Technical Note—Determining All Optimal and Near-Optimal Solutions when Solving Shortest Path Problems by Dynamic Programming

Abstract

This paper presents a new algorithm for finding all solutions with objective function values in the neighborhood of the optimum for certain dynamic programming models, including shortest path problems. The new algorithm combines the depth-first search with stacking techniques of theoretical computer science and principles from dynamic programming to modify the usual backtracking routine and list all near-optimal policies. The resulting procedure is the first practical algorithm for a variety of large problems that are of interest.