Swarm intelligence
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
The particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters
Rigorous runtime analysis of a (μ+1)ES for the sphere function
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
How the (1 + 1) ES using isotropic mutations minimizes positive definite quadratic forms
Theoretical Computer Science - Foundations of genetic algorithms
Information Processing Letters
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
Theoretical Computer Science
Runtime analysis of binary PSO
Proceedings of the 10th annual conference on Genetic and evolutionary computation
A fast particle swarm optimization algorithm with cauchy mutation and natural selection strategy
ISICA'07 Proceedings of the 2nd international conference on Advances in computation and intelligence
Simulated annealing beats metropolis in combinatorial optimization
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients
IEEE Transactions on Evolutionary Computation
Lower bounds for randomized direct search with isotropic sampling
Operations Research Letters
Runtime analysis of a binary particle swarm optimizer
Theoretical Computer Science
Theoretical analysis of evolutionary computation on continuously differentiable functions
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Particle swarm optimization almost surely finds local optima
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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A recent trend in the theoretical analysis of randomised search heuristics deals with their optimisation time, also called runtime, for selected problems. Such results exist for several bio-inspired search heuristics including Evolutionary Algorithms and Ant Colony Optimisation but not for standard Particle Swarm Optimisers (PSO). This paper points out why a runtime analysis of standard PSO algorithms and many proposed variants does not make sense and why existing convergence analyses thereof do not contribute to our understanding of the success of PSO as observed in practice either. As one of the few PSO variants that allow for a rigorous runtime analysis, the Guaranteed Convergence PSO (GCPSO) by van den Bergh and Engelbrecht is studied in the case of a single particle, and a theorem showing theoretically optimal convergence speed on a test function is derived. In the course of our paper, it is elaborated why a runtime analysis of PSO, when possible, is seemingly closely related to the analysis of simple Evolutionary Algorithms.