Finding the [formula omitted] shortest paths by ripple-spreading algorithms

Abstract

The k shortest paths problem (k-SPP) is fundamentally important to both theoretical and application researches on computational intelligence. Inspired by the natural ripple-spreading phenomenon that occurs on a water surface, this paper proposes a novel ripple-spreading algorithm (RSA). RSA differs from many existing methods which need to reconstruct route networks or to sweep the network for k times, and it can identify the k shortest paths by a single run of ripple relay race in the original route network. Besides the k-SPP in normal route networks, the RSA can also be extended, without losing optimality and effectiveness, to some time-window networks (where various waiting behaviors at nodes are introduced) and dynamical networks (where the network topology and link costs may change over time due to factors such as moving obstacles and spreading disasters). For one-to-all k-SPP, which aims to find all the k shortest paths from a given source to every other node in a network (no matter with or without time windows at nodes, and no matter whether the network topology and link costs can change over time or not), the RSA can still find out all required solutions using only a single run, while the computational complexity is exactly the same as that for the one-to-one k-SPP, i.e., O(k×NL×NATU), where NL is the number of links in the network, and NATU is the average simulated time units for a ripple to travel through a link. The comparative experimental results illustrate the effectiveness and efficiency of the proposed RSA.