Abstract
A novel dynamic interacting particle swarm optimization algorithm (DYN-PSO) is proposed. The algorithm can be considered to be the synthesis of two established trajectory methods for unconstrained minimization. In the new method, the minimization of a function is achieved through the dynamic motion of a strongly interacting particle swarm, where each particle in the swarm is simultaneously attracted by all other particles located at positions of lower function value. The force of attraction experienced by a particle at higher function value due to a particle at a lower function value is equal to the difference between the respective function-values divided by their stochastically perturbed position difference. The resultant motion of the particles under the influence of the attracting forces is computed by solving the associated equations of motion numerically. An energy dissipation strategy is applied to each particle. The specific chosen force law and the dissipation strategy result in the rapid collapse (convergence) of the swarm to a stationary point. Numerical results show that, in comparison to the standard particle swarm algorithm, the proposed DYN-PSO algorithm is promising.
Highlights
A new direct search method using only function values is proposed for finding a local minimizer x∗ with associated function value f ∗ of a real valued function f (x), x = [x1, x2, . . . , xn]T ∈ Rn
Known as the leap-frog algorithm, the minimum of the function is sought by considering the dynamic motion of a single particle of unit mass in an ndimensional force field, where the potential energy of the particle is represented by the function to be minimized
We have proposed a novel dynamic interacting particle swarm optimization algorithm
Summary
In the computation of the numerical trajectory (by means of the leap-frog integration scheme of Greenspan [4]), an interfering strategy is applied to the motion of the particle by extracting kinetic energy whenever it moves “uphill” along its trajectory In this way, the particle is forced to converge to a local minimum. In the PSO method, the motion of a swarm of loosely interacting particles is considered In this method, each particle is attracted to the best location (lowest function value position) along its path, as well as to the globally overall best position over all the particle trajectories to date. Each particle is attracted to the best location (lowest function value position) along its path, as well as to the globally overall best position over all the particle trajectories to date This method requires no gradient information and may be considered a direct search method.
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