Stochastic Simulators Based Optimization by Gaussian Process Metamodels ‐ Application to Maintenance Investments Planning Issues

This paper deals with the optimization of industrial asset management strategies, whose profitability is characterized by the Net Present Value (NPV) indicator which is assessed by a Monte Carlo simulator. The developed method consists in building a metamodel of this stochastic simulator, allowing to obtain, for a given model input, the NPV probability distribution without running the simulator. The present work is concentrated on the emulation of the quantile function of the stochastic simulator by interpolating well chosen basis functions and metamodeling their coefficients (using the Gaussian process metamodel). This quantile function metamodel is then used to treat a problem of strategy maintenance optimization (four systems installed on different plants), in order to optimize an NPV quantile. Using the Gaussian process framework, an adaptive design method (called quantile function expected improvement) is defined by extending in our case the well‐known efficient global optimization algorithm. This allows to obtain an ‘optimal’ solution using a small number of simulator runs.