# Co-Simulation of Multiple Vehicle Routing Problem Models
###### Abstract  
Complex systems are often designed in a decentralized and open way so that they can operate on heterogeneous entities that communicate with each other. Numerous studies consider the process of components simulation in a complex system as a proven approach to realistically predict the behavior of a complex system or to effectively manage its complexity. The simulation of different complex system components can be coupled via co-simulation to reproduce the behavior emerging from their interaction. On the other hand, multi-agent simulations have been largely implemented in complex system modeling and simulation. Each multi-agent simulator's role is to solve one of the VRP objectives. These simulators interact within a co-simulation platform called MECSYCO, to ensure the integration of the various proposed VRP models. This paper presents the Vehicle Routing Problem (VRP) simulation results in several aspects, where the main goal is to satisfy several client demands. The experiments show the performance of the proposed VRP multi-model and carry out its improvement in terms of computational complexity.  
complex system; multi-simulation; vehicle routing problem +
Footnote †: journal: Future Internet  
to improve the performance of VRP by modeling different methods for solving various VRP objectives.  
Co-simulation is applied in many different multidomain systems [10]. It is proposed to address the issues and challenges of complex systems [11]. In this context, decomposed components of a complex system are modeled by different sub-models, then simulated using a simulator for each sub-model. Co-simulation enables exchanging coupling connections to achieve the behavior of the whole complex system as shown in Figure 1. The co-simulation middleware named Multi-agent Environment for Complex SYstem CO-simulation (MECSYCO) allows the integration of several modeling and simulation software to co-simulate the dynamic behavior of a complex system. MECSYCO makes the possibility to compare simulation results, swap, add, or remove models.  
This paper aims to address the challenge of showing the impact of simulating a VRP multi-model as several interacting simulators by reducing the traveled distance and the obtained time during vehicles routing with the aim to satisfy clients demands. In this context, we will design and implement multiple VRP models as complex systems with several perspectives of multi agent simulators. Each simulator in the proposed solution solves different objectives of the VRP and then makes them interact into the co-simulation platform. Multi agent simulators that represent the VRP models are developed using Netlogo and the whole system is reproduced based on the MECSYCO co-simulator. We observed that the interacting VRP models provide high quality solutions by minimizing significantly the cost of services offered to the clients, in terms of computational time and travel distance.  
The rest of this work is organized as follows: In Section 2, we present the summary of the related multi-simulation of complex system research and introduce an overview of the used platform in the co-simulation and we describe the problem formulation of the VRP. The proposed solution is presented in Section 3. Section 4 provides the implementation details and the experiments results. Section 5 concludes the work and give some future work avenues.