Evolving test instances of the Hamiltonian completion problem

TL;DR

This paper introduces an evolutionary algorithm-based methodology to generate diverse and representative graph instances for benchmarking the Hamiltonian completion problem, enabling better analysis of algorithm performance.

Contribution

It presents a novel approach to create diverse graph instances for benchmarking, addressing limitations of existing generators and providing insights into algorithm performance.

Findings

Generated diverse graph instances with evolutionary algorithms

Analyzed algorithm performance on generated instances

Identified key attributes influencing solver efficiency

Abstract

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.