Co-Evolutionary path optimization by Ripple-Spreading algorithm

Static path optimization (SPO) is a foundation of computational intelligence, but in reality, the routing environment is usually time-varying (e.g., moving obstacles, spreading disasters and uncertainties). Thanks to scientific and technical advances in many relevant domains nowadays, changes in the routing environment are often more or less predictable. This study mainly focuses on path optimization in a given dynamic routing environment (POGDRE). A common practice to deal with dynamic routing environment is to conduct online re-optimization (OLRO), i.e., at each time t, environmental parameters are measured/predicted first, and then the best path is re-calculated by resolving SPO based on the newly measured/predicted environmental parameters. In theory, POGDRE is equivalent to time-dependent path optimization (TDPO), which is usually resolved as SPO on a time-expanded hypergraph (TEHG) with a significantly enlarged size. In other words, during a single online run of OLRO-based methods or a single run of TEHG-based methods, the route network is actually fixed and static. Inspired by the multi-agent co-evolving nature reflected in many methods of evolutionary computation, this paper proposes a methodology of co-evolutionary path optimization (CEPO) to resolve the POGDRE. Distinguishing from OLRO and TEHG methods, in CEPO, future routing environmental parameters keep changing during a single run of optimization on a network of original size. In other words, the routing environment co-evolves with the path optimization process within a single run. This paper then reports a ripple-spreading algorithm (RSA) as a realization of CEPO to resolve the POGDRE with both optimality and efficiency. In just a single run of RSA, the optimal actual travelling trajectory can be achieved in a given dynamic routing environment. Simulation results clearly demonstrate the effectiveness and efficiency of the proposed CEPO and RSA for addressing the POGDRE.