Structural learning of the Boltzmann machine and its application to life cycle management

The objective of this research is to realise structural learning within a Boltzmann machine (BM), which enables the effective solution of problems defined as mixed integer quadratic programming. Simulation results show that computation time is reduced by up to one-fifth compared to conventional BMs. The computational efficiency of the resulting double-layer BM is approximately expressed as the ratio n divided by N, where n is the number of selected units (neurons/nodes) and N is the total number of units. The double-layer BM was applied to efficiently solve a mean-variance problem using mathematical programming with two objectives: the minimisation of risk and the maximisation of expected return. Finally, the effectiveness of our method is illustrated by way of a life cycle management example. The double-layer BM was able to more effectively select results with lower computational overhead. The results also enable us to more easily understand the internal structure of the BM. Using our proposed model, decision makers are able to select the best solution based on their risk preference from the alternative solutions provided by the proposed method.