Evolving test instances of the Hamiltonian completion problem
This work addresses the problem of limited and non-diverse benchmarking sets for researchers in combinatorial optimization, though it is incremental as it builds on existing evolutionary methods for instance generation.
The paper tackled the challenge of benchmarking algorithm performance on graph instances by proposing an evolutionary algorithm to generate diverse and difficult instances for the Hamiltonian completion problem, resulting in insights into key attributes affecting performance and the ability to create graphs with novel feature combinations.
Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are usually not diverse enough to draw sound conclusions. That is why recent work proposes a new methodology to generate a diverse set of instances by using an evolutionary algorithm. We can then analyze the resulting graphs and get key insights into which attributes are most related to algorithm performance. We can also fill observed gaps in the instance space in order to generate graphs with previously unseen combinations of features. This methodology is applied to the instance space of the Hamiltonian completion problem using two different solvers, namely the Concorde TSP Solver and a multi-start local search algorithm.