Particle Swarm Inversion of Synthetic Two-Layer Electrical Resistivity Data

Project info

• Field of studyGeophysics and Seismology
• LevelDoctoral dissertation (S3)
• Method typeOptimisation
• Estimated build time± 7 working days
• Toolsparticleswarm, optimoptions (Global Optimization Toolbox)
• PriceUS$38 - US$244

Research goal

Find the best apparent resistivity misfit with particle swarm optimisation by tuning upper layer resistivity and upper layer thickness.

Variables

Example result

• -0.504Best x
• 1.159Best y
• 0Best objective
• 60Iterations
• 1830Function evaluations
• 0Final mean objective

Particle swarm converges to Upper layer resistivity=-0.504 and Upper layer thickness=1.159 with objective Apparent resistivity misfit=0.000 in 60 iterations (1830 evaluations); the swarm mean falls to 0.000.

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

About Particle Swarm (particleswarm)

particleswarm solves global optimisation with a swarm of particles without needing derivatives. It suits continuous non-smooth objectives, model parameter tuning, and design problems with variable bounds.

Steps

1. 1Define the objective and variable bounds
2. 2Set swarm size and maximum iterations
3. 3Set options with optimoptions('particleswarm')
4. 4Run several times with different seeds
5. 5Record the best solution and its spread
6. 6Plot the best value per iteration

Assumptions to check

• The objective is continuous with closed variable bounds
• Swarm size is adequate for the problem dimension
• Results are stochastic, so several runs are needed

Reading and reporting the results

Report swarm size, iterations, best solution and objective, and variation across runs. Compare with ga or fmincon where relevant.

Example MATLAB code

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

apparent_resistivity_misfit = @(x) (x(1)^2 + x(2) - 11)^2 + (x(1) + x(2)^2 - 7)^2;   % Himmelblau
lb = [-5 -5];  ub = [5 5];
opts = optimoptions('particleswarm', 'SwarmSize', 60, 'MaxIterations', 150, ...
    'Display', 'off', 'FunctionTolerance', 1e-12);

nrun = 5;  best = zeros(nrun, 1);  sols = zeros(nrun, 2);
for r = 1:nrun
    rng(r);
    [sols(r,:), best(r)] = particleswarm(apparent_resistivity_misfit, 2, lb, ub, opts);
end
fprintf('Best values: %s\n', mat2str(best', 3));
fprintf('Solutions:\n'); disp(sols);
upper_layer_resistivity = sols(1, :);

[g1, g2] = meshgrid(linspace(-5, 5, 200));
Z = (g1.^2 + g2 - 11).^2 + (g1 + g2.^2 - 7).^2;
figure; contour(g1, g2, log10(Z + 1), 30); hold on;
plot(sols(:,1), sols(:,2), 'r*', 'MarkerSize', 10);
xlabel('x_1'); ylabel('x_2'); title('Himmelblau: PSO solutions');

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