  In real-world optimisation, it is common to face several sub-problems
interacting and forming the main problem. There is an inter-dependency between
the sub-problems, making it impossible to solve such a problem by focusing on
only one component. The traveling thief problem~(TTP) belongs to this category
and is formed by the integration of the traveling salesperson problem~(TSP) and
the knapsack problem~(KP). In this paper, we investigate the inter-dependency
of the TSP and the KP by means of quality diversity~(QD) approaches. QD
algorithms provide a powerful tool not only to obtain high-quality solutions
but also to illustrate the distribution of high-performing solutions in the
behavioural space. We introduce a MAP-Elite based evolutionary algorithm using
well-known TSP and KP search operators, taking the TSP and KP score as the
behavioural descriptor. Afterwards, we conduct comprehensive experimental
studies that show the usefulness of using the QD approach applied to the TTP.
First, we provide insights regarding high-quality TTP solutions in the TSP/KP
behavioural space. Afterwards, we show that better solutions for the TTP can be
obtained by using our QD approach and it can improve the best-known solution
for a number of TTP instances used for benchmarking in the literature.
