Review and comparison of algorithms and software for mixed-integer derivative-free optimization

This paper reviews the literature on algorithms for solving bound-constrained mixed-integer derivative-free optimization problems and presents a systematic comparison of available implementations of these algorithms on a large collection of test problems. Thirteen derivative-free optimization solvers are compared using a test set of 267 problems. The testbed includes: (i) pure-integer and mixed-integer problems, and (ii) small, medium, and large problems covering a wide range of characteristics found in applications. We evaluate the solvers according to their ability to find a near-optimal solution, find the best solution among currently available solvers, and improve a given starting point. Computational results show that the ability of all these solvers to obtain good solutions diminishes with increasing problem size, but the solvers evaluated collectively found optimal solutions for 93% of the problems in our test set. The open-source solvers MISO and NOMAD were the best performers among all solvers tested. MISO outperformed all other solvers on large and binary problems, while NOMAD was the best performer on mixed-integer, non-binary discrete, small, and medium-sized problems.