Uncertain multi-objective optimization for the water–rail–road intermodal transport system with consideration of hub operation process using a memetic algorithm

Abstract

This paper addresses the multi-objective optimization of water–rail–road (WRR) intermodal transport system under uncertainty by explicitly capturing intermodal hub operation activities. Through the use of hub-and-spoke-type network, we formulate an uncertain multi-objective programming model for the WRR intermodal transportation network design problem, in which the cost, time and reliability objectives are simultaneously considered. Subsequently, we turn the original model into a deterministic equivalent multi-objective programming model under mild assumptions. Eventually, we utilize the $$\varepsilon $$-constraint method to reformulate the crisp multi-objective programming model to a modified mono objective one, which has proven to be NP-hard. Hence, we develop a memetic algorithm (MA) by combining a genetic algorithm and local intensification to solve the proposed problem. When designing the MA, we propose a combination encoding scheme to represent the location of intermodal hubs, the allocation of the demand nodes and the assignment of transportation modes. Moreover, we provide two local intensification operators to enhance exploitation ability. Finally, we implement a series of numerical experiments based on the Turkish network data set to verify the practicability of the proposed model and effectiveness of the solution approach developed in the paper.