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The travelling thief problem (TTP) is a representative of multi-componentoptimisation problems with interacting components. TTP combines the knapsackproblem (KP) and the travelling salesman problem (TSP). A thief performs acyclic tour through a set of cities, and pursuant to a collection plan,collects a subset of items into a rented knapsack with finite capacity. The aimis to maximise profit while minimising renting cost. Existing TTP solverstypically solve the KP and TSP components in an interleaved manner: thesolution of one component is kept fixed while the solution of the othercomponent is modified. This suggests low coordination between solving the twocomponents, possibly leading to low quality TTP solutions. The 2-OPT heuristicis often used for solving the TSP component, which reverses a segment in thetour. Within TTP, 2-OPT does not take into account the collection plan, whichcan result in a lower objective value. This in turn can result in the tourmodification to be rejected by a solver. We propose an expanded form of 2-OPTto change the collection plan in coordination with tour modification. Itemsregarded as less profitable and collected in cities located earlier in thereversed segment are substituted by items that tend to be more profitable andnot collected in cities located later in the reversed segment. The collectionplan is further changed through a modified form of the hill-climbing bit-flipsearch, where changes in the collection state are only permitted for boundaryitems, which are defined as lowest profitable collected items or highestprofitable uncollected items. This restriction reduces the time spent on the KPcomponent, allowing more tours to be evaluated by the TSP component within atime budget. The proposed approaches form the basis of a new cooperativecoordination solver, which is shown to outperform several state-of-the-art TTPsolvers.

A Cooperative Coordination Solver for Travelling Thief Problems