An Efficient Nature-Inspired Method to Solve the Shortest Path Tour Problem

Abstract

The shortest path tour problem (SPTP) is the abstract model of many practical applications, such as network function virtualization (NFV) and warehouse management. The aim of SPTP is to find the shortest path that passes multiple disjoint node subsets in a given order. The challenging part is the computational redundancy of existing decomposition-based algorithms, which is caused by determining the shortest paths from all pairs of sources and destinations in each subproblem. Inspired by the ripple spreading motions on water surface, a ripple-spreading algorithm (RSA) is proposed to solve SPTP in this paper. RSA outperforms other algorithms by forming connections among subproblems, and each subproblem can be solved in a single run to determine the shortest paths to every destination node. The time complexity is irrelevant to node quantities, so RSA is more efficient on large scale networks with sparse connections theoretically. Comparative experiments were conducted on fully random networks, and RSA was validated to be the most powerful algorithm by promoting the efficiency several times. Additionally, layered graphs were designed to simulate the topology of NFV. The computational efficiency of RSA also surpassed other algorithms on layered graphs with various parameters. This brand new algorithm should help to endow the SPTP-related problems with excellent solving efficiency and scalability.