  The Conditional Markov Chain Search (CMCS) is a framework for automated
design of metaheuristics for discrete combinatorial optimisation problems.
Given a set of algorithmic components such as hill climbers and mutations, CMCS
decides in which order to apply those components. The decisions are dictated by
the CMCS configuration that can be learnt offline. CMCS does not have an
acceptance criterion; any moves are accepted by the framework. As a result, it
is particularly good in exploration but is not as good at exploitation. In this
study, we explore several extensions of the framework to improve its
exploitation abilities. To perform a computational study, we applied the
framework to the three-index assignment problem. The results of our experiments
showed that a two-stage CMCS is indeed superior to a single-stage CMCS.
