| 摘要: | 當面臨困境時，人們往往會感到迷惘，不確定下一步該如何行動。在這種情況下，許多人會依
賴 recourse system（補救系統） 來尋找具成本效益的策略，以達成他們的目標。然而，現有的
recourse system 普遍存在一個限制：它們通常僅從單一準則（single-criterion) 的角度出發，缺
乏處理問題多維度特性的彈性。因此，若僅針對某一個面向進行優化，可能會忽略其他層面的
不利影響，導致原本看似可行的路徑在實際執行時變得困難甚至不切實際。
在本研究中，我們提出一種基於圖論 (graph-theoretical) 框架的 recourse system，將問題轉
化為一個最短路徑 (shortest path) 問題。為了能同時考量多個準則，我們採用帕雷托最適路
徑 (pareto-optimal path) 的方式，找出在整體成本與實際可行性之間達到更佳平衡的解。此外
，我們也設計了一種新穎的演算法來提升所產生路徑的多樣性，從而為使用者提供更豐富、具
行動性的個人化 recourse 選擇。
另外，我們亦結合了計算幾何 (computational geometry) 的概念，開發出一種可降低圖結構複
雜度的方法，使得在處理大型資料集時能夠更高效地計算 recourse。
;When facing challenging situations, such as being denied a bank loan, individuals often
struggle to determine the appropriate next steps to improve their circumstances. In such
cases, many turn to recourse systems[15, 17, 16] to identify cost-effective strategies for
achieving their goals. However, existing recourse systems share a common limitation: they
typically operate from a single-criterion perspective, lacking the flexibility to account for
multiple dimensions of a problem. As a result, solutions optimized for one criterion may
overlook adverse effects from other aspects, leading to unexpectedly difficult or impractical
paths to success.
In this paper, we propose a recourse system based on a graph-theoretical framework,
where the problem is formulated as a shortest path problem. To accommodate multi-
ple criteria, we adopt a pareto-optimal path approach[30], enabling the identification of
solutions that strike a better balance between overall cost and practical feasibility. Fur-
thermore, we introduce a novel algorithm designed to enhance the diversity of the gener-
ated paths, thereby offering users a wider range of actionable and personalized recourse
options.
Additionally, we develop a method that integrates principles from computational ge-
ometry to reduce the complexity of the graph, allowing for more efficient recourse com-
putation, especially when dealing with large-scale datasets. |
