  Understanding the interactions between different combinatorial optimisation
problems in real-world applications is a challenging task. Recently, the
traveling thief problem (TTP), as a combination of the classical traveling
salesperson problem and the knapsack problem, has been introduced to study
these interactions in a systematic way. We investigate the underlying
non-linear packing while traveling (PWT) problem of the TTP where items have to
be selected along a fixed route. We give an exact dynamic programming approach
for this problem and a fully polynomial time approximation scheme (FPTAS) when
maximising the benefit that can be gained over the baseline travel cost. Our
experimental investigations show that our new approaches outperform current
state-of-the-art approaches on a wide range of benchmark instances.
