Diversified Late Acceptance Search

The well-known Late Acceptance Hill Climbing (LAHC) search aims to overcome the main downside of traditional Hill Climbing (HC) search, which is often quickly trapped in a local optimum due to strictly accepting only non-worsening moves within each iteration. In contrast, LAHC also accepts worsening moves, by keeping a circular array of fitness values of previously visited solutions and comparing the fitness values of candidate solutions against the least recent element in the array. While this straightforward strategy has proven effective, there are nevertheless situations where LAHC can unfortunately behave in a similar manner to HC. For example, when a new local optimum is found, often the same fitness value is stored many times in the array. To address this shortcoming, we propose new acceptance and replacement strategies to take into account worsening, improving, and sideways movement scenarios with the aim to improve the diversity of values in the array. Compared to LAHC, the proposed Diversified Late Acceptance Search approach is shown to lead to better quality solutions that are obtained with a lower number of iterations on benchmark Travelling Salesman Problems and Quadratic Assignment Problems.