A Simulation-Infused Optimization Approach for Decomposing Nonlinear Systems

Introduction

This article presents an advanced vehicle routing optimization approach that integrates simulation with optimization to solve the Multi-Depot Vehicle Routing Problem (MDVRP).

The MDVRP is a complex logistics challenge where multiple depots dispatch vehicles to serve customers while minimizing travel time and costs. Traditional optimization techniques struggle with real-world constraints such as road networks, vehicle capacities, and uncertain travel times, making it difficult to find efficient routing solutions.

To overcome these challenges, the study introduces a simulation-infused optimization framework that combines mathematical optimization with AnyLogic simulation software. This approach significantly improves computational efficiency and solution quality by modeling real-world travel conditions and iteratively refining solutions. The key innovation lies in using simulation as an optimization substitute, allowing the algorithm to navigate complex decision-making problems more effectively than traditional mathematical models.

Simulation model

The simulation model is built using AnyLogic, a powerful platform that supports agent-based modeling and GIS integration. The key components of the vehicle routing optimization model include:

• Depots (Hubs): Locations where vehicles originate and return after deliveries.
• Trucks (Vehicles): Each truck follows an optimized route based on assigned deliveries.
• Customers: Delivery points with specific demands and locations.

Unlike conventional optimization models that rely on simplified distance calculations, this research leverages GIS data to incorporate real-world road networks into the Multi-Depot Vehicle Routing Problem. The simulation dynamically adjusts travel times based on realistic routing conditions, making the optimization model more accurate and applicable to real-world logistics.

The vehicle routing optimization process follows an iterative approach:

1. Customer assignment: the master problem assigns customers to depots based on demand and capacity constraints.
2. Vehicle routing optimization: the subproblem finds the most efficient delivery routes for each truck.
3. Simulation validation: AnyLogic evaluates travel times using road data.
4. Iterative refinement: the optimization algorithm adjusts routing decisions based on simulation results, improving efficiency with each iteration.

A learning rate parameter is introduced to balance exploration (searching for new routing solutions) and exploitation (improving existing routes), ensuring faster convergence and higher solution quality.

Results

The proposed vehicle routing optimization approach was tested on three MDVRP instances, varying in size (12, 23, and 34 nodes). Key findings included:

• 70% faster computation time compared to traditional optimization methods.
• Up to 8% improvement in delivery times when using real-world road networks instead of estimated distances.

This paper explores how simulation modeling enhances vehicle routing optimization, making it a powerful solution for the multi-depot vehicle routing problem. Using AnyLogic, the proposed approach delivers faster, more accurate, and scalable vehicle routing optimization.

This method is highly beneficial for supply chain management, urban logistics, and transportation planning, where real-world factors like traffic, road constraints, and delivery schedules challenge traditional optimization methods.