Given a directed, discrete-time temporal graph $G=(V,R)$, a start node $s\in V$, and $p\geq1$ objectives, the single-source multiobjective temporal shortest path problem asks, for each $v\in V$, for the set of nondominated images of temporal $s$-$v$-paths together with a corresponding efficient path for each image. A recent general label setting algorithm for this problem relies on two properties of the objectives - monotonicity and isotonicity. Monotonicity generalizes the nonnegativity assumption required by label setting methods for the classical additive single-objective shortest path problem on static graphs, while isotonicity ensures that the order of the objective values of two paths is preserved when both are extended by the same arc. In this paper, we study the problem without assuming monotonicity and/or isotonicity. A key difficulty in this setting is that zero-duration temporal cycles may need to be traversed an arbitrary finite number of times to generate all nondominated images. This motivates the study of a restricted problem variant in which a maximum admissible path length $K$ is imposed, and only paths containing at most $K$ arcs are considered. We develop general label correcting algorithms for this setting and establish several sufficient conditions under which such a bound is not required, implying that the algorithms compute all nondominated images.

翻译：考虑一个有向离散时间时序图 $G=(V,R)$、起始节点 $s\in V$ 及 $p\geq 1$ 个目标，单源多目标时间最短路径问题要求，对于每个 $v\in V$，计算出时间 $s$-$v$ 路径的所有非支配像及其对应的有效路径。针对该问题，近期提出的一种通用标签设定算法依赖于目标的两种性质——单调性与等调性。单调性将静态图中经典加性单目标最短路径问题标签设定方法所需的非负假设进行了推广，而等调性则确保当两条路径均被同一弧扩展时，其目标值的顺序保持不变。本文研究在不假设单调性和/或等调性条件下的该问题。此设定下的关键难点在于，零持续时间的时间循环可能需要被遍历任意有限次数才能生成所有非支配像。这促使我们研究一种受限问题变体：引入最大可接受路径长度 $K$，仅考虑包含至多 $K$ 条弧的路径。我们为此设定开发了通用标签修正算法，并建立了若干充分条件，使得在此类条件下无需路径长度限制，从而算法可计算所有非支配像。