用支持的非支配点表示多目标网络问题的非支配集
Representing the Non-dominated Set of Multi-objective Network Problems by Supported Non-dominated Points
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中文总结 AI 辅助
研究多目标网络问题中，针对无支持非支配点计算难及支持点集可能过大的问题，建议用（极端）支持点作子集选择候选集，数值结果显示其能产生与完整非支配集质量相近的固定大小表示。
中文摘要 AI 辅助
在多目标组合优化中，无支持的非支配点通常比有支持的点多，且计算难度大。近期研究表明，极端支持的非支配点可为某些二元问题的非支配集提供高质量表示。但本文证明这一结论不适用于容量网络优化问题，随着弧容量增加，其表示质量下降，而支持的非支配点在多个质量指标上始终能提供高质量表示。不过在实际应用中，支持点集可能过大，从非支配集中选择固定大小的表示需耗费大量计算。因此建议将（极端）支持点作为子集选择问题的候选集。数值结果表明，将候选集限制为支持的非支配点可产生与从完整非支配集中选择的质量几乎相同的固定大小表示。总体而言，支持的非支配点既是高质量表示，也是子集选择的合理候选集。
英文摘要
In multi-objective combinatorial optimization, unsupported non-dominated points typically outnumber supported points and are often significantly more challenging to compute. Recent studies show that extreme supported non-dominated points provide high-quality representations of the non-dominated set for certain binary problems. We demonstrate that this observation does not generalize to capacitated network optimization problems: representation quality decreases with increasing arc capacities, whereas supported non-dominated points consistently provide high-quality representations with respect to several quality indicators. However, supported point sets may still be too large in practical applications, where only a small, fixed number of alternatives is typically desired. Selecting fixed-size representations from the non-dominated set requires its computationally expensive generation and thus diminishes the computational advantages that representations are intended to provide. We therefore suggest the (extreme) supported points as alternative candidate sets in subset selection problems. Our numerical results show that restricting the candidate set to supported non-dominated points yields fixed-size representations of nearly the same quality as those selected from the complete non-dominated set. Overall, supported non-dominated points serve both as high-quality representations and as reasonable candidate sets for subset selection.
