A Sustainable Multimodal Transport System: The Two-Echelon Location-Routing Problem with Consolidation in the Euro-China Expressway

Sustainable development of transport systems is a common topic of concern and effort in multiple countries, in which reducing carbon emissions is one of the core goals. Multimodal transport is an effective way to achieve carbon emission reduction and to efficiently utilize transport resources. The intercontinental transport system, represented by the Euro-China Expressway, is a prominent exploration that has recently received attention, which promotes the sustainable development of transport between countries and carbon emission reduction. In the intercontinental multimodal transport system, the reasonable connection of roads and railways, especially the optimization of consolidation, is an important link which affects the system's carbon emissions. This paper focuses on the consolidation of sustainable multimodal transport and summarizes the multimodal transport two-echelon location-routing problem with consolidation (MT-2E-LRP-C). We aim to solve multimodal consolidation optimization problem, especially locations of multimodal station, by routing of highway and railway. We propose a two-layer mixed integer linear problem (MILP) model, which highlights the consolidation of roads and railways, focuses on road and rail transport connections, and optimizes road routes and railway schemes. To validate the MT-2E-LRP-C model, we design a series of random instances for different quantities of nodes. In order to solve large-scale instances and realistic transport problems, we propose a hybrid differential evolution algorithm, which decomposes the problem into a railway layer and a highway layer for heuristic algorithm solving. Furthermore, the MILP model and algorithm are tested by small-scale random instances, and the hybrid differential evolution algorithm is solved for the large-scale random instances. Finally, we solve the realist instance from the Euro-China Expressway to develop instructive conclusions.