A New Multi-Objective Firework Algorithm to Solve the Multimodal Planning Network Problem

Introduction

Nowadays, the transportation problem occupies a critical position in the economy service of import or export companies. The improvement of the multimodal transportation planning system, and the assignment of the transport mode have gained momentum in the areas of research. This article aims to improve and optimize the decision-making over a planning system on the national and the international freight flows. In fact, various optimization criteria can be considered in the multimodal transportation network problem (MTNP) such as the total cost and the total time of transport. These criteria depend on the application case and the variant of transportation problem to be solved.

However, this problem is popularly known for their richness to the research studies, they include several sub-problems that need to be examined separately such as the planning problem, scheduling problem or the containers’ assignment, etc.

Nevertheless, the multimodal transportation network (MTN) studies contain various interdependent sub-problems viz. planning networks on urban areas, maritime or airlines path, environmental issues, multimodal shortest path, transshipment or loading-unloading of the commodity, the assignment containers problem, etc.

The PNMT problem aims to determine the multiple transportation flows. The resolution are made by both the selection of the transport mode and the visited nodes as well as the optimization of the planning paths by making them connected in order to guarantee the corresponding links on the multimodal network, while satisfying the set objectives. An objective can include various criteria such as the minimizing of the total cost can includes the transshipment cost, the transportation costs, the costs of delays and the transportation distance criterion, etc.

However, a very few studies have taken into account both planning and assignment problem in order to solve the MTNP. The researchers distinguish several criteria that define the MTNP, incorporating the diversity of the transport modes and paths and their characteristics. The transshipment must synchronize between the various modes and satisfy the exchange of information. The assignment problem of conveyance includes other interdependent sub-problems, including the selection of intermediary nodes, the transport mode, and transport itineraries. These sub-problems will significantly be influenced by decision-making. In this manuscript, the authors develop and adopt a new optimization method to solve MTNP. The proposed approach aims to satisfy the customers' wishes by achieving the optimization solution, will select the best performing transport mode and itinerary.

In (Mnif & Bouamama, 2017a, 2017b), a Multi-objective mathematical model was proposed to solve MTNP. This model is developed by using the Cplex optimizer with concert technology. The key advantage of the complete methods is the possibility to provide an optimal solution, nevertheless, its exponential complexity hampers this advantage. In fact, the multi-objective optimization (MOO) in the MTNP is NP-hard.

With the computational time and multiple constraints and criteria of this problem, the resolution of the latter becomes very difficult, as it requires the use of incomplete optimization methods. However, several techniques adopted to prevent algorithms from getting trapped in local optima, such as the Genetic Algorithms, the Tabu Search, the Particle Swarm Optimization Algorithm, the Fireworks Algorithm, etc. These algorithms sacrifice completeness in favor of computational feasibility, applicability, and efficiency (Bouamama & Ghedira, 2006).

In this article, authors contribute to the development of the optimization method. The main aim of the proposed method is to achieve or approach to the optimal solution in a faster computation time. This method defined as a new evolutionary optimizer algorithm, based on the firework algorithm and the Pareto dominance method, attempts to reach the best compromise solution. The purpose of this optimization method is to provide a set of feasible solutions for this problem. The optimization included the total cost and time of transport, by minimizing the total multimodal transport cost and the total duration of transport while respecting the arrival to the customer at definite time windows.