Multiple solutions of mixed variable optimization by multistart hooke and jeeves filter method

Abstract

In this study, we propose a multistart method based on an extended version of the Hooke and Jeeves (HJ) algorithm for computing mul- tiple solutions of mixed variable optimization problems. The inequal- ity and equality constraints of the problem are handled by a filter set methodology. The basic ideas present in the HJ algorithm, namely the exploratory and pattern moves, are extended to consider two objective functions and to handle continuous and integer variables simultaneously. This proposal is integrated into a multistart method as a local search procedure that is repeatedly invoked to converge to different global and non-global optimal solutions starting from randomly generated points. To avoid repeated convergence to previously computed solutions, the concept of region of attraction of an optimizer is implemented. The performance of the new method is tested on benchmark problems. Its effectiveness is emphasized by a comparison with a well-known solver.