No abstract
The travelling thief problem (TTP) is a combination of two interdependent NP-hard components: travelling salesman problem (TSP) and knapsack problem (KP). Existing approaches for TTP typically solve the TSP and KP components in an interleaved fashion, where the solution to one component is held fixed while the other component is changed. This indicates poor coordination between solving the two components and may lead to poor quality TTP solutions. For solving the TSP component, the 2-OPT segment reversing heuristic is often used for modifying the tour. We propose an extended and modified form of the reversing heuristic in order to concurrently consider both the TSP and KP components. Items deemed as less profitable and picked in cities earlier in the reversed segment are replaced by items that tend to be equally or more profitable and not picked in the later cities. Comparative evaluations on a broad range of benchmark TTP instances indicate that the proposed approach outperforms existing state-of-the-art TTP solvers.
The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify the underlying TSP and KP solutions in an iterative and interleaved fashion. The TSP solution (cyclic tour) is typically changed in a deterministic way, while changes to the KP solution typically involve a random search, effectively resulting in a quasi-meandering exploration of the TTP solution space. Once a plateau is reached, the iterative search of the TTP solution space is restarted by using a new initial TSP tour. We propose to make the search more efficient though an adaptive surrogate model (based on a customised form of Support Vector Regression) that learns the characteristics of initial TSP tours that lead to good TTP solutions. The model is used to filter out non-promising initial TSP tours, in effect reducing the amount of time spent to find a good TTP solution. Experiments on a broad range of benchmark TTP instances indicate that the proposed approach filters out a considerable number of non-promising initial tours, at the cost of missing only a small number of the best TTP solutions.
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