A New Last Mile Delivery Approach for the Hybrid Truck Multi-Drone Problem Using a Genetic Algorithm

Abstract

In this study, the use of drones in transportation and some optimization studies carried out in the literature so far were examined. Based on these investigations, a genetic algorithm-based method has been proposed to solve the hybrid truck multi-drone problem. With the proposed algorithm, scenarios have been created using single or multiple drones and one truck for a certain number of customers to be delivered, and results have been obtained. In these scenarios, the main aim is to minimize delivery time. The results obtained have also been compared with other optimization algorithms and other results in the literature, and in addition, it has been proven that there is an inverse relationship between the number of drones and the delivery time. As a result of the comparisons, it has been clearly seen that the proposed algorithm is quite successful in finding the most suitable route in the shortest time compared to other studies. A solution has been created for a real-world problem with the proposed genetic algorithm-based algorithm, and it has been concluded that it is quite successful here as well.

1. Introduction

The main purpose of the logistics and transportation sectors is to transport the requested product or object from one point to another. Today, motor vehicles and electronic vehicles are at the forefront of the realization of logistics services. With the increasing competition in the business world and in electronic commerce, companies have been obliged to produce solutions that are compatible with the technology of the time in order to maximize customer satisfaction [1,2,3,4,5,6,7]. The most important example that can be given for this situation is that cargo and transportation companies have started to use drones in the process of delivering a package from the transportation center to the final destination, also known as “last-mile delivery”. Minimizing transportation costs is a vital issue for all companies and has been the subject of many studies to date. Most of these studies are aimed at calculating the most suitable route in terms of delivery points. Additionally, as a result of the research, transportation costs have found their place among the most important expense items in the logistics industry. Therefore, calculating the most appropriate route will be beneficial in terms of customer satisfaction as it will reduce costs and shorten delivery time [8,9].

1.1. Motivation

Vehicle Routing Problem (VRP) and Traveling Salesman Problem (TSP) are the most well-known studies, which are relatively old methods and are used to reduce costs by finding the optimum route in the distribution method made only by trucks. TSP is a problem in which a seller who has products that need to be distributed to different cities with known distances between each other uses a vehicle to deliver these products to all delivery points in the shortest way possible without repetition. TSP is basically an optimization problem and is defined as an NP-hard problem. VRP is a generalized version of TSP, and it is a problem that aims to minimize the cost by finding the most suitable route, as in TSP. Furthermore, VRP is defined as an NP-hard problem like TSP. VRP differs from TSP in that it can include multiple routes rather than a single route, and it also considers vehicle capacity limitations [10,11,12].

Another delivery method that is becoming widespread in transportation today is the use of drones as well as the traditional method. Studies on the use of drones, which are used in many fields, such as logistics and transportation, date back to the early 2000s in the literature. A study conducted in 2004 focused on aerial cargo robots, and the first flight of the prototype of these aerial cargo robots was carried out in 2005 [13]. Drones are preferred due to their advantages, such as being lightweight, being able to work in large areas in the field without the need for any human control, and having fast movement capabilities. In addition to these advantages, there are also disadvantages, such as the difficulty of coordinating multiple drones that will work together and the difficulty of calculating the most appropriate route. Due to the stated advantages of drones, their use is increasing day by day in the transportation and logistics sector, as well as in other sectors [14,15]. For example, in the study [16], an optimization study was carried out that allowed multiple transportation with only a single drone without using a truck. The TSP algorithm was used to determine the order in which drone deliveries should occur, with a maximum of three deliveries being made at the same time. It was planned that customers would receive the package by scanning the QR code on the drone camera during the delivery phase. Here, not proposing a truck-drone delivery-based approach and delivering using only one drone instead of multiple vehicles was seen as a shortcoming. Therefore, the algorithm proposed in this study was developed to overcome its shortcomings.

In terms of delivering cargo to more than one customer at the same time, instead of just trucks or only drones, the application of hybrid trucks and multiple drones is increasing today and is seen as an inevitable solution in the future. Especially with the growth of electronic commerce, the intensification of city traffic, and the formation of high-rise buildings, the hybrid truck multi-drone application has been developed as one of the new cargo distribution solutions. In terms of truck and drone hybrid studies in the literature, the carrying potential of drones has not been sufficiently taken into account in mathematical modeling; the fact that drones can have different flight altitudes has not been adequately reflected; and in truck and multi-drone studies, only energy consumption, package weight, and drone weight are taken into account. In this article, a dynamic genetic algorithm-based approach has been discussed, especially in terms of ensuring this synchronization, and various results have been obtained for the mathematically modeled system. Drones can fly at various altitudes and offer lower-cost solutions for cargo delivery.

In this study, a GA-based hybrid truck multi-drone system was created to reduce delivery time by presenting a different perspective for truck-drone delivery. In the scenarios created in this study, there is a truck that will leave the warehouse and a variable number of drones that will accompany the truck to deliver the relevant packages to the delivery points. These vehicles should be able to work in coordination with each other. The drone leaving for delivery should be able to schedule an appointment with the truck to meet at one of the next delivery points. In addition, a GA-based algorithm, which is one of the heuristics, is used as a solution method in the proposed scenario.

1.2. Related Works

Many of the large-scale companies engaged in delivery and transportation businesses already use drones in their transportation operations. With the Prime Air system introduced by Amazon, it is planned to deliver packages to customers in thirty minutes or less using drones. The first delivery of Prime Air was completed on 7 December 2016 in thirteen minutes [17]. In a study carried out by Dalsey, Hillblom, and Lynn (DHL), a logistics company, deliveries were made using drones. In the tests, in which drugs were delivered to an island on Lake Victoria for six months with the drone they named Parcelcopter, the drone was able to cover the sixty-kilometer distance between the mainland and the island in forty minutes. At the end of six months, this drone had flown a total of 2200 km [18]. Swiss Post, a Swiss postal service, started to transmit laboratory samples using drones, which were previously transmitted by land, and thus managed to reduce the transmission time from up to 45 min to a few minutes. This development has resulted in much faster delivery of healthcare shipments that often need urgent delivery [19]. In Turkey, companies are also working on and making breakthroughs in the use of drones in their deliveries.

In addition, studies on truck-drone delivery and route optimization have also found important places in the literature. These studies mostly consisted of different variations of TSP and VRP, which included solution methods for different scenarios. These scenarios, in which it is aimed to find the optimum route for truck-drone delivery, are considered problems, and many of them are defined as “NP-hard”; that is, they are difficult to solve. Generally, heuristic methods and dynamic programming methods have been proposed as solutions to such problems [20,21,22,23,24,25,26]. A genetic algorithm (GA) is one of the heuristic methods, and it is an algorithm created by applying the idea of natural selection in a computer environment. According to the GA, in each new generation, individuals with high-quality and low-quality genes from the previous generation and the most appropriate distribution of traits survive, but incompetent individuals cannot. In this way, the tendency for good and strong traits to be seen in new generations is greater [27,28,29,30].

Truck-drone delivery is basically the delivery of trucks and drones working together in delivery operations. These operations can have different scenarios. For example, one scenario may contain only one truck and one drone, while another scenario may not limit the number of trucks and drones. Or, in one scenario, while the drone moves from the warehouse independently of the truck and returns to the warehouse after completing the delivery, in another scenario, the truck and the drone may be considered as a whole, and the drone may not be allowed to operate independently of the truck. Since many different scenarios can be created in such studies, there are different scenarios for different operations in the literature.

In The Flying Sidekick Traveling Salesman Problem (FSTSP), a study by Murray et al., deliveries were realized by one truck and one drone. According to the scenario of FSTSP, the drone, which can carry a single package, left the truck when the time came and met the truck at the next stop of the moving truck after delivery. This study aimed to minimize the time until the return to the warehouse, i.e., the total delivery time. This was an NP-hard problem. Heuristic methods were proposed to solve this problem because it is an NP-hard problem. In the same study, it was suggested that delivery to remote locations can be executed by truck if most of the delivery points are close to the warehouse. It has also been suggested that drones can complete the delivery by constantly commuting between the central warehouse and nearby points and delivering to locations close to the central warehouse. This scenario was called the Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP). In this method, since the truck and the drone work independently of each other, the routes of the truck and the drone were considered independent from each other, and route calculations were made separately to solve this problem. As with FSTSP, PDSTSP was an NP-hard problem. Heuristic methods have been proposed to solve this problem [31].

The aim of the study by Kim et al. called The Traveling Salesman Problem with Drone Station (TSP-DS), was to solve the shortcomings of a PDSTSP. Drones have a range where they can operate in a healthy way. In the study, it was stated that the advantage of PDSTSP disappears when the number of delivery points within the distance that drones can serve from the central warehouse is very low. TSP-DS proposed using a “drone station” that can manage multiple drones to solve this problem. It was planned to deliver the packages by truck to the drone station, which was located far from the central warehouse. Afterward, it was thought that the truck would continue to deliver while the drones, which accepted the drone station as the center, delivered. To reduce the complexity of the situation, the problem was divided into two parts: the TSP and the parallel identical machine scheduling problem (PMS) [32].

In [33], the concept of the Traveling Salesman Problem with Drone (TSP-D) was emphasized. The most important difference between this scenario and FSTSP is that the location where the drone will meet with the truck after completing the delivery is the point where it starts moving from the truck. FSTSP does not allow this situation. The aim of the study was to minimize the service time, as in previous studies, and a dynamic programming-based solution method was presented.

In the study by Oberlin et al., the aim was to reduce the overall travel cost of drones. At the same time, in this study, the heterogeneity of vehicle means was explained. A heterogeneous drone is a team of drones with different sensing capabilities and different movement constraints that work together. The main process in the study was to transform a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, asymmetric TSP [34].

Boone et al. have defined the Multiple Traveling Salesman Problem (MTSP) in their study. According to the MTSP, a team of drones should visit target points in the most efficient way possible. In this approach, trucks were not used in the realization of deliveries, and primarily, the destination points were clustered using the K-means clustering method. Afterwards, these clusters were analyzed with a heuristic structure of their choice [35].

1.3. Hybrid Truck Multi-Drone Problem Description

This study aimed to find the most suitable route with the lowest cost for the last mile of the hybrid truck multi-drone delivery problem. When defining the hybrid truck multi-drone delivery problem, a G-directional graph, as shown in Figure 1, is used to represent the warehouse and delivery points as nodes and the route to be followed as branches. One truck and k drones are used on the graph $G=\left(V, E, C\right)$, a representative image of which is given in the figure. It is planned to find the least costly route, provided that all n nodes on this graph are visited once.

A graph defined as $G=\left(V, E, C\right);$

• $V$ is a cluster of nodes on the graph.
• $E$ is a cluster of branches on the graph.
• $C$ is the cluster of the weights of the branches.

There are n points on this graph to be delivered by the drone. These points are represented by $d_i$; they are the nodes shown as the red square in Figure 1, and they are the elements of the cluster $V_d$ given in Equation (1). At the same time, there are m points on this graph to be delivered by the truck. These points are represented by $t_i$; they are the nodes shown as gray circles in the figure, and they are the elements of the cluster $V_t$ given in Equation (2). Node $t_0$, another node on the graph, is the starting point called the warehouse and returns to this point after all deliveries are made. This node is shown with a blue triangle in the figure, and it is an element of the cluster, as shown in Equation (3). Additionally, in Figure 1, straight lines represent truck movement, and dashed lines represent drone movement.

$$V_d=\left\{d_1, d_2, d_3,\dots , d_n\right\}$$

(1)

$$V_t=\left\{t_1, t_2, t_3,\dots , t_m\right\}$$

(2)

$$V_0=\left\{t_0\right\}$$

(3)

If all the nodes of this G graph are represented as members of a cluster $V$, a cluster will be formed from the combination of the clusters given in the above three equations. Equation (4) shows this cluster of $V$.

$$V=V_d \cup V_t \cup V_0$$

(4)

If we examine the branches on the G graph, we see that there are two types of branches. Dotted arrows show movement by the drone, while arrows without dots show movement by the truck. If these different types of branches are defined as the elements of the $E_d$ and $E_t$ clusters, respectively, then the $E$ cluster with the branches of the $G$ graph can be considered the combination of these two different branch sets. This situation is seen in Equation (5).

$$E=E_d \cup E_t$$

(5)

The weights of the branches on a weighted graph are called $c$. In this problem, where the shortest route is trying to be found by using the $G$ graph, the total cost value obtained at the end of the route should be minimized. When the graph in Figure 1 is examined, it can be seen that there are two different types of costs. The first of these is the cost of the branches, which are the members of the $E_d$ cluster. Another is the cost of branches, which are members of the $E_t$ cluster. The main purpose of defining two different costs in this way is to make deliveries using different vehicles on these two different types of branches. It is clear that deliveries by one truck and one drone will not cost the same, given that they both have different speeds. The $c$ cost value can be represented as $C=(c_d, c_t)$. Here, $c_d$ and $c_t$ can take different values only when they are negative and are defined on the functions in Equations (6) and (7).

$$c_d:E_d \to {\mathbb{R}}_{\ge 0}$$

(6)

$$c_t:E_t \to {\mathbb{R}}_{\ge 0}$$

(7)

1.4. Proposed Approach

In the proposed approach for this study, it is assumed that there is a dataset of n customers, one truck, and k drones traveling with the truck to deliver to these customers. The main goal in this scenario is to minimize the delivery completion time. The completion time of the delivery is the sum of the time taken by the entire process, starting with the truck leaving the warehouse and ending with the truck returning to the warehouse. If the stages of the process for the proposed approach are listed:

• There is only one warehouse, and its location is fixed;
• Initially, vehicles leave the warehouse and return to the warehouse after completing the delivery;
• Delivery vehicles include one truck and one or more drones;
• All drones are identical and can operate within a certain range;
• Drones start their movement from the truck and can only deliver to one point at a time, and after completing the delivery, they go to the appointment point and complete their movement when they reach the truck;
• The speeds of the vehicles are constant;
• All packages expected to be delivered can be delivered by both truck and drone (in terms of size, weight, etc.);
• The locations to be delivered to and the distances between these locations are known in advance and are fixed; they do not change after the delivery has started;
• Only one delivery should be made to all customers on the route.

1.5. Contribution and Outline

As a result of scientific studies and technological developments, different scenarios in which drones are included in the delivery processes have been put forward, and different route improvement studies have been carried out for the problems in different scenarios in this field. The truck multi-drone problem is one of these scenarios, and it is the problem focused on in this study. Within the scope of this study, first of all, information about the last mile concept and the use of truck-drones in the field of transportation has been presented, and a literature review has been made. Studies of delivery problems started with applications using only trucks or drones and continued with applications where these vehicles were used together. Apart from these, there have been many studies in the literature in which trucks and drones are used together, and their routes are independent of each other. However, since the routes were independent of each other in these studies, different warehouses were used for both vehicles and different solution calculations were required. In particular, the use of different solution calculations and different solution algorithms has created a disadvantage for these studies. In order to contribute to the literature in line with the research we have conducted, a hybrid truck multi-drone problem has been created in this study, and GA has been proposed as the solution algorithm. Then, the system theory created in this study and the proposed algorithm has been explained in detail. In the created scenarios, there is only one warehouse, one truck, and multiple drones. Trucks and drones leave the warehouse at the same time and come together again in the warehouse after completing the delivery. Also, different scenarios have been created, results have been obtained for these scenarios, and the results have been given in a comparative way. The success of the system and the proposed algorithm has been demonstrated by the results obtained and its ability to handle a real-world problem.

2. Materials and Methods

The GA is a method inspired by nature and based on the application of evolutionary processes in a computer environment. In addition, GAs are an optimization method that uses evolutionary processes. Therefore, it is particularly suitable for use in optimization problems. Since GAs are one of the heuristic solution techniques, they do not guarantee that the best result will be found. Its advantage over algorithms that guarantee the absolute best result is that it takes less time to reach the solution. GAs can calculate exceptionally good results at an exceptionally fast rate [28,29].

In this section, a GA-based method is presented for calculating the shortest route for deliveries to points with certain coordinates using one truck and k drones. When calculating the appropriate scenario with this algorithm, priority is given to the use of drones. A drone has been assigned to deliver to all points that it can reach according to its range, idle, or in-use status. It should be ensured that the drone and the truck going to the delivery point meet at the next delivery point.

Since the proposed algorithm is based on GAs, the processing steps basically consist of the application steps of GAs. The GA-based flow diagram of the proposed algorithm is shown in Figure 2.

2.1. Creating the Initial Population

During the GA design phase, “permutation coding” is preferred for the representation of individuals. To understand permutation coding, each individual in the initial population is considered. The number of delivery points for each individual generated by permutation coding is represented by the variable n. Each of these numbers takes a value in the range [1, n], and the number in each cell is different from the numbers in other cells. These numbers represent customers who will be delivered from first to last. The initial population, consisting of individuals with permutation coding and containing as many individuals as the population size, is randomly generated.

2.2. Calculation of Edge Costs on the Graph

A graph that assumes delivery points as nodes is a weighted graph. The distances between all nodes (i.e., delivery points) on this graph are calculated, and the distance matrix is created. Since these distance values will be used while calculating the cost of any route in the next stages, they are stored for the next steps.

2.3. Getting Road Condition Data via the Internet

Since one of the main vehicles used in delivery is the truck, the traffic density on the roads along the route is an important factor that will affect the delivery time. Calculations made independent of traffic density values remain only in theory. Even the most optimal route to be calculated may take longer to complete than routes that were not previously considered optimal due to traffic on the road along the route. In order to prevent this, road condition data is taken into consideration while finding the optimum route.

The traffic data for the relevant roads on the graph are obtained via the Internet, and the traffic density is numbered 1–4. Afterward, an updated distance matrix is created using traffic data. While calculating the route cost, the updated cost matrix is used instead of the standard distance matrix for deliveries made by the truck.

With this method, the proposed GA will have the ability to choose the traffic-free route, which has the shortest distance in terms of distance but is slightly longer and less costly than the route with heavy traffic.

2.4. Calculation of the Compatibility Score

The purpose of this algorithm is to find the shortest path, that is, to minimize the transportation cost. For this reason, the “fitness function” calculates how low the transportation cost is. The fitness function:

$$F\left(t\right)=\frac{1}{TC}$$

(8)

where:

• $F\left(t\right)$: Fitness function,
• $TC$: The value of the total transportation cost relative to the current individual.

As can be seen from Equation (8), in order to calculate the compatibility scores of individuals, first of all, the total transportation cost of each individual’s route must be calculated. In this study, the total transportation cost is the time from the start of the delivery on the route of an individual to the completion of the delivery.

Considering that there are two different types of vehicles, trucks, and drones, and considering that these two vehicles will travel a certain distance at different times depending on their speed and the traffic situation on the road on which the truck is traveling, it is clear that the transportation costs of these two vehicles will be different. For this reason, the current route is evaluated in the context of two sub-routes: the truck and drone routes. Different parameters are used to calculate the costs of the movements of the vehicles on these two sub-routes.

2.5. Creating Sub-Routes and Examining How Vehicles Are Assigned on the Existing Route

There are two different methods for performing deliveries in the proposed method. The first is to assign the truck for delivery. Another method is to assign the drones for delivery. The assigned drone carries the package to the delivery point, delivers it, and makes an appointment to meet the truck again at the truck’s next delivery point.

The proposed algorithm places emphasis on employing drones as long as the conditions under which delivery can be achieved by the drone remain favorable in order to take advantage of the drones. In Figure 3, a flowchart of how vehicles are assigned so that deliveries can be made to delivery points with the proposed algorithm is given.

If the working principle of the algorithm and the calculation of individual transportation costs are examined through a scenario:

• According to the scenario shown in Figure 4, there is one truck and one drone at point 1 that have made their deliveries. At this stage, it is necessary to decide how to deliver to the next delivery points. In the decision-making process, the total number of drones and drone range values are used. The algorithm first sets the truck’s movement from point 1 to point 2, and the distance that the truck will travel is set at ℓ12.
• The drone is then checked to see if it can deliver to the next delivery point. When the drone’s movement is from point 1 to point 3, which is the next delivery point, the point where it will make an appointment with the truck will be point 2. Accordingly, the expected distance to be covered by the drone will be ℓ13 + ℓ32.
• After calculating the distance that the drone will travel, there are two conditions for determining whether the drone can make this delivery. If the total number of drones is greater than the number of drones currently on duty, that is, if there are drones available for the mission and the drone range is greater than or equal to ℓ13 + ℓ32 distance, the drone is suitable for delivery.
• Assuming that these conditions are met in the current scenario, the drone will go from point 1 to point 3, and then from point 3 to point 2. It will also meet the truck at point 2.
• Afterward, the algorithm checks whether the next delivery point, point 4, is suitable for the drone to deliver. There is only one drone in the scenario, and since one of the conditions, the number of drones, cannot be met, the drone will not be assigned to delivery point number 4.
• If a drone could be sent to point 4, this drone would also meet with the truck at point 2. After it is understood that no drone will be sent to point 4, the truck starts to move toward point 2, and the drone starts to move toward point 3, as seen in Figure 4b. They come together again at point 2, as seen in Figure 4c.

In the given scenario, the total transportation cost is calculated for each individual, and the suitability score is obtained according to this calculated value. Afterward, since it is still in the initial population, the most suitable individual in the current population, that is, the individual with the highest compatibility score, is found and adjusted as the “global best fit”. While the updated weight matrix is used to calculate the cost of the truck’s movement, the standard weight matrix is used for the drone’s movement. By dividing the relevant distance value by the speed of the vehicle, the cost value is calculated in terms of how long it will take the vehicle to cover that distance.

When these movements are taken into consideration, two different situations can occur. The first of these is that the truck arrives at point 2 before the drone and waits for it to arrive. The other is the scenario where the drone arrives at point 2 before the truck and waits for the truck to arrive. Since these two situations are likely to happen, the value to be added to the total transportation cost is the arrival time of the vehicle that reaches point 2 at the latest.

2.6. Application of Genetic Operators

The next step is to apply genetic operators to the current population. In this way, it is expected that strong individuals will be obtained in the new generations, as well as individuals with shorter delivery times, according to the scenario. Dynamic mutation was used in the genetic algorithm structure to prevent falling into local optimum.

2.7. Stopping Condition of the Algorithm

The stopping condition of the algorithm looks at the progress of iterations as much as the predetermined number of iterations. If the predetermined number of iterations is reached, the algorithm stops.

2.8. Finding the Optimal Route

During the operation of the algorithm, the “local best fit” values are found among the individuals in the current population by looking at the fitness score in each iteration, and they are compared and updated with the “global best fit” value (that is, the best-fit individual found considering all previous populations). When the algorithm stops, the route to which the global best value belongs is named “the fittest” and recorded as the result found by the algorithm.

Within the scope of the paper, a solution is provided for the distribution of more than one different type of cargo with more than one same or different type of drone working hybrid with a truck. In this respect, considering that there are multiple drones, it is decided that the relevant drone will deliver by taking into account the current battery charge rate of the drones, the distances required by subsequent delivery tasks, the characteristics of the location where the cargo will be distributed and the route status parameters of the truck. The basic algorithmic structure of the GA used in the article is given in Algorithm 1.

Algorithm 1: The basic algorithmic structure of the genetic algorithm.

Genetic algorithm with dynamic operators ( ) { Initialize population randomly; Evaluate fitness of each individual in the population; While stopping condition met {   Perform selection;   Perform crossover and dynamic mutation;   Evaluate fitness of each individual;   Change selection, crossover and mutation operators. } }

The operators and explanations of the genetic algorithm used for the proposed approach can be given as follows: Average/Min-Max crossover has been used as the crossover operator and consists of the change of behavior between the two parents based on the average of the absolute processing time of the chromosome segments [36]. The main role of the mutation operator in the genetic algorithm is to create new genetic information and produce new individuals that will enable the main solution to be approached. A high probability of mutation may help produce better production, but in larger than average individuals, this may lead to the loss of good individuals. In adaptive mutation, individuals above the average in a population mutate with a very low probability, and individuals below the average mutate with a high probability. The parameters of the genetic algorithm used in the article are given in

Table 1. Parameters of genetic algorithm.

Parameters	Values
Crossover probability	0.79–0.99
Mutation probability	0.01–0.2
Crossover operator	Mean/Min–Max 2 point crossover
Mutation operator	Dynamic mutation
Selection procedure	The roulette wheel selection
Number of iteration	100
Population size	30–120

below.

To increase the understandability of the approach proposed in this paper, a numerical example is given below, as shown in Figure 5. In the numerical example given below (

Table 2. (a) Parameter values used in numerical example, (b) Numerical results for solving a delivery scenario.

(a) Parameters for Numerical Example
Parameter	Numerical value
N: Number of nodes (a, b, c, d, e, f)	6
D: Number of drones	2
C: Number of customers	3
t: The amount of time a drone can stay at the node for deployment	4 min
b: Battery capacity of the drones	1.8 kWh
w: Weight capacities of drones	5 kg and 10 kg
(b) Numerical results
	Route	Arrival time (minutes)	Leaving time (minutes)
Truck	a–c–a	99 (for a)–11 (for c)	0–88
Drone 1	c–e–c	11 (for c)–42 (for e)	88–45
Drone 2	c–d–f–c	11 (for c)–23 (for d)–60 (for f)	76–26–63

), an example with six nodes (a, b, c, d, e, and f) has been selected. For these nodes, one central node (a), two intermediate nodes (b, c), and three customer nodes (d, e, f) have been created. The number of drones, the number of customers, the time the drones can stay at a node during the distribution mission, the battery capacities of the drones, and the weight capacities of each drone are shown in the table. In this numerical example, it is taken into account that drones can move at three different altitudes.

In the scenario consisting of one truck and two drones, the results obtained if the first drone makes one distribution and the second drone makes two distributions are given in Table 2b. In addition, the time graph obtained from the results obtained with ten different scenarios of these numerical examples is given in Figure 6. As can be seen here, in the truck-drone hybrid system, as the capacity of the drones increases, the time duration decreases significantly.

3. Results

This section examines the concrete responses to the situations realized in the scenarios determined within the scope of the study. It is also desirable to make certain comparisons and inferences thanks to the numerical data obtained as a result of the simulations.

In the first simulation, the effectiveness of these algorithms is compared according to the data obtained by solving different optimization algorithms developed for TSP of different routes and the GA proposed in the method. In the first column of

Table 3. Results obtained by running the PSO, GWO, and GA algorithms on six different samples.

Sample	Calculated Parameter	PSO	GWO	GA
Oliver30 (423)	Best Result	500.20	449.86	423.74
	Worst Result	592.66	601.78	424.69
	Average Result	542.08	522.74	423.93
	Error Rate (%)	0.29	0.24	0.003
	Runtime (s)	1289.25	108.17	38.60
	Best Result	723.41	532.20	439.31
	Worst Result	776.43	827.32	448.14
Eil51 (429)	Average Result	745.65	666.53	442.89
	Error Rate (%)	0.75	0.58	0.03
	Runtime (s)	2385.41	208.86	72.88
	Best Result	12,489.38	10,981.60	7762.72
	Worst Result	13,731.19	13,539.54	8316.30
Berlin52 (7542)	Average Result	13,103.28	12,447.52	8021.78
	Error Rate (%)	0.74	0.63	0.07
	Runtime (s)	2506.23	239.16	80.05
	Best Result	1572.10	1194.62	695.40
	Worst Result	1883.93	1616.17	715.87
st70 (675)	Average Result	1686.88	1373.35	704.52
	Error Rate (%)	1.56	1.08	0.05
	Runtime (s)	3896.87	274.51	121.83
	Best Result	1212.12	927.09	578.22
	Worst Result	1416.46	1115.37	592.97
Eil76 (538)	Average Result	1287.18	997.37	588.04
	Error Rate (%)	1.44	0.90	0.09
	Runtime (s)	4036.43	282.94	103.94
	Best Result	73,889.32	46,057.62	23,961.88
	Worst Result	83,672.94	123,953.40	27,348.95
KroA100 (21282)	Average Result	78,544.64	79,129.14	25,371.21
	Error Rate (%)	2.70	2.99	0.21
	Runtime (s)	4951.84	389.70	132.78

, there are six different test routes taken from the TSPLIB library [37]. After the names of the test routes, the optimum result for the relevant route is given in parentheses [38]. These routes include a minimum of 30 and a maximum of 100 cities. Parameters calculated in the second column; Particle Swarm Optimization (PSO) in the third column; Gray Wolf Optimizer (GWO) in the fourth column; and in the fifth column, there are data obtained as a result of solving the TSP of the current route with the GA, which is the method proposed in this study.

While filling out the table, the current problem has been solved with the given algorithm 10 times, and as a result, the best result, worst result, average result, average algorithm run time, and error rate values have been entered into the table. The calculation of the error rate is seen in Equation (9) [38].

$$Error Rate=\frac{\frac{Best Result+Worst Result}{2}-Optimal Value}{Optimal Value}$$

(9)

Considering the values given in the table, Figure 7 and Figure 8 for the average result are examined, and it is seen that the average result parameter obtained by GA is close to the optimum value. In PSO and GWO algorithms, values close to each other are obtained, but the success of these values is worse than in GA. On the other hand, as seen in Figure 9, a lower error rate is obtained with GA compared to other methods. When the algorithms are evaluated in terms of running times, it is seen that the algorithm with the shortest time is again GA. On all routes, GA calculates the shortest route in a shorter time than the other two algorithms. Also, the GWO algorithm manages to compute up to 10 times faster than PSO, but it appears to be 3 times slower than GA.

In fact, this simulation provided a very clear view of the features of the GA. As seen in Table 3, the GA succeeded in finding the near-optimal result in a short time. The PSO reached a working time of up to 5000 s, and the performance of its results could not tolerate this slowness. GWO, on the other hand, worked at an acceptable speed for a transportation problem, but its performance lagged behind GA based on its results. For this reason, GA has been the preferred algorithm in this study, thanks to its fast work and the success of the results obtained.

3.1. Multi-Drone Results

The samples from the TSPLIB library used in Table 3 are then simulated using GA with different drone number parameters, and

Table 4. Calculation results for scenarios with different numbers of drones.

Sample	Parameter	n = 1	n = 2	n = 3
	Shortest Time	268.57	225.53	199.22
Oliver30	Average Time	286.17	230.7	203.11
	Longest Time	298.89	237.55	204.34
	Shortest Time	275.86	228.95	197.79
Eil51	Average Time	293.42	233.6	205.43
	Longest Time	301.79	236.37	213.24
	Shortest Time	5464.90	4547.6	3851.57
Berlin52	Average Time	5769.94	4676.11	3992.83
	Longest Time	5970.97	4817.53	4094.61
	Shortest Time	485.96	403.75	345.95
st70	Average Time	497.2	411.49	360.44
	Longest Time	517.53	427.88	378.7
	Shortest Time	395.67	309.23	260.54
Eil76	Average Time	412.61	316.04	265.98
	Longest Time	430.79	329.88	272.2
	Shortest Time	19,788.83	16,207.64	13,718.63
KroA100	Average Time	20,593.88	16,786.1	14,017.2
	Longest Time	21,083.2	17,577.64	14,755.49

is created. The population size is set to 200, the number of iterations to 1000, and the drone speed to be twice the truck speed. The drone range is not restricted because the areas covered by the cities used in the simulation and the distances between each other vary greatly. The purpose of the difference in the number of drones from scenario to scenario is to observe the effect of the number of drones on the result obtained. The table is created according to the shortest time, average time, and longest time values obtained as a result of running each scenario ten times.

As the number of drones used increases, it is seen in Figure 10 that the delivery time tends to decrease. Some values appear to overlap in the figure because they are smaller and closer to each other than the clearly visible values. In addition, when the results of another simulation performed on the same routes are examined in Table 3 and compared with the results in Table 4, it is determined that the results obtained in the scenarios using drones on the same dataset are smaller than the results of the scenario solved like a standard TSP (as in Table 3). This simulation demonstrates the importance of using drones for deliveries.

The locations of the cities for the test routes in the six different data sets used are given on the coordinate plane in the figures below. In addition, in the case of using one drone, the most suitable routes obtained for the drone and truck in terms of the shortest time values in Table 4 are also shown in the figures.

Oliver30 is a dataset of 30 samples in a 100 × 100 area taken from TSPLIB [37]. In Figure 11, the locations of the cities to be delivered in the Oliver30 sample data set are given in the coordinate plane. According to TSP, the length of the optimum route that can be found in its solution is 423. In Figure 12, the route with the shortest time value is given in Table 4 and is made using one drone with the algorithm proposed in this study. The black lines on the route in Figure 12 show the route of the truck, and the red dashed lines show the drone route. The value found for this route is 268.57. The starting points of the truck are indicated in all relevant Figures with a black star icon.

Eil51 is a dataset of 51 samples in a 70 × 70 area taken from TSPLIB [37]. In Figure 13, the locations of the cities to be included in the Eil51 sample set are given in the coordinate plane. According to TSP, the length of the optimum route to be found is 429. In Figure 14, the route with the shortest time value is given in Table 4 and is made using one drone with the algorithm proposed in this study. The value found for this route is 275.86.

Berlin52 is a dataset of 52 samples in an area of 1800 × 1200 taken from TSPLIB [37]. In Figure 15, the locations of the cities to be included in the Berlin52 sample set are given in the coordinate plane. According to the TSP, the length of the optimum route that can be found is 7542. Figure 16 shows the route with the shortest time value in Table 4, which was made using one drone with the algorithm proposed in this study. The value found for this route is 5464.90.

St70 is a dataset of 70 samples in a 100 × 100 area taken from TSPLIB [37]. In Figure 17, the locations of the cities to be included in the St70 sample set are given in the coordinate plane. According to TSP, the length of the optimum route to be found is 675. Figure 18 shows the route with the shortest time value in Table 4, which was made using one drone with the algorithm proposed in this study. The value found for this route is 485.96.

Eil76 is a dataset of 76 samples in a 70 × 80 area taken from TSPLIB [37]. In Figure 19, the locations of the cities to be included in the Eil76 sample set are given in the coordinate plane. According to TSP, the length of the optimum route that can be found in its solution is 538. Figure 20 shows the route with the shortest time value in Table 4, which was made using one drone with the algorithm proposed in this study. The value found for this route is 395.67.

KroA100 is a dataset of 100 samples in a 4000 × 2000 area taken from TSPLIB [37]. In Figure 21, the locations of the cities to be included in the KroA100 sample set are given in the coordinate plane. According to TSP, the length of the optimum route that can be found in its solution is 21,282. Figure 22 shows the route with the shortest time value in Table 4, which was made using a drone with the algorithm proposed in this study. The value found for this route is 19,788.83.

Applications carried out in terms of the effectiveness of the algorithm proposed in this study:

• First of all, in simulations, comparisons were made with some optimization algorithms in the solution of the TSP problem with scenarios where drones are not used in order to measure the effectiveness of the proposed algorithm. As a result of these comparisons, the advantages and some disadvantages of GA were seen, and why it was preferred in this study was explained. In terms of the problem presented in the article, the genetic algorithm has advantages such as being able to provide optimum solutions in variable scenarios, not needing additional information, and being able to work with a large number of variables. Selecting parameters such as initial population size, mutation-crossover probability, and selection technique has partial effects and is useful in finding the global optimum. It has some disadvantages, such as sometimes experiencing convergence problems. However, in the hybrid truck and multi-drone distribution problem given in this article, these disadvantages are minimized, and an approach and results are presented.
• Then, new simulations were carried out on the same datasets using drones, and it was observed that the use of the drone had a positive effect on the result.

3.2. Results for Test Algorithm

At this stage, the proposed method will be tested on the scenario in a previously published study that provides a solution to the truck multi-drone problem similar to this study. In this study, the proposed method will be compared with the results obtained in previous studies on the truck multi-drone problem in the literature. In the scenario prepared for the simulation, there are a total of ten points, consisting of nine delivery points produced uniformly in a 100 × 100 area and a warehouse generated at a random location close to the origin (within the area between the x = 5 and y = 5 lines and the origin). By starting the number of drones at zero, scenarios including one drone, two drones, and three drones are created, and each scenario is run ten times. The smallest, largest, and average values obtained according to the results obtained are given in

Table 5. Experimenting with the proposed method at random points with different drone numbers.

Parameter	k = 0	k = 1	k = 2	k = 3
Shortest Time	260.42	191.47	143.71	131.16
Average Time	299.11	226.33	161.46	153.62
Longest Time	336.23	251.89	178.17	181.70

.

The same scenario was tested in the study prepared by Kilian Seifried et al. [39], and in this study, a Mixed Integer Programming (MIP)-based formulation was presented for the solution of the truck multi-drone problem. The results of the simulations made on the same scenario and the average time parameter in Table 5 obtained by the proposed method (a mixed integer programming-based hybrid method with branch and bound and heuristics approaches.) in this study are given in a comparative way in Figure 23. In the figure, the blue column for the different numbers of drones shows the results of the proposed method, and the black column shows the results of the previous study in the literature. It is clearly seen in Figure 23 that while the results obtained by both methods are close to each other, the method proposed in this study is superior in two of the four different scenarios where the number of drones changed.

The comparative situation showing the improvements in deployment times for different numbers of drones is given in

Table 6. Comparative results for the proposed approach with the state-of-the-art algorithms.

	Delivery Time Savings for Scenario 1 20 Instances and Low Flight Ranges
	Distribution types and Number of drones
Ref.	RD-2	RD-3	RD-4	CD-2	CD-3	CD-4
[23]	3.3%	5.2%	8.7%	4.1%	7.1%	7.9%
[21]	7.5%	10.1%	12.6%	6.0%	9.9%	11.2%
[40]	7.2%	9.1%	13.6%	6.4%	10.1%	14.4%
This paper	8.1%	12.9%	15.2%	9.0%	11.1%	17.4%
	Delivery Time Savings for Scenario 2 50 Instances and High Flight Ranges
	Distribution types and Number of drones
Ref.	RD-2	RD-3	RD-4	CD-2	CD-3	CD-4
[23]	% 4.6	% 6.8	% 7.9	% 5.1	% 7.5	% 8.6
[21]	% 7.2	% 11.7	% 14.3	% 8.7	% 12.1	% 13.9
[40]	% 7.2	% 12.2	% 10.2	% 6.3	% 11.0	% 12.9
This paper	% 8.9	% 13.1	% 16.3	% 9.7	% 12.6	% 16.6

. Here, RD: Random Distribution (RD-2: 2 drones for RD, RD-3: 3 drones for RD, RD-4: 4 drones for RD) and CD: Certain Distribution (CD-2: 2 drones for CD, CD-3: 3 drones for CD, CD-4: 4 drones for CD). The convergence rates of the genetic algorithm are given in Figure 24.

In addition, with the algorithm developed in the paper, an average of 15% better rate in terms of deployment time was achieved compared to studies in the literature for both short-distance and long-distance missions by using a multi-drone and truck hybrid consisting of two, three, and four drones.

3.3. Results for a Real-World Problem

After the simulations in which the advantages of the proposed method are examined, the solution brought by the method to an important real-world problem will be examined in the simulation to be carried out at this stage. In the new simulations:

• In terms of delivery, it is assumed that there are ten points on the map shown in Figure 25. The points on the figure are numbered for ease of identification, regardless of the order of delivery.
• In Figure 26, the traffic situation on the roads between these points is given.
• In this scenario, it is assumed that only one truck is used for delivery.
• The difference in the solutions obtained in cases where the number of drones changes and whether traffic data is taken into account is examined.
• The distances between the delivery points are shown in the distance matrix in Figure 27.
• In Figure 28, these points are seen as nodes of a representative graph.

In the first case, the result obtained by making deliveries using only one truck, without considering the traffic data, was found. The route found in this case is shown in Figure 29, and the result is 13,142.43 km. However, the real-world equivalent of the result obtained in this case is a matter open to discussion.

In a real-world delivery, the traffic situation is a very important parameter. In the new case made to simulate this situation, traffic data is pulled over the internet and evaluated between 1 and 4. In this way, the algorithm tends to calculate a route where the truck will not use congested roads. In this case, according to the traffic data, the road between delivery points 1 and 2, seen in Figure 26, has been evaluated as having level 4 traffic density. For this reason, the updated distance matrix, which is a clone of the distance matrix in Figure 27, is created first, and then the relevant distance values are updated according to the traffic density.

In the case of using the updated distance matrix, a solution, as in Figure 30, is obtained. The proposed algorithm predicted that the traffic situation on the road between nodes 1 and 2 would extend the delivery time and reach these nodes via node 8 without using the road between nodes 1 and 2 in the new route calculated by taking this into account.

When the map in Figure 25 is examined, it is seen that the road between the 1 and 2 delivery points coincides with Ciragan Street. Ciragan Street is one of the streets where traffic is very busy at many hours of the day in Istanbul. In other words, if the route in Figure 30 is followed in real life, it can be seen that this route may not actually be a route that will enable the delivery to be completed as soon as possible due to the traffic on Ciragan Street. This situation can also be seen when the roads used in the new route, which the algorithm calculates by considering the traffic situation, are examined. The cost of the new route calculated by the algorithm considering the traffic situation is 13,929.03, as seen in Figure 30. This value is greater than the value found as a result of the previous case, 13,142.43. However, since the algorithm predicts that it will take shorter in practice than in theory, it has chosen this route, which seems to have a higher cost. The route given in Figure 30 clearly demonstrates that the algorithm proposed in this study provides a nice solution to an important real-world problem by diverting the truck to low-traffic roads to make deliveries.

Finally, it is considered how the newly calculated route and delivery time will be affected if a drone is used in addition to the truck while delivering to the delivery points. In order to examine the changes in this situation, a drone that accompanies the truck has a range of 5 km and can move twice as fast as the truck used in the new situation. The resulting route is shown in Figure 31, where the black lines represent the truck’s route, and the red lines represent the drone’s route. It should be noted that no trucks are deployed on the road between nodes 1 and 2 with heavy traffic. As it is not affected by traffic on this road, even though it is among the options to assign a drone and obtain a route similar to that in Figure 30, the algorithm has obtained a different route, which it has found to be the shortest as a result of the calculations it has made. The calculated cost of this route in Figure 31 is 10,638.16. In other words, it has been observed that using drones reduces the cost compared to previous experiments.

As a result, in this paper, an effective and new approach based on a dynamic genetic algorithm is proposed for the single-truck multi-drone problem. The results obtained in this article can also be used for the multi-truck multi-drone problem. For this, an effective solution will be obtained by taking into account the necessary input parameters for multiple trucks and by assigning them to the single-truck multi-drone sub-problems that will work independently and verified in this paper, thanks to an assignment algorithm that will be configured according to the carrying and other capacity values of the relevant trucks. Although no analysis application has been made for this in this paper, it is planned to develop this application within the scope of future studies and obtain a comparative analysis of the solution obtained. A schematic representation of a solution for the planned multi-truck multi-drone problem is given in Figure 32.

4. Discussion and Conclusions

The use of drones in transportation, besides being environmentally friendly, also shortens delivery times considerably, as seen in this study. In addition, their use continues to become more widespread day by day, thanks to their ability to deliver to regions with geographical restrictions. With the increased use of drones, there are drone-containing versions of the problems of calculating the shortest route, which plays an important role in delivery.

There are different scenarios in the literature where drones are included in the delivery problems. The scenario discussed in this study is the hybrid single-truck multi-drone scenario. This scenario is based on the coordinated operation of one truck and k drones. The most basic and important feature of this scenario is that the drone that leaves the truck and goes to the delivery makes an appointment with the truck at one of the next delivery points.

In this context, different simulations have been created, results have been obtained, and comparisons have been made. First of all, route calculations have been made for a TSP by taking six different test routes in the first simulation. Two different optimization algorithms, PSO and GWO, and the algorithm proposed in this study have been evaluated together. The obtained data have been given in the tables in a comparative way according to the optimum result, and the success of the proposed GA-based algorithm has been clearly seen in the tables. As a result of the comparisons made in terms of error rate, it has been observed that a lower error rate occurred with GA. Moreover, since the running time is the determining factor for the calculation of the most appropriate route when an evaluation is made in this respect, the proposed GA-based algorithm has shown that it is more advantageous than other algorithms in terms of running time. In this case, the proposed GA-based solution manages to calculate the most suitable route with the shortest working time and the least error rate, which reveals why it was preferred in this study.

Afterward, the same simulation was performed again for the same six different test routes, taking into account the variable number of drones. The obtained results have been evaluated comparatively in figures and tables. The results clearly show that as the number of drones increases, the delivery time gets shorter. This situation clearly emphasizes the importance of multi-drone use, which is the main purpose of this study. In addition, the cities in these six data sets have been shown on the coordinate plane, and the most suitable route for the use of a single truck and a single drone has been given in the visuals. Also, in this section, the proposed algorithm in the scenario created has been tested with a previous study in a similar field, and the results have been given. With the test and comparison, it has been seen that the proposed method is superior to the previous similar study in the literature.

Finally, the proposed algorithm has been applied to a real-world problem. Traffic data for randomly determined delivery points in the mapped region has been obtained from the internet, and deliveries have been expected to take place using one truck and a variable number of drones. The operation of the proposed algorithm has been analyzed by examining the situations where the drone is used and the situations where the traffic density is taken into account or not. When the results are examined, drones are directed to areas with heavy traffic with the proposed method, and it is ensured that the most suitable route is found in the shortest time and with the least cost in solving a hybrid truck multi-drone problem in the real world. With the proposed system in this study, the use of drones in transportation has been emphasized, and it has been seen that it is a method that provides great advantages. If the relevant infrastructure is provided, the delivery time of the packages expected to be delivered to the end user is significantly reduced, and it is predicted that these times will get shorter as drone technology continues to develop day by day.

Creating an autonomous structure for drones is of great importance in terms of literature and practical applications. Therefore, the aim of future work is to deliver cargo in a fully autonomous manner without giving any input or even route information to the drone. In the simulation map to be created, the drone is planned to move autonomously and deliver cargo to the specified address. It is being considered to train the drone using reinforcement learning in order to be able to move forward without hitting an obstacle, to continue the mission without being affected by weather conditions, to find the cargo vehicle, and to return the cargo to its owners. Additionally, it is desired to test the algorithms by integrating RGB and depth cameras into the drone.