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

TL;DR

This paper introduces the asteroid routing problem (ARP) as a benchmark for expensive black-box permutation optimization, comparing two algorithms and analyzing factors affecting their performance.

Contribution

It presents the ARP benchmark, provides open-source tools, and offers a preliminary comparison of Bayesian and estimation-of-distribution algorithms for the problem.

Findings

Bayesian optimizer (CEGO) and UMM perform differently depending on permutation representation.

Providing a good initial solution improves algorithm performance.

Open-source code enables future research and benchmarking.

Abstract

Inspired by the recent 11th Global Trajectory Optimisation Competition, this paper presents the asteroid routing problem (ARP) as a realistic benchmark of algorithms for expensive bound-constrained black-box optimization in permutation space. Given a set of asteroids' orbits and a departure epoch, the goal 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 as the sum of the magnitude of velocity changes required to complete the trip, and the time, measured as the time elapsed from the departure epoch until visiting the last asteroid. We provide open-source code for generating instances of arbitrary sizes and evaluating solutions to the problem. As a preliminary analysis, we compare the results of two methods for expensive black-box optimization in permutation spaces, namely, Combinatorial Efficient Global Optimization (CEGO), a Bayesian optimizer based on Gaussian processes, and Unbalanced Mallows Model (UMM), an estimation-of-distribution algorithm based on probabilistic Mallows models. We investigate the best permutation representation for each algorithm, either rank-based or order-based. Moreover, we analyze the effect of providing a good initial solution, generated by a greedy nearest neighbor heuristic, on the performance of the algorithms. The results suggest directions for improvements in the algorithms being compared.