Robust solutions for vehicle routing problems via evolutionary multiobjective optimization

In many practical applications it is observable that optimal solutions are vulnerable to changes in environmental-or decision-variables and therefore become suboptimal or even infeasible in uncertain environments. Solutions immune or less vulnerable to such uncertainties are called robust. In this paper we present and compare two algorithms for creating robust solutions to the vehicle routing problem with time-windows (VRPTW) in which travel times are uncertain. In the first approach robustness is defined as a dedicated optimization objective and the NSGA2 algorithm is used to solve the VRPTW as a multi-objective optimization problem. A Pareto-front is generated that displays the trade-off between robustness and the total distance to be minimized. A second approach uses a modified predator-prey algorithm, that implicitly takes robustness into account by defining different travel-time-matrices for each predator. It can be shown that the predator-prey approach is much faster than the NSGA2 and still delivers viable results.