Evolutionary Diversity Optimisation for The Traveling Thief Problem

TL;DR

This paper explores evolutionary diversity optimization for the Traveling Thief Problem, introducing a bi-level algorithm to maximize solution diversity and comparing it with a Quality Diversity framework, showing significant improvements.

Contribution

It is the first to apply evolutionary diversity optimization to TTP, proposing a bi-level algorithm and analyzing component inter-dependencies for enhanced diversity.

Findings

Bi-level evolutionary algorithm effectively maximizes diversity.

Quality Diversity approach outperforms in structural diversity.

Empirical results demonstrate significant improvements on TTP benchmarks.

Abstract

There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the solution space and robustness against imperfect modelling and minor problems' changes. It also enables the decision-makers to involve their interests and choose between various solutions. In this study, we investigate for the first time a prominent multi-component optimisation problem, namely the Traveling Thief Problem (TTP), in the context of evolutionary diversity optimisation. We introduce a bi-level evolutionary algorithm to maximise the structural diversity of the set of solutions. Moreover, we examine the inter-dependency among the components of the problem in terms of structural diversity and empirically determine the best method to obtain diversity. We also conduct a comprehensive experimental investigation to examine the introduced algorithm and compare the results to another recently introduced framework based on the use of Quality Diversity (QD). Our experimental results show a significant improvement of the QD approach in terms of structural diversity for most TTP benchmark instances.