Solving Scalarized Subproblems within Evolutionary Algorithms for Multi-criteria Shortest Path Problems

The $$\textbackslash mathcal NP$$-hard multi-criteria shortest path problem (mcSPP) is of utmost practical relevance, e.~g., in navigation system design and logistics. We address the problem of approximating the Pareto-front of the mcSPP with sum objectives. We do so by proposing a new mutation operator for multi-objective evolutionary algorithms that solves single-objective versions of the shortest path problem on subgraphs. A rigorous empirical benchmark on a diverse set of problem instances shows the effectiveness of the approach in comparison to a well-known mutation operator in terms of convergence speed and approximation quality. In addition, we glance at the neighbourhood structure and similarity of obtained Pareto-optimal solutions and derive promising directions for future work.