A novel expected hypervolume improvement algorithm for Lipschitz multi-objective optimisation: Almost Shubert’s algorithm in a special case

An algorithm is proposed for multi-objective optimisation of Lipschitz objective functions that each satisfy a Lipschitz condition of which a Lipschitz constant is a priori known. The number of function evaluations is reduced by determining a good next point of evaluation using an Expected Hypervolume Improvement (EHVI) approach. It is closely related to Shubert’s Algorithm for single objective optimisation on one-dimensional decision space, but sampling sequences can be slightly different.