A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues

Abstract

This paper presents a filter-based artificial fish swarm algorithm for solving non- convex constrained global optimization problems. Convergence to an ε-global minimizer is guaranteed. At each iteration k, the algorithm requires a (ρ(k),ε(k))-global minimizer of a bound constrained bi-objective subproblem,where as k →∞ ,ρ(k) →0 gives the constraint violation tolerance and ε(k) → ε is the error bound defining the accuracy required for the solution.The subproblems are solved by a population-based heuristic known as artificial fish swarm algorithm. Each subproblem relies on the approximate solution of the previous one, randomly generated new points to explore the search space for a global solution, and the filter methodology to accept non-dominated trial points.Convergence to a (ρ(k),ε(k))-global minimizer with probability one is guaranteed by probability theory. Preliminary numeri- cal experiments show that the algorithm is very competitive when compared with known deterministic and stochastic methods.