A shifted hyperbolic augmented Lagrangian-based artificial fish two swarm algorithm with guaranteed convergence for constrained global optimization

摘要

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-basedalgorithm for non-convex constrained global optimization problems. Convergence to an ε-global minimizeris proved. At each iteration k, the algorithm requires the ε(k)-global minimization of a boundconstrained optimization subproblem, where ε(k) → ε. The subproblems are solved by a stochasticpopulation-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy.To enhance the speed of convergence, the algorithm invokes the Nelder–Mead local search with a dynamicallydefined probability. Numerical experiments with benchmark functions and engineering designproblems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangiancompares favorably with other deterministic and stochastic penalty-based methods.