A New Derivative-Free Algorithm for Blackbox Optimization with Mixed-integer Variables

The rising complexity of mathematical models and the widespread use of high-fidelity simulations have led to a growing demand for derivative-free optimization techniques. This work reviews the historical development of direct search methods, from early embryonic algorithms like Exhaustive Search to the state of the art NOMAD. It then introduces primBFO, a new version of the Brute Force Optimizer (BFO) for blackbox problems with bound-constrained and mixed-integer variables. The key innovation of primBFO is the introduction of a poll step based on primitive directions to explore the integer lattice, replacing BFO original recursive search. Numerical experiments show that the new framework yields a clear improvement over the original BFO and performs well against NOMAD.