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Particle Swarm Search

The Particle Swarm Search is one of the Search Method options in Slide3 for locating critical slip surfaces. The Particle Swarm Search is also known as Particle Swarm Optimization (PSO).

The Particle Swarm Search is a metaheuristic search method in which randomness is introduced in some steps of the algorithm.

To enable a Particle Swarm Search:

  1. In the Slip Surface Options dialog, set the Search Method = Particle Swarm Search.
  2. Set the number of Mins to One or Multiple.

The Particle Swarm Search requires no user defined search objects, the algorithm will run automatically when you select Compute.

One Min or Multiple Mins

It is often the case that a slope will have multiple critical regions that may fail, instead of a single critical region. However, slope stability analyses generally focus on the search for the single global minimum surface.

With the Multiple min option, the user can now let the algorithm search for multiple local mins instead of the single critical one – this is called multimodal optimization (MMO). The parameter of note is the “radius span of search space.” The number of local mins found will be equivalent to the number of particles in the search. As such many of these will be very similar. The radius option filters out the surfaces that are similar and only takes the most critical local minima in each region. The default value of 10% is recommended. The user can also set a maximum value for mins to view as well as a maximum FS on the viewed mins.

The Multiple option considers both the global minimum computed from the One option as well as the local minima computed from the Multiple option and provides the user with the three most critical minima. This means the global minimum of the “Multiple” option will always be at least as critical as or more critical than the one from the “One” option. As with all non-circular search methods, optimization is strongly recommended with PSO. It is worth noting that since optimization is being performed on several mins instead of the single global min, computation time tends to be longer with the MMO or multiple min option.

Particle Swarm Search Method

  • Search starts with a random population of failure surfaces in the search scope (known as particles)
  • Particle Swarm Search can use either spherical or ellipsoidal surfaces
  • The search proceeds by updating each particle for the next iteration: Particle Search Equation
  • One min case (unimodal): Updating parameters in Vi are selected randomly such that the new particle is inspired by the best found solution among all particles (SG) and best found solution by that particle in the previous iterations (SB)
    Unimodal Equation
  • Multiple min case (multimodal): Updating parameters in Vi are selected randomly such that the new particle is inspired by the two closest neighbouring particles (N1, N2):
    Multimodal Equation
  • Search process is stopped after a finite number of iterations

Schematic illustration of Particle Swarm Search algorithm

Schematic Illustration of Particle Swarm Search Algorithm

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