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Solving the pre-marshalling problem to optimality with A* and IDA*

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Abstract

We present a novel solution approach to the container pre-marshalling problem using the A* and IDA* algorithms combined with several novel branching and symmetry breaking rules that significantly increases the number of pre-marshalling instances that can be solved to optimality. A* and IDA* are graph search algorithms that use heuristics combined with a complete graph search to find optimal solutions to problems. The container pre-marshalling problem is a key problem for container terminals seeking to reduce delays of inter-modal container transports. The goal of the container pre-marshalling problem is to find the minimal sequence of container movements to shuffle containers in a set of stacks such that the resulting stacks are arranged according to the time each container must leave the stacks. We evaluate our approach on three well-known datasets of pre-marshalling problem instances, solving over 500 previously unsolved instances to optimality, which is nearly twice as many instances as the current state-of-the-art method solves.

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Notes

  1. We note that multiple containers may have the same priority, but in order to make containers easily identifiable, in this example we have assigned a different priority to each container.

  2. We note that this may be a fruitful direction for future work.

  3. Moving container 4 to stack a is actually a move reversal as discussed in Sect. 5.1, which is a special case of successive transitive moves.

  4. We note that we cannot use the exact same instances as in Expósito-Izquierdo et al. (2012) because their instances were unfortunately lost by those authors.

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Tierney, K., Pacino, D. & Voß, S. Solving the pre-marshalling problem to optimality with A* and IDA*. Flex Serv Manuf J 29, 223–259 (2017). https://doi.org/10.1007/s10696-016-9246-6

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