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 nonconvex constrained global optimization problems. Convergence to an $$\varepsilon $$ -global minimizer is guaranteed. At each iteration $$k$$ , the algorithm requires a $$(\rho ^{(k)},\varepsilon ^{(k)})$$ -global minimizer of a bound constrained bi-objective subproblem, where as $$k\rightarrow \infty $$ , $$\rho ^{(k)}\rightarrow 0$$ gives the constraint violation tolerance and $$\varepsilon ^{(k)} \rightarrow \varepsilon $$ 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 $$(\rho ^{(k)},\varepsilon ^{(k)})$$ -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.