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Inspired by the recent 11th Global Trajectory Optimisation Competition, thispaper presents the asteroid routing problem (ARP) as a realistic benchmark ofalgorithms for expensive bound-constrained black-box optimization inpermutation space. Given a set of asteroids' orbits and a departure epoch, thegoal of the ARP is to find the optimal sequence for visiting the asteroids,starting from Earth's orbit, in order to minimize both the cost, measured asthe sum of the magnitude of velocity changes required to complete the trip, andthe time, measured as the time elapsed from the departure epoch until visitingthe last asteroid. We provide open-source code for generating instances ofarbitrary sizes and evaluating solutions to the problem. As a preliminaryanalysis, we compare the results of two methods for expensive black-boxoptimization in permutation spaces, namely, Combinatorial Efficient GlobalOptimization (CEGO), a Bayesian optimizer based on Gaussian processes, andUnbalanced Mallows Model (UMM), an estimation-of-distribution algorithm basedon probabilistic Mallows models. We investigate the best permutationrepresentation for each algorithm, either rank-based or order-based. Moreover,we analyze the effect of providing a good initial solution, generated by agreedy nearest neighbor heuristic, on the performance of the algorithms. Theresults suggest directions for improvements in the algorithms being compared.

The Asteroid Routing Problem: A Benchmark for Expensive Black-Box Permutation Optimization