Unbalanced Mallows Models for Optimizing Expensive Black-Box Permutation Problems

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Ekhine Irurozki and Manuel López-Ibáñez. Unbalanced Mallows Models for Optimizing Expensive Black-Box Permutation Problems. In Genetic and Evolutionary Computation Conference (GECCO ’21), July 10–14, 2021, Lille, France. ACM, New York, NY, USA, 9 pages. https://doi.org/10.1145/3449639.3459366

Expensive black-box combinatorial optimization problems arise in practice when the objective function is evaluated by means of a simulator or a real-world experiment. Since each fitness evaluation is expensive in terms of time or resources, only a limited number of evaluations is possible, typically several orders of magnitude smaller than in non-expensive problems. In this scenario, classical optimization methods such as mixed-integer programming and local search are not useful.  In the continuous case, Bayesian optimization, in particular using Gaussian processes, has proven very effective under these conditions. Much less research is available in the combinatorial case. In this paper, we propose and analyze UMM, an estimation-of-distribution (EDA) algorithm based on a Mallows probabilistic model and unbalanced rank aggregation (uBorda). Experimental results on black-box versions of LOP and PFSP show that UMM is able to match, and sometimes surpass, the solutions obtained by CEGO, a Bayesian optimization algorithm for combinatorial optimization. Moreover, the computational complexity of UMM increases linearly with both the number of function evaluations and the permutation size.