Efficient algorithm for finding k shortest paths based on re-optimization technique

A fast algorithm for finding K shortest paths using generalized spur path reuse technique

“…The problem of finding the K shortest paths (KSPs) (i.e., the shortest path, the second shortest path, and so on until the shortest path) between a pair of nodes in a road network is an important network optimization problem with broad applications in various fields (Chen, Chen, Chen, & Lam, 2020; Liu et al, 2020; Sester, 2020). For example, KSPs are often found to solve complex network optimization problems with multiple constraints and/or objectives.…”

“…The KSP problem can be further classified into two variants. The first variant is to find the K shortest simple paths, in which repeated nodes are not allowed (Chen et al, 2020; Martins & Pascoal, 2003; Vanhove & Fack, 2012; Yen, 1971). The second variant is to find the K shortest non‐simple paths, in which repeated nodes may exist (Eppstein, 1998; Martins, 1984; Minieka, 1974).…”

“…In the literature, considerable effort has been devoted to developing effective algorithms for finding KSPs exactly. Among early KSP algorithms (Clarke, Krikorian, & Rausen, 1963; Hoffman & Pavley, 1959; Lawler, 1972; Yen, 1971), Yen's algorithm (Yen, 1971) was recognized as having the best worst‐case complexity (Chen et al, 2020; Vanhove & Fack, 2012). This algorithm builds on the deviation path concept [i.e., the shortest path deviates at a certain node—called the deviation node—from a previously determined () shortest path].…”

“…It was reported that this algorithm (Martins & Pascoal, 2003) ran even slower than the improved Yen's algorithm in most cases (Vanhove & Fack, 2012). Along the line of re‐optimization techniques, Chen et al (2020) further proposed an efficient KSP algorithm, called KSP‐LPA*, by explicitly formulating the spur path calculation process as subsequent iterations of one‐to‐one shortest path searches. They incorporated the lifelong planning A* technique to improve spur path calculation performance by reusing the results of one‐to‐one shortest path searches in the previous iteration.…”

“…When the reuse failed (i.e., forming cycles), the V–F algorithm simply used the one‐to‐one Dijkstra's algorithm to calculate the spur path. Empirical studies have shown that the V–F algorithm can reuse 10–50% of spur paths and speed up the improved Yen's algorithm by about 10–50% (Chen et al, 2020; Vanhove & Fack, 2012).…”