Random Flights for Particle Swarm Optimisers

Abstract

Parametric Optimisation is an important problem that can be tackled with a range of bio-inspired problem space search algorithms. We show how a simplified Particle Swarm Optimiser (PSO) can efficiently exploit advanced space exploration with Lévy flights, Rayleigh flights and Cauchy flights, and we discuss hybrid variations of these. We present implementations of these methods and compare algorithmic convergence on several multi-modal and unimodal test functions. Random flights considerably enhance the efficient simplified PSO and the Lévy flight gives good balance between local space exploration and local minima avoidance. We discuss computational tradeoffs involved in generating such flights. In summary, these modifications show varying success between themselves for problem solving, but outperforms the uniform random exploration technique in most cases.

Particle Swarm-based Meta-Optimising on Graphical Processing Units

“…We present our results for the Meta PSO only, as the fitnesses obtained from the sub-optimisers were themselves a measure of the efficacy of the final result in using a MOL PSO to optimise each of the test functions. In our experience in [35] we observed that small differences in ω and large differences in θ were necessary to optimise the MOL PSO for these different test functions. What the super-optimiser generated had dramatic variations, but as Pedersen and Chipperfield note, they too are undecided on whether there can exist multiple parameter sets which give approximately equal results [15].…”

“…In our previous experiments in [35] using higher qual- Lower Upper Optimum Rosenbrock -2 2 0 Rastrigin -5 5 0 Schwefel -500 500 -3351.8632 Ackley -20 20 0 Griewangk -600 600 0 Michalewicz 0 π/2 -4.687 Table 3. The boundaries imposed on the particles in the sub-optimisers and the optimum value for each test function.…”

“…The θ chosen for the Schwefel function reflects this. For ease of reference, the θ variable corresponds to the c variable of the Lévy distribution which we use for higher quality exploration [35]. For brevity, this value simply corresponds to the magnitude of the Lévy distribution.…”

Simulating Growth Kinetics in a Data-Parallel 3D Lattice Photobioreactor

“…We attempt to mitigate this somewhat by holding all parameters constant. There may be scope in the future for using metaheuristics [33] in fitting data. Metaheuristic algorithms are particularly well suited to dealing with problems containing many parameters.…”