Abstract
Abstract This paper employs uncertain programming to investigate the uncertain multi-modal shortest path problem, in which the arc weights (arc travel time, arc travel costs) associated with different transport modes are characterized by uncertain variables. By using the chance-constrained programming approach, we firstly formulate a bi-objective optimization model to minimize the total travel time and travel costs simultaneously with the given confidence levels. Moreover, using the basic concepts and properties in the uncertainty theory, we transform the proposed model into its deterministic crisp equivalent with an explicit proof. Finally, some numerical experiments are implemented to show the performance of the proposed approaches on a multi-modal transportation network with three specific modes.
Highlights
The shortest path problem is widely applied to network optimization and has been studied by a lot of researchers
This paper aims to investigate the multi-modal shortest path problem, in which both travel time and travel costs are regarded as uncertain variables
Uncertainty theory is a branch of mathematics to study the characteristics of nondeterministic phenomenon
Summary
The shortest path problem is widely applied to network optimization and has been studied by a lot of researchers. Due to the failure, maintenance, and other uncertain factors, arc weights are usually non-deterministic in a busy transportation network In view of this fact, some researchers introduced probability theory into the shortest path problem and used probability distributions to describe the existing indeterminacy, such as Frank [4], Loui [5], Mirchandani [6], Yang et al [7], and Yang and Zhou [8]. This method is typically imprecise when we are lack of a priori data information with respect to networks. Some other routing optimization with fuzzy information can be referred to Ji et al [10], Hernandes et al [11], and Yang et al [12]
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