Bandits Help Simulated Annealing to Complete a Maximin Latin Hypercube Design

Abstract

Simulated Annealing (SA) is commonly considered as an efficient method to construct Maximin Latin Hypercube Designs (LHDs) which are widely employed for Experimental Design. The Maximin LHD construction problem may be generalized to the Maximin LHD completion problem in an instance of which the measurements have already been taken at certain points.

As the Maximin LHD completion is NP-complete, the choice of SA to treat it shows itself naturally. The SA performance varies greatly depending on the mutation used. The completion problem nature changes when the number of given points varies. We thus provide SA with a mechanism which selects an appropriate mutation. In our approach the choice of a mutation is seen as a bandit problem. It copes with changes in the environment, which evolves together with the thermal descent.

The results obtained prove that the bandit-driven SA adapts itself on the fly to the completion problem nature. We believe that other parametrized problems, where SA can be employed, may also benefit from the use of a decision-making algorithm which selects the appropriate mutation.