Hooke-Jeeves revisited

The Hooke-Jeeves (HJ) Pattern Search, which seems to be the most popular choice among the local search algorithms, was used as an alternative to the dimensional local search (DLS), which has provided excellent results in previous work. In this paper, the question whether the well-known Hooke-Jeeves pattern search could outperform the DLS algorithm that was devised somewhat ad-hoc, is to be investigated. The Moving Peaks (MP) function is used as a benchmark. In our experiments, the algorithms performed almost identically well on the problem instances used. However, it was observed that the pattern move, an intrinsic part of the HJ algorithm, hardly contributed to the quality of the outcome, in fact less than the number sequence used as step sizes for both local searches. We provide some investigations into why the pattern move is less successful than most authors---including the original inventors of the Hooke-Jeeves search---seem to anticipate.