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

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an $$\varepsilon $$ ε -global minimizer is guaranteed. At each iteration $$k$$ k , the algorithm requires a $$(\rho ^{(k)},\varepsilon ^{(k)})$$ ( ρ ( k ) , ε ( k ) ) -global minimizer of a bound constrained bi-objective subproblem, where as $$k\rightarrow \infty $$ k → ∞ , $$\rho ^{(k)}\rightarrow 0$$ ρ ( k ) → 0 gives the constraint violation tolerance and $$\varepsilon ^{(k)} \rightarrow \varepsilon $$ 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 $$(\rho ^{(k)},\varepsilon ^{(k)})$$ ( ρ ( k ) , ε ( k ) ) -global minimizer with probability one is guaranteed by probability theory. Preliminary numerical experiments show that the algorithm is very competitive when compared with known deterministic and stochastic methods. Copyright Springer Science+Business Media New York 2014