Multi-Objective Optimization Methods for Transportation Network Problems: Definition, Taxonomy, and Annotation

Introduction

The transportation system defined as the displacement of the goods or passengers between two terminals or cities in the international or national network. The national and international networks include the conveyances, corresponding network, transportation mode, networks paths, itineraries, cities, depots, customers, stations, and terminals. The network defined by a set of nodes connected by one or more itineraries in the transportation system, each itinerary represents a transportation mode. The itinerary is represented by only one connection and one transportation mode between two nodes. The nodes are described as exchange stations that can include the transshipment, the delivery or the load and unload of the merchandise.

This article provides an overview of the literature researches based on the optimization of transport problem as well as the optimization methods applied to solve these problems in multi-objective and single objective case. The goal is to distinguish the objectives functions of the optimization transport problem to better satisfy the customer's demands. This satisfaction incorporates a set of objectives, such as minimizing the total cost of transport, the total time of transport or maximizing the quality of service, etc., in order to transfer the merchandise from a departure node to a destination node. These objectives are measured and evaluated differently according to the criteria and the parameters defined by the decision-maker depending on the case study.

The optimization methods and operations research play an important role in solving these problems. The role of the decision-maker is to adopt the optimization methodology or techniques to better optimize and solve the problem after having defined and modeled it. The modeling step consists to define the assumptions, the sets, and settings of the problem, the decision variables and the objectives functions that defined by the set of criteria and the set of constraints to be respected.

The aim of this paper is to recapitulate the existent optimization and resolution methods applied to solve the planning transportation networks problem, in order to help the decision-maker to identify the type of problem to be solved and to select the criteria to be optimized.

The structure of this paper is organized as follows: Section 2 outlines a classification relying on the existent characteristics of transportation problems and presents a taxonomy of objectives functions based on optimization and transportation problems. Section 3 discusses an overview of the modeling and resolution method that solves the most common transportation problems by means of a single objective. Section 4 discusses an overview of the modeling and resolution methods that solve the principal transportation problems using multiple objectives. This section ends with a synthesis and criticizes main literature researches. Section 5 focuses on a survey of the existent researches dealing with multimodal transportation problems and defining their main extensions. This section is split into three sub-sections, i.e., the single objective optimization problems, the multi-objective optimization and ultimately, a critical comment, which is discussed. Besides, a multi-objective mathematical formulation is cited. Correspondingly, the readers are referred to (Mnif & Bouamama, 2017b, 2017a). Finally, section 6 concludes with a summary and suggests some future research directions.