Data-driven derivative-free trust-region model-based method for resource allocation problems

Allocating a limited available resource between a set of units is a problem that arises in several application areas. We propose an online derivative-free trust-region model-based method to tackle a fairly general version of the resource allocation problem where units may be turned on or off. The units are considered as black boxes which may only be evaluated given that all the other units are evaluated simultaneously, and no gradient information is available. This method was inspired by an industrial problem and emphasis is put on both providing feasible points during the optimization and on not incurring additional increase in cost while searching for the optimum. The latter cannot be guaranteed, but the algorithm allows for automatic or manual ranking of the different units to attempt to reduce negative impact on the cost. The algorithm was applied to a case study from the petroleum industry where fast convergence was observed.