SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications. This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization problems, meaning that the relaxed optimization problems have many local optima. However, the method is also shown to perform well on many local optimization problems, and problems with linear objective functions. The performance of SO-I, a genetic algorithm, Nonsmooth Optimization by Mesh Adaptive Direct Search (NOMAD), SO-MI (M”uller et al. in Comput Oper Res 40(5):1383-1400, 2013), variable neighborhood search, and a version of SO-I that only uses a local search has been compared on 17 test problems from the literature, and on eight realizations of two application problems. One application problem relates to hydropower generation, and the other one to throughput maximization. The numerical results show that SO-I finds good solutions most efficiently. Moreover, as opposed to SO-MI, SO-I is able to find feasible points by employing a first optimization phase that aims at minimizing a constraint violation function. A feasible user-supplied point is not necessary.

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  1. Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables (2020)
  2. Audet, Charles; Le Digabel, Sébastien; Tribes, Christophe: The mesh adaptive direct search algorithm for granular and discrete variables (2019)
  3. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  4. Müller, Juliane; Day, Marcus: Surrogate optimization of computationally expensive black-box problems with hidden constraints (2019)
  5. Müller, Juliane: SOCEMO: surrogate optimization of computationally expensive multiobjective problems (2017)
  6. Müller, Juliane; Woodbury, Joshua D.: GOSAC: global optimization with surrogate approximation of constraints (2017)
  7. Vu, Ky Khac; D’Ambrosio, Claudia; Hamadi, Youssef; Liberti, Leo: Surrogate-based methods for black-box optimization (2017)
  8. Akhtar, Taimoor; Shoemaker, Christine A.: Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection (2016)
  9. Müller, Juliane: MISO: mixed-integer surrogate optimization framework (2016)
  10. Müller, Juliane; Shoemaker, Christine A.; Piché, Robert: SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications (2014)