 This study presents a new discrete sampling method, DreamD, that uses the Dream algorithm as its main building block and implements two novel proposal distributions to solve discrete and combinatorial optimization problems. The method maintains detailed balance and ergodicity and is designed for optimal experimental design problems. Three case studies are used to benchmark the performance of DreamD, which can be easily integrated into other adaptive MCMC algorithms. This article was authored by C.J.F. Turbrick and J.A. Vrugged.