Fully informed particle swarm optimizer: Convergence analysis

At present, the explicit conditions necessary for order-2 stability of the fully informed particle swarm optimizer (FIPS) have not be derived. This paper theoretically derives the criteria for order-2 stability of the FIPS algorithm under the stagnation assumption. The exact relationship between the criteria for order-2 stability and the neighborhood size is presented. The maximum possible convergence region is also presented for an arbitrarily large neighborhood size. Unlike the vast body of theoretical research on particle swarms, this paper validates its conclusions empirically against an assumption free FIPS algorithm. This empirical validation is necessary for a truly accurate representation of FIPS´s convergence criteria.