Route Stability in the Uncertain Capacitated Arc Routing Problem

Abstract

Power line inspections in a microgrid can be modeled as the uncertain capacitated arc routing problem, which is a classic combinatorial optimization problem. As an evolutionary computation method, genetic programming is used as a hyper-heuristic method to automatically evolve routing policies that can make real-time decisions in an uncertain environment. Most existing research on genetic programming hyper-heuristic for the uncertain capacitated arc routing problem only focuses on optimizing the total cost of solutions. As a result, the actual routes directed by the routing policies evolved by genetic programming hyper-heuristic are usually not stable, i.e., the routes have large fluctuations in different uncertain environments. However, for marketing or considering the drivers’ and customers’ perspectives, the routes should not be changed too often or too much. Addressing this problem, this study first proposes a method to estimate the similarity between two routes and then extends it for evaluating the stability of the routes in uncertain environments. A novel genetic programming hyper-heuristic, which considers two objectives, i.e., the solution quality (total cost) and the stability of routes, was designed. Experimental studies demonstrate that the proposed genetic programming is hyper-heuristic with stability in consideration and can obtain more stable solutions than the traditional algorithm, without deteriorating the total cost. The approach provided in this study can be easily extended to solving other combinatorial optimization problems in the microgrid.