restore feasibility;
- ○
- Compute Objective
- (i)
- The maximum number of generations is reached,
- (ii)
- Fitness has not improved for a preset stall window (stagnation), or
- (iii)
- The target fitness exceeds a threshold.
2.1.3. MILP—Based Optimization
- ‑
- are continuous decision variables representing interpolation weights (values between 0 and 1) assigned to the k-th breakpoint of pump i.
- ‑
- are the shaft power values corresponding to breakpoint k for pump i.
3. Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
WWTP | Waste Water Treatment Plant |
SDGs | Sustainable and Development Goals |
MA | Memetic Algorithm |
GA | Genetic Algorithm |
M&S | Modeling and Simulation |
AI | Artificial Intelligence |
GUI | Graphical User Interface |
SCADA | Supervisory Control and Data Acquisition |
MILP | Mixed-Integer Linear Programming |
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Pump Case | Metric | |||||
---|---|---|---|---|---|---|
1 | flow | 0 | 1100 | 2100 | 3100 | 4100 |
1 | shaft_power | 285 | 460 | 566.7 | 673.3 | 740 |
2 | flow | 0 | 1100 | 2100 | 3100 | 4100 |
2 | shaft_power | 308.7 | 500 | 606.7 | 726.7 | 806.7 |
3 | flow | 0 | 1100 | 2100 | 3100 | 4100 |
3 | shaft_power | 380 | 540 | 673.3 | 806.7 | 886.7 |
4 | flow | 0 | 1100 | 2100 | 3100 | 4100 |
4 | shaft_power | 393.3 | 553.3 | 686.7 | 820 | 913.3 |
5 | flow | 0 | 1100 | 2100 | 3100 | 4100 |
5 | shaft_power | 423.3 | 606.7 | 753.3 | 900 | 1006.7 |
Metric | Time [s] | Generations | ||
---|---|---|---|---|
GA | MA | GA | MA | |
Mean | 0.16 | 0.12 | 20.4 | 14.8 |
Minimum | 0.06 | 0.02 | – | – |
Maximum | 0.33 | 0.22 | – | – |
Std. Deviation | 0.05 | 0.04 | 5.6 | 5.0 |
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Bruzzone, A.G.; Gotelli, M.; Massei, M.; Sina, X.; Giovannetti, A.; Ghisi, F.; Cirillo, L. Memetic Optimization of Wastewater Pumping Systems for Energy Efficiency: AI Optimization in a Simulation-Based Framework for Sustainable Operations Management. Sustainability 2025, 17, 6296. https://doi.org/10.3390/su17146296
Bruzzone AG, Gotelli M, Massei M, Sina X, Giovannetti A, Ghisi F, Cirillo L. Memetic Optimization of Wastewater Pumping Systems for Energy Efficiency: AI Optimization in a Simulation-Based Framework for Sustainable Operations Management. Sustainability. 2025; 17(14):6296. https://doi.org/10.3390/su17146296
Chicago/Turabian StyleBruzzone, Agostino G., Marco Gotelli, Marina Massei, Xhulia Sina, Antonio Giovannetti, Filippo Ghisi, and Luca Cirillo. 2025. "Memetic Optimization of Wastewater Pumping Systems for Energy Efficiency: AI Optimization in a Simulation-Based Framework for Sustainable Operations Management" Sustainability 17, no. 14: 6296. https://doi.org/10.3390/su17146296
APA StyleBruzzone, A. G., Gotelli, M., Massei, M., Sina, X., Giovannetti, A., Ghisi, F., & Cirillo, L. (2025). Memetic Optimization of Wastewater Pumping Systems for Energy Efficiency: AI Optimization in a Simulation-Based Framework for Sustainable Operations Management. Sustainability, 17(14), 6296. https://doi.org/10.3390/su17146296