Particle Swarm Optimization for Placing Air Quality Monitoring Stations to Maximise Coverage

Project info

• Field of studyForestry and Environment
• LevelDoctoral dissertation (S3)
• Method typeOptimisation
• Estimated build time± 7 working days
• Toolsnumpy (implementasi manual PSO); matplotlib
• PriceUS$34 - US$213

Research goal

Optimise monitoring coverage by tuning number of stations and coverage radius with Particle Swarm Optimization.

Variables

Example result

• 30.592Best objective
• 30.581Global optimum
• 0.039Gap to optimum %
• 14Particles
• 22Iterations
• 0.494Final spread

PSO (14 particles, 22 iterations) minimises Monitoring coverage to 30.59 at Number of stations = 18.28 and Coverage radius = 26.07, within 0.04% of the global optimum.

Computed from illustrative synthetic data, not from a real study.

About Particle Swarm Optimization

Particle Swarm Optimization moves a swarm of particles through the solution space, combining personal experience with the best experience of the group. It suits continuous nonlinear optimisation, including model parameter tuning.

Steps

1. 1Define the objective and variable bounds
2. 2Randomly initialise particle positions and velocities
3. 3Compute fitness and update pbest and gbest
4. 4Update velocity with inertia weight and cognitive/social coefficients
5. 5Update positions and keep them within bounds
6. 6Repeat until convergence and plot the convergence curve

Assumptions to check

• The objective is continuous and can be evaluated repeatedly
• Parameters w, c1, c2 are reasonable (for example 0.7, 1.5, 1.5)
• Run several times because results are stochastic

Reading and reporting the results

Report swarm size, PSO parameters, the best solution, objective value, and convergence curve. Compare with other methods to show effectiveness.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt

def sphere_shift(p):
    return ((p - np.array([1.5, -2.0])) ** 2).sum(axis=1) + 0.5 * np.sin(3 * p[:, 0]) ** 2

rng = np.random.default_rng(33)
n, dim, iters = 40, 2, 100
lo, hi = -10, 10
w, c1, c2 = 0.7, 1.5, 1.5
number_of_stations = rng.uniform(lo, hi, (n, dim))      # positions
v = rng.uniform(-1, 1, (n, dim))
pbest = number_of_stations.copy()
pbest_f = sphere_shift(number_of_stations)
gbest = pbest[pbest_f.argmin()].copy()
monitoring_coverage = []

for _ in range(iters):
    r1, r2 = rng.random((n, dim)), rng.random((n, dim))
    v = w * v + c1 * r1 * (pbest - number_of_stations) + c2 * r2 * (gbest - number_of_stations)
    number_of_stations = np.clip(number_of_stations + v, lo, hi)
    fit = sphere_shift(number_of_stations)
    better = fit < pbest_f
    pbest[better], pbest_f[better] = number_of_stations[better], fit[better]
    gbest = pbest[pbest_f.argmin()].copy()
    monitoring_coverage.append(pbest_f.min())

print("Best position:", gbest.round(4))
print("Best objective:", round(pbest_f.min(), 6))

plt.semilogy(monitoring_coverage)
plt.xlabel("Iteration"); plt.ylabel("Best objective")
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions