Convergence analysis of swarm intelligence metaheuristic methods

Abstract

Intensive applications and success of metaheuristics in practice have initiated research on their theoretical analysis. Due to the unknown quality of reported solution(s) and the inherently stochastic nature of metaheuristics, the theoretical analysis of their asymptotic convergence towards a global optimum is mainly conducted by means of probability theory. In this paper, we show that principles developed for the theoretical analysis of Bee Colony Optimization metaheuristic hold for swarm intelligence based metaheuristics: they need to implement learning mechanisms in order to properly adapt the probability rule for modification of a candidate solution. We propose selection schemes that a swarm intelligence based metaheuristic needs to incorporate in order to assure the so-called model convergence.