Journal of Industrial Engineering

Volume 2017, Article ID 3019523, 13 pages

https://doi.org/10.1155/2017/3019523

## Machine Learning-Based Parameter Tuned Genetic Algorithm for Energy Minimizing Vehicle Routing Problem

Department of Industrial Management, University of Kelaniya, Kelaniya, Sri Lanka

Correspondence should be addressed to Thashika D. Rupasinghe; kl.ca.nlk@akihsaht

Received 6 September 2016; Revised 17 December 2016; Accepted 21 December 2016; Published 18 January 2017

Academic Editor: Shu-Chu Liu

Copyright © 2017 P. L. N. U. Cooray and Thashika D. Rupasinghe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

During the last decade, tremendous focus has been given to sustainable logistics practices to overcome environmental concerns of business practices. Since transportation is a prominent area of logistics, a new area of literature known as Green Transportation and Green Vehicle Routing has emerged. Vehicle Routing Problem (VRP) has been a very active area of the literature with contribution from many researchers over the last three decades. With the computational constraints of solving VRP which is* NP-hard*, metaheuristics have been applied successfully to solve VRPs in the recent past. This is a threefold study. First, it critically reviews the current literature on EMVRP and the use of metaheuristics as a solution approach. Second, the study implements a genetic algorithm (GA) to solve the EMVRP formulation using the benchmark instances listed on the repository of CVRPLib. Finally, the GA developed in Phase 2 was enhanced through machine learning techniques to tune its parameters. The study reveals that, by identifying the underlying characteristics of data, a particular GA can be tuned significantly to outperform any generic GA with competitive computational times. The scrutiny identifies several knowledge gaps where new methodologies can be developed to solve the EMVRPs and develops propositions for future research.

#### 1. Introduction

*Background of Research*. Vehicle Routing Problem (VRP) can be described as the problem of finding optimal routes for delivery or collection from one to many depots to many customers who are geographically distributed. This problem has been the core for many operations research problems and has many variations. Later, with the focus on sustainable business practices, a novel category of VRP has emerged, known as Green VRP. In this category, the objectives are different from original VRP where it minimizes the travelled distance ultimately, thus reducing the cost. However, GVRP attempts to minimize the impact on environment of routing using different approaches [1]. Energy Minimizing VRP (EMVRP) has been developed to minimize the energy consumption of a fleet while serving all the customers. It has been identified that energy consumption has a direct impact on carbon dioxide emission.

Metaheuristics are used for combinatorial optimization in which an optimal solution is sought over a discrete search space. VRP is one of the most known NP-hard problems; thus, metaheuristics have been widely used to find near-optimal solutions for VRP problems [2].

Machine learning is a subfield of computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. Machine learning explores the construction and study of algorithms that can learn from and make predictions on data. In this research, the intention is to use machine learning to tune the developed metaheuristics to solve the formulated routing problem [3]. The overall objective of this study is to develop a set of genetic algorithms to solve the EMVRP and apply machine learning techniques to tune the developed algorithms to enhance the quality of the solutions. Energy Minimizing VRP has been formulated by Kara et al. [1] with the objective of minimizing energy consumption while serving a distributed set of customers. Though it minimizes the energy consumption, the calculated reduction of carbon dioxide emission has not been calculated; thus, the environmental sustainability of EMVRP has not been stated in the original paper. The study has used CPLEX® for solving moderate sized problems and the computational times were not promising. It is therefore necessary to develop efficient solution procedures for the EMVRP and in this study the authors implement genetic algorithms (GAs) for the genetic EMVRP formulation. The aforementioned GA was enhanced through machine learning techniques to tune its parameters based on the underlying characteristics of the data being used. In the book* Tuning Metaheuristics* by Birattari [3], it has been mentioned that tuning is crucial to metaheuristic optimization both in academic viewpoint and for practical applications. Nevertheless, relatively less research has been devoted to the issue and shows that the problem of tuning a metaheuristic can be described and solved as a machine learning problem. To the authors’ knowledge, this will be the first instance of machine learning being used as a mechanism to tune the domain of VRP.

#### 2. Literature Review

##### 2.1. Vehicle Routing Problem

Vehicle Routing Problem (VRP) can be described as the problem of finding optimal routes for delivery or collection from one to many depots to many customers who are geographically distributed. VRP is at the core of a huge number of practical applications in the area of transportation. It is one of the most studied classes of problems in operations research (OR) according to Gendreau et al. [4]. The list of variants according to a recent survey by Lin et al. [5] can be classified as Capacitated VRP (CVRP), Time Dependent VRP (TDVRP), Pickup and Delivery Problem (PDP), Multidepot VRP (MDVRP), Stochastic VRP (SVRP), Location Routing Problem (LRP), Periodic VRP (PVRP), Dynamic VRP (DVRP), Inventory Routing Problem (IRP), Fleet Size and Mix Vehicle Routing Problem (FSMVRP), Generalized VRP, Multicompartment VRP (MCVRP), Site Dependent VRP, Split Delivery VRP (SDVRP), Fuzzy VRP, Open VRP (OVRP), VRP with Loading Constraints (VRPLC), and Multiechelon VRP (MEVRP).

##### 2.2. Green VRP

Green Logistics has recently received a lot of interest from governments and business organizations. The main reason behind this is that the current logistics practices are not sustainable in the long term and sometimes in the literature there are instances where the improved performance in terms of economic performance has caused a decrease in environmental performance. A classic example can be found in the study done by Yazan et al. [6] where they reengineered the supply chain, but, however, their reengineering outcomes seem to have been unsuccessful with regard to CO_{2} emission, since CO_{2} emission has been increased after the study, and this shows reengineering failure in environmental sense, although the economic performance has been increased by reengineering the system. With these reasons, the focus is automatically given to sustainable transportation practice which is generally known as Green Transportation. Björklund [7] defines “Green Transportation” as “transportation service that has a lesser or reduced negative impact on health and natural environment when compared with competing transportation services that serve the same purpose.” Under this category, a subcategory has been defined as “Green Vehicle Routing Problems” and they are characterized by the objective of harmonizing the environmental and economic costs by implementing effective routes to meet the environmental concerns and financial indexes [5]. The importance of Green VRP is characterized mainly by CO_{2} emission by vehicles since they are one of the prime consumers of petroleum products. The sector contributes to 15% of overall greenhouse gas (GHG) emissions and 23% of overall CO_{2} emissions, which is the highest found GHG [8]. The different variants of Green VRP have been introduced to the literature which have various objectives to support sustainable VRP. Those can be listed as Pollution Routing Problem (PRP), Green Vehicle Routing Problem (GVRP), and VRP in Reverse Logistics (VRPRL) [5].

##### 2.3. Energy Minimizing Vehicle Routing Problem

Under the GVRP aimed problems, one problem introduced in 2007 by Kara et al. [1] is Energy Minimizing VRP (EMVRP). EMVRP has been identified in the survey by Lin et al. [5] under the category of GVRP. The objective of EMVRP is to reduce the energy consumption and energy has been justified to be the product of distance travelled by the load of the vehicle. Concretely, EMVRP aims at minimizing the sum of the product of load and distance for each arc. However, in the original paper, the authors have not justified the CO_{2} emission reduction of EMVRP. Furthermore, the problem has been solved using CPLEX 8.0 for small sized instances and it is mentioned that the CPU times over moderate sized problems have not been optimized. Thus, this raises the need for developing efficient heuristics for solving moderate and large instances.

EMVRP is mathematically formulated first by Kara at el. [1] as in the following: Objective function is Constraints are as follows:The cost of traversing an arc () is the product of the distance between the nodes and and weight on this arc. Constraints (2) and (3) ensure that vehicles are used. Constraints (4) and (5) are the degree constraints for each node. Constraint (6) is the classical conservation of flow equation balancing inflow and outflow of each node, which also prohibits any illegal subtours. Constraint (7) initializes the flow on the first arc of each route; the cost structure of the problem necessitates such initialization. Capacity restrictions are considered and force to zero when the arc () is not on any route. Then, the constraint produces lower bounds for the flow on any arc.

##### 2.4. Metaheuristics for Solving VRP

Metaheuristics are categories of heuristics used for solving optimization problems, mostly* NP-hard* problems, which cannot be optimally solved within feasible time. Lenstra and Kan [9] have shown that all the Vehicle Routing Problems are* NP-hard* and cannot be solved in polynomial time. In the literature, there are many instances where metaheuristics have been applied to solve VRP. Among them, the most applied path-based and population-based metaheuristics can be selected using the categorized bibliography done by Gendreau et al. [4].

###### 2.4.1. Genetic Algorithm (GA)

Genetic algorithms (GAs) are adaptive methods which may be used to solve a wide variety of optimization problems. They are based on the genetic processes of biological organisms. Over many generations, natural populations evolve according to the principles of natural selection and “survival of the fittest.” By mimicking this process, genetic algorithms are able to “evolve” solutions to real world problems, if they have been suitably encoded. The basic principles of GAs were first laid down rigorously by Holland [10]. GA is more applicable for solving an optimization problem where the optimum result is derived from a large random dataset like the scenario in the research problem.

##### 2.5. Machine Learning for Metaheuristics

Machine learning is an area of computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. It explores the construction and study of algorithms that can learn from and make predictions on data. When metaheuristics are developed, the algorithms can be tuned for better performance (Birattari [3]). Each metaheuristic has already set parameters that have to be initialized before the execution of the algorithm. The metaheuristics adaptation requires the adjustment of these parameters according to the problem at hand. This is known as parameter tuning. An appropriate initial parameter setting has a noteworthy impact on the solving progress, such as the exploitation or exploration rate of the search space, and therefore the quality of the solution [11]. Tuning metaheuristics using machine learning techniques is a novel approach and there is not much literature on the area.

#### 3. Methodology

##### 3.1. Research Approach

In the first phase of the study, Green VRP methodologies will be systematically reviewed to identify important characteristics of problem solving methodologies [12]. In the second phase of the study, GA-based metaheuristics are developed to solve the routes which minimize the energy consumption of a vehicle fleet while serving a set of customers. In the third phase, the applicability of machine learning techniques for parameter tuning of metaheuristics will be tested (Figure 1).