Uncertain multi-objective multi-route shortest path problem by robust enhanced non-dominated sorting genetic algorithms: Application to emergency medical services

Abstract

The shortest path problem has emerged as one of the most significant problems in network optimization with broad applications in the real world. Modeling these real-world applications includes a variety of ambiguous phenomena that can be estimated using human beliefs. In dealing with such uncertainty, Liu's uncertainty theory is considered a legitimate tool. This paper examines the uncertain multi-objective multi-route shortest path problem (UMOMRSPP) for directed graphs. The zigzag uncertain variables are used to represent uncertain parameters. For UMOMRSPP, the expected and optimistic value models are developed, and their corresponding deterministic transformation is provided. The deterministic models are solved using three existing multi-objective genetic algorithms (MOGAs), namely the hybrid genetic algorithm, non-dominated sorting genetic algorithm (NSGA)-II & NSGA-III and two proposed aspiration level (AL)-based algorithms: AL-based NSGA-II and AL-based NSGA-III. An emergency medical services problem is studied as an application in the context of UMOMRSPP. A comparison between the proposed methods and the MOGAs mentioned above is presented. A sensitivity analysis of objective functions regarding the shape parameter and AL is performed. The performance measure coverage is computed to demonstrate the effectiveness of the proposed methods. This study suggests that AL-based NSGA-II & III provide solutions based on the decision-maker's AL and can handle real-world UMOMRSPP effectively with efficient outputs.