A multi-start methodology for constrained global optimization using novel constrained local optimizers

Abstract

The constrained global optimization problem is addressed using two relatively new local constrained optimization algorithms, namely the GLS1C and the Dynamic-Q algorithms. Both have relatively good global convergence capabilities. They are used in a multi-start strategy in combination with a Bayesian global stopping criterion. The suitability of the Bayesian stopping criterion is demonstrated for both the chosen local optimization algorithms when used in multi-start mode and applied to an initial set of small sized and relatively simple test functions. The results show that for both algorithms the proposed methodology reliably and efficiently yields the global optimum of each problem. Particularly outstanding for this set of problems is the performance of the Dynamic-Q algorithm used in multi-start mode. In addition, parallelization of the sequential multi-start Dynamic-Q algorithm is shown to have the potential to effectively reduce the computational expense associated with solving these global optimization problems. Finally, the multi-start Dynamic-Q algorithm is shown to perform exceptionally well when applied to a further set of more challenging test problems.