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.

本文回顾了有关求解有界约束混合整数无导数优化问题的算法的文献，并在大量测试问题上对这些算法的可用实现进行了系统比较。使用包含 267 个问题的测试集对 13 个无导数优化求解器进行了比较。测试平台包括：(i) 纯整数和混合整数问题，以及 (ii) 涵盖应用程序中广泛特征的小、中和大问题。我们根据求解器找到接近最优解的能力来评估求解器，在当前可用的求解器中找到最佳解决方案，并改进给定的起点。计算结果表明，所有这些求解器获得好的解决方案的能力随着问题规模的增加而降低，但是经过评估的求解器共同为我们测试集中的 93% 的问题找到了最佳解决方案。开源求解器 MISO 和 NOMAD 在所有测试的求解器中表现最好。MISO 在大型和二元问题上的表现优于所有其他求解器，而 NOMAD 在混合整数、非二元离散、小型和中型问题上表现最佳。