Multi-objective search via lazy and efficient dominance checks

Multi-objective search can be used to model many real-world problems that require finding Pareto-optimal paths from a specified start state to a specified goal state, while considering different cost metrics such as distance, time, and fuel. The performance of multi-objective search can be improved by making dominance checking--an operation necessary to determine whether or not a path dominates another--more efficient. This was shown in practice by BOA*, a state-of-the-art bi-objective search algorithm, which outperforms previously existing bi-objective search algorithms in part because it adopts a lazy approach towards dominance checking. EMOA*, a recent multi-objective search algorithm, generalizes BOA* to more-than-two objectives using AVL trees for dominance checking. In this paper, we first propose Linear-Time Multi-Objective A* (LTMOA*), a multi-objective search algorithm that implements more efficient dominance checking than EMOA* using simple data structures like arrays. We then propose LazyLTMOA*, which employs a lazier approach by removing dominance checking during node generation. Our experimental results show that LazyLTMOA* outperforms EMOA* by up to an order of magnitude in terms of runtime.