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.