Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm (Q721156)

This paper proposes an extension of the well-known Thompson sampling method for multi-armed bandit problems to approximate Pareto sets in continuous multiobjective optimization in a small number of function evaluations. In the proposed algorithm, each objective function is modelled by an independent Gaussian process model, which allows to incorporate a priori knowledge on the objective function by the choice of the covariance function, such as continuity or smoothness. The parameters are adjusted using the data available by maximum likelihood estimation. Given the fitted Gaussian process model, a rule based on the Thompson sampling method is used to choose the next point to evaluate the vector of objectives. The specific implementation of the algorithm presented in Section 6 is illustrated in Section 7 with an application to a simple bi-objective problem. The paper is hardly readable as a number of figures have moved to the wrong positions and have the wrong caption. A correction has been published in the same journal, see [\textit{E. Bradford} et al., J. Glob. Optim. 71, No. 2, 439--440 (2018; Zbl 1471.90115)].