Boltzmann machine generation of initial asset distributions

Boltzmann machines have been used to solve a variety of combinatorial optimization problems. The use of simulated annealing allows the network to evolve into a state of maximum consensus (or minimum energy) corresponding to an optimal solution of the given problem. In this paper, Boltzmann machine neural networks (without learning) are used to generate initial configurations of assets for a generic game (e.g. chess). The desired distribution of playing pieces is subject to restrictions on the number of pieces (of several different types) that are present, as well as some preferences for the relative positions of the pieces. The rules implemented in the network allow for flexibility in assigning locations for available resources while the probabilistic nature of the network introduces a degree of variability in the solutions generated. The architecture of the network and a method for assigning the weights are described. Results are given for several different examples.