Data-Driven Robust Optimization for Solving the Heterogeneous Vehicle Routing Problem with Customer Demand Uncertainty

Jingling Zhang,Mengfan Yu,Qinbing Feng,Yanwei Zhao,Longlong Leng,Matilde Santos

doi:10.1155/2021/6634132

Abstract

In practice, the parameters of the vehicle routing problem are uncertain, which is called the uncertain vehicle routing problem (UVRP). Therefore, a data-driven robust optimization approach to solve the heterogeneous UVRP is studied. The uncertain parameters of customer demand are introduced, and the uncertain model is established. The uncertain model is transformed into a robust model with adjustable parameters. At the same time, we use a least-squares data-driven method combined with historical data samples to design a function of robust adjustable parameters related to the maximum demand, demand range, and given vehicle capacity to optimize the robust model. We improve the deep Q-learning-based reinforcement learning algorithm for the fleet size and mix vehicle routing problem to solve the robust model. Through test experiments, it is proved that the robust optimization model can effectively reduce the number of customers affected by the uncertainty, greatly improve customer satisfaction, and effectively reduce total cost and demonstrate that the improved algorithm also exhibits good performance.

Highlights

To effectively allocate logistics resources and reduce transportation costs, the vehicle routing problem (VRP) has been a key topic in the field of logistics scheduling. e VRP was first introduced by Dantzig and Ramser in 1959 [1]
Its basic form is the capacitated vehicle routing problem (CVRP), a problem that needs to meet some constraints, such as known vehicle capacity and customer demand. e objective of the CVRP is to minimize the distance traveled by vehicles to serve all customers and achieve the goal of reducing logistics and distribution costs
In designing robust models related to the heterogeneous vehicle routing problem with uncertain demand (HVRPUD), Γk is used to control for the uncertainty, taking the value of the demand at the customer point that each vehicle corresponds to serve

Summary

Introduction

To effectively allocate logistics resources and reduce transportation costs, the vehicle routing problem (VRP) has been a key topic in the field of logistics scheduling. e VRP was first introduced by Dantzig and Ramser in 1959 [1]. Solanocharris et al used the minimum and maximum principle to establish a robust optimization model of vehicle routing with uncertain time in the discrete scenario, and they solved the problem by using the genetic algorithm [22]. They built a robust optimization model based on novel route-dependent uncertainty sets and designed a two-stage algorithm to solve the problem [23]. With minimizing transport time as the goal, Ma et al considered charging facilities and uncertain road conditions, established a robust optimization model of electric vehicle distribution routes with adjustable robustness, and used a three-stage genetic algorithm to solve the model [26]. Rough test experiments, it is proved that the robust optimization model designed for this problem can effectively reduce the number of customers affected by uncertainty, greatly improve customer satisfaction, and effectively reduce total costs. e improved algorithm exhibits better performance

Heterogeneous VRP with Uncertain Demand Formulation

Hyperheuristic Algorithm Design

G-14 G-15 G-16

Findings

Conclusions