Uncertain Chinese postman problem with budget constraint: a robust optimization approach

The Chinese postman problem (CPP) is a widely recognized combinatorial optimization problem with numerous real-world applications. Modeling such real-world applications often involves considering uncertain variables. Robust optimization is one of the prominent approaches for solving optimization problems when uncertainties are present in the parameters of the optimization problem. In this paper, we delve into the realm of the uncertain multi-objective Chinese postman problem, incorporating budget constraints while simultaneously optimizing profit maximization and time minimization, all within the framework of robust optimization methodology. We formulate the deterministic form of uncertain multi-objective CPP for three different types of uncertainty sets: ellipsoidal, polyhedral, and budgeted. To tackle these formulations, we employ four established multi-objective solution strategies: the global criteria approach, the fuzzy programming method, \(\epsilon \)-constraint, and the Genetic algorithm. Subsequently, we conduct numerical experiments to verify the proposed models.