Metaheuristic Search (PSO, Cuckoo, DE)
Population-based metaheuristic search with PSO, Cuckoo, and Differential Evolution.
The metaheuristic methods optimize non-circular polyline surfaces using population-based algorithms. Instead of generating many independent random surfaces, a population of candidate surfaces evolves over a number of iterations toward the lowest factor of safety. Three algorithms are available: Particle Swarm Optimization (PSO), Cuckoo Search, and Differential Evolution (DE).
All three operate within the block-search windows (see Block Search) and represent each candidate as a polyline with a fixed number of internal vertices. Candidate surfaces are evaluated in parallel across background workers.
Selecting an algorithm
Choose the algorithm directly from the search-method menu:
- Particle Swarm Optimization (Non-Circular)
- Cuckoo Search (Non-Circular)
- Differential Evolution (Non-Circular)
Shared parameters
| Parameter | Default | Description |
|---|---|---|
| Population | 30 | Number of candidate surfaces in the population. |
| Iterations | 40 | Number of generations the population evolves. |
| Internal vertices | 4 | Number of internal vertices defining each non-circular surface. |
PSO parameters
Each candidate moves through the search space with a velocity blending inertia, a pull toward its own best position (cognitive), and a pull toward the population best (social).
| Parameter | Default | Description |
|---|---|---|
| Inertia (start → end) | 0.9 → 0.4 | Inertia weight, decaying linearly from start to end across the iterations. |
| Cognitive weight | 1.6 | Attraction toward each particle's own best position. |
| Social weight | 1.8 | Attraction toward the population's best position. |
Cuckoo Search parameters
New candidates are generated by Lévy flights, and a fraction of the worst nests are abandoned each iteration.
| Parameter | Default | Description |
|---|---|---|
| Discovery rate | 0.25 | Fraction of candidates abandoned and replaced each iteration. |
| Lévy beta | 1.5 | Exponent of the Lévy-flight step distribution. |
| Step scale | 0.01 | Scaling applied to Lévy-flight step sizes. |
Differential Evolution parameters
New candidates are formed by combining differences between existing members (mutation) and mixing them with a target (crossover).
| Parameter | Default | Description |
|---|---|---|
| Mutation factor (F) | 0.6 | Scale applied to the difference vector during mutation. |
| Crossover rate (CR) | 0.85 | Probability that a trial component is taken from the mutant. |
The population and iteration counts above are also scaled together by the search complexity slider.
Choosing a method
- PSO converges quickly and is a strong general-purpose choice for smooth, well-bounded problems.
- Cuckoo Search explores broadly via Lévy flights and can escape local minima on rugged, multi-modal problems.
- Differential Evolution is robust on irregular landscapes and benefits from a larger population.
For difficult sites, run more than one method and compare. Increasing population and iterations improves the chance of finding the global minimum at the cost of runtime. As with other methods, you can follow the search with surface-altering optimization.