###### Abstract  
Growing competition in the world enforces the need for an efficient design of transportation networks. Furthermore, a competitive transportation network should also be eco-friendly. As road transportation is responsible for the largest quantities of CO\({}_{2}\) emissions, Intermodal Transportation (IT) might be a potential alternative. From this perspective, intermodal terminals location is a cornerstone for building a sustainable transportation network. The purpose of this paper is to study and efficiently solve the Intermodal Terminal Location Problem on incomplete networks. We model this problem as a mixed integer linear program and develop a simulated annealing algorithm to tackle medium and large instances. The computational results show that the obtained solutions using simulated annealing are competitive and close to the exact solutions found by CPLEX solver for small and medium instances. The same developed algorithm outperforms the best found solutions from the literature using heuristics for larger instances. terminal location; intermodal transportation; simulated annealing; mixed integer program; incomplete networks +
Footnote †: journal: Applied  
**Citation:** [PERSON] [PERSON] A Simulated Annealing Algorithm for Intermodal Transportation on Incomplete Networks. _Appl. Sci._**2021**, _11_, 4467. [[https://doi.org/10.3300/app11104467](https://doi.org/10.3300/app11104467)]([https://doi.org/10.3300/app11104467](https://doi.org/10.3300/app11104467))  
Academic Editors: [PERSON], [PERSON] and [PERSON] Received: 22 February 2021  
Accepted: 16 April 2021  
Published: 14 May 2021  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. IT is a competitive alternative for door- to-door road transport when the unit cost of the consolidation mode (the second segment) is smaller than in road mode and compensates the additional fees of transshipment operations. IT is very successful and even crucial when we have the two following situations: (i) when the transport is not time critical; and (ii) when there is a large volume of goods. In fact, despite the great speed of the carriage (e.g., rail mode), the overall journey of an intermodal transport chain takes more than door-to-door road. Accordingly, intermodal transportation is not suitable for urgent deliveries. In addition, having a large amount of goods is necessary to benefit from the scale economy generated by the consolidation mode. Intermodal terminals are equipped centers for the transshipment of goods between different modes of transportation. The location of such terminals is a strategic decision that may have a strong and direct influence on the overall operational costs. This problem is addressed in the scientific literature by analogy to well-known Facility Location Problems (FLP) and to Hub Location Problems (HLP). The pioneering paper of [1] is the starting point of Intermodal Terminal Location Problem. The majority of later studies were based on this paper. The authors either proposed a modified version of the models or proposed solving approaches. The proposed works commonly assume that all located terminals are fully connected in a generated solution. The main contributions of the current paper are the following:  
* We propose a generalization of a well-known problem in the literature, namely the Intermodal Terminal Location Problem (ITLP) by introducing the incomplete version of the problem relaxing the completeness of the inter-terminal network. * We build a mathematical MIP (Mixed Integer Program) model to formulate the problem and we discuss the meaning of each components. * We solve small and medium instances to optimality using CPLEX solver. * We develop an efficient simulated annealing is adopted to solve real life size instances. * We present extensive numerical experiments and analyze the obtained results. The remainder of the paper is structured as follows. We review related works in Section 2.