The late acceptance Hill-Climbing heuristic

This paper introduces a new and very simple search methodology called Late Acceptance Hill-Climbing (LAHC). It is a one-point iterative search algorithm, which accepts non-improving moves when a candidate cost function is better (or equal) than it was a number of iterations before. This value appears as a single algorithmic input parameter which determines the total processing time of the search procedure. The properties of this method are experimentally studied in this paper with a range of Travelling Salesman and Exam Timetabling benchmark problems. In addition, we present a fair comparison of LAHC with well-known search techniques, which employ different variants of a cooling schedule: Simulated Annealing (SA), Threshold Accepting (TA) and the Great Deluge Algorithm (GDA). Moreover, we discuss the method's success in winning an international competition to automatically solve the Magic Square problem. Our experiments have shown that the LAHC approach is simple, easy to implement and yet is an effective search procedure. For all studied problems, its average performance was distinctly better than GDA and on the same level as SA and TA. One of the major advantages of LAHC approach is the absence of a cooling schedule. This makes it significantly more robust than cooling-schedule based techniques. We present an example where the rescaling of a cost function in the Exam Timetabling Problem dramatically deteriorates the performance of three cooling-schedule based techniques, but has absolutely no influence upon the performance of LAHC.