Efficient Interactive Methods for a Class of Multiattribute Shortest Path Problems
研究在无环网络中,如何结合贝尔曼最优性原理与交互式编程,高效找到基于多属性偏好的最优路径,并指出最优性原理成立的条件是偏好可由属性的线性价值函数表示。
Given an acyclic network and a preference-order relation on paths, when and how can Bellman's principle of optimality be combined with interactive programming to efficiently locate an optimal path? We show that if preferences are defined via a collection of attributes, then, under common conditions, the principle of optimality is valid if and only if the preferences can be represented by a linear (value) function over the attributes. Consequently, an interactive programming method is suggested which assesses the value function while using the principle of optimality to efficiently search for an optimal path.