Determining All Pareto-Optimal Paths for Multi-category Multi-objective Path Optimization Problems

Increasing criteria have been involved in the path evaluation, and path optimization with multiplicative objectives becomes essential in the real world, such as the reliability of paths. Firstly, we define the multi-category multi-objective path optimization problem (MCMOPOP), in which each path simultaneously has multiple additive and multiplicative weights. Secondly, this paper proposes an agent-based and nature-inspired algorithm, the ripple-spreading algorithm (RSA), to solve the MCMOPOP. To the best of our knowledge, the newly proposed RSA is the first algorithm for the MCMOPOP that can find all Pareto-optimal paths. An illustrative example is provided to make the processes of the RSA more comprehensible. Comparative experiments demonstrate that the RSA outperforms other compared methods in computational efficiency and solution quality. Furthermore, the RSA maintains applicability when the number of objectives is large. The RSA can be expected to efficiently provide complete solutions for the practical applications modeled as the MCMOPOP.