A Heuristic-Based Methodology for Collecting Irregular Waste in Sustainable Cities

Abstract

This study develops a mobile-supported system that municipalities can use in their irregular waste collection services within the scope of smart cities. Irregular waste refers to waste that individuals or organizations produce non-periodically, which arises unexpectedly or in an unusual manner. Unlike small-volume household waste collected at routine times, irregular waste is generally large-volume waste such as construction rubble, vegetable oil, mineral oil, and garden waste. In the irregular waste collection system developed in this study, waste locations are marked on the map of an application running on mobile devices, and notifications are sent to the municipality. The Google Distance Matrix API was used for processing and visualizing the notification locations on the map. Daily or 4 h planning is carried out using this data. In this study, a genetic algorithm and a differential evolution algorithm were used for vehicle routing and vehicle type optimization. To compare the efficiency of both methods, four different scenarios were designed with different numbers of waste locations and different types and amounts of waste, and the successes of the methods were compared. Differential evolution is found to be on average 0.8% better. Optimizations performed with actual road distances were found to be 8.0% more successful than optimizations performed with Euclidean distances.

1. Introduction

Today, environmental pollution is a serious problem harming human health and ecosystems. Waste management is of paramount importance, especially in urban areas. Collecting irregular waste as soon as it is generated, effectively managing recycling processes, and disposing of environmentally harmful waste are essential for a sustainable future. The rapid pace of urbanization, the rapid population growth, and the increasing pressure on the environment from both human and other pollutants are all contributing to this growing trend [1]. To ensure the sustainability of a modern and proper urban life and the efficient use of resources, one of the most important services is the implementation of a technologically advanced waste management system.

The regular and periodic collection of waste within a specific plan contributes to the protection of public health, a more environmentally friendly and sustainable life, pollution prevention, and the circular economy [2]. It is known that when waste collection services are disrupted and not carried out regularly in communal living areas, diseases increase, disasters such as fires occur, esthetic problems arise due to odors, and natural resources such as water and soil are significantly polluted [3]. In this context, the necessity of regular waste collection is examined in many dimensions and is justified under the headings of health, environment, and resource efficiency.

Waste collection processes are traditionally carried out through door-to-door methods, collection via containers, and transfer to waste disposal stations. Route planning and vehicle optimization for waste collection vehicles are key factors affecting the operating costs of waste collectors [4,5]. Today, with technological advancements, the digitalization of these managed operations through sensors, geographic information systems, the Internet of Things, and mobile applications has come to the forefront, leading to numerous studies aimed at increasing the efficiency and reducing the cost of waste collection activities.

The use of mobile applications in waste management processes brings benefits to both local governments and citizens. Citizens, the most important participants in waste management, can increase their level of participation in management by reporting container fill levels and other negative situations via mobile applications [6,7]. Furthermore, thanks to applications integrated with sensors and Internet of Things (IoT) applications, collection frequency can be dynamically adjusted, and fuel consumption can be reduced in line with low-carbon policies [8,9]. Thus, mobile applications not only increase operational efficiency but also enhance community participation, raise awareness, and strengthen waste management processes.

The primary motivation for this study is as follows: studies in the literature focus on regular waste generated as a result of normal daily activities, and there is no research on irregular waste. Furthermore, those studies do not include an integrated system that incorporates waste notification, the use of a database to record notifications, route optimization based on location and waste type, vehicle type optimization, and the creation of task schedules for each vehicle based on the optimization results. The literature generally includes studies that plan vehicle routes for fixed household waste locations in a region and use the same route for a long time as long as the locations do not change.

This study makes three main contributions to the literature. First, it focuses on collection of irregular waste which refers to waste that individuals or organizations produce non-periodically, which arises unexpectedly or in an unusual manner. Second, with the developed application running on mobile devices waste locations are notified to the municipality and these notifications are recorded in a database, and daily or 4 h planning is carried out using this data. Third, as far as we can see in the literature, there is not any benchmark problem for collecting irregular waste. Therefore an irregular waste collection scenario was developed to build a benchmark, which includes different locations, varying quantities and types of waste, and vehicles with different capacities and suitability for each waste type. Finally, for the benchmark problem, route and vehicle optimization was made using a genetic algorithm (GA) and a differential evolution (DE) algorithm, and the shortest route between waste locations and the most efficient vehicle types were found. The remainder of the paper is structured as follows. Section 2 presents the literature review, Section 3 presents the benchmark developed for collecting irregular waste, Section 4 outlines the methodology used in the study, Section 5 discusses the results and empirical findings, and Section 6 concludes.

2. Literature Review

In their study, Paolo et al. [10] developed a new method based on the idea that solid waste collection is one of the largest expense items for local governments and that even small improvements in this area can lead to significant gains. In their paper, the researchers used a GA to minimize the shortest path function. The proposed algorithm was able to find better solutions than the traditional algorithm, achieving an improvement of up to 21% in the best-case scenario.

In their article, Karadimas et al. [11] simulated different scenarios using a GA to optimize urban solid waste collection routes in Athens, Greece. Their study showed a 9.62% reduction in route cost for waste collection across the city compared to the existing method.

In a paper by Fujdiak et al. [12], an advanced waste collection system based on a GA was developed for smart cities. The study shows that they developed a system that detects whether trash cans are empty or full and creates a collection route accordingly.

In a study conducted by Melo et al. [13], it was stated that the problem of garbage collection in metropolitan areas has become a real problem in many cities worldwide. The study emphasized that it is possible to reduce costs by up to 15% by routing garbage collection vehicles to locations that do not exceed their capacity.

In the research conducted by Şuhan et al. [14], the aim was to improve the solution to the multi-purpose municipal solid waste collection problem. Waste collection routes are presented in a way that minimizes not only cost but also carbon emissions and job changes simultaneously. The method of achieving this capability is the elimination of herd replacement and genetic work together with an industrial hybrid approach. In the study conducted by Zhang et al. [15], the capacity vehicle routing problem for optimizing urban solid waste collection routes was modeled. The obtained results were tested using various algorithms. The study focuses on real road network data and aims to achieve gains in terms of cost, distance, and carbon emissions. Vehicle suitability according to waste type, capacity constraint, and penalty functions were not included in the study. In the study conducted by Roy et al. [16], the problem of an Internet of Things-based trash can placement and vehicle routing was addressed. Using IoT sensors, the fill levels of trash cans are monitored, and full cans send data to the system. The aim is to collect the appropriate cans with the most suitable vehicles.

A comprehensive literature review revealed that no studies have been conducted on daily irregular waste collection as proposed in our study. As far as we can see, all existing studies focus on optimizing the collection of regular waste periodically, establishing a fixed daily routine route. Since the same vehicle is used to collect waste on the same route every day, vehicle optimization is not performed along with route optimization [17,18]. Those studies do not use any databases for data recording, nor do they include any synchronized applications utilizing real-time route information on a daily basis. Common aspects, like our study, include the aim of achieving savings in terms of distance, time, and cost in all the existing literature [19].

3. Designing a Test Problem

This section includes a design of a test problem, which is one of the contributions of this study. As far as we can see in the literature, there is no benchmarking problem regarding irregular waste collection. Therefore, an irregular waste collection problem has been developed that includes numerous locations, different types and quantities of waste expected to be collected from these locations, and collection vehicles with different capacities suitable for each type of waste.

In the benchmark we developed, there is only one waste collection repository and numerous waste locations. Collection vehicles start from the repository, visit all waste notification locations, and finish the route back at the waste collection repository. The geographical location (latitude–longitude) of a waste, waste type, waste quantity, and optionally an image of the waste are reported to the municipality by waste owners via mobile devices. The waste locations used in the study are given in

Table 1. Waste locations, types and quantities of 10 notifications.

Locations of 10 Notifications
Waste Locations	Location’s Latitude	Location’s Longitude	Waste Quantities and (Types) in Scenarios (kg)
			S1	S2	S3	S4
Repository	41.4588092	27.3872315	-	-	-	-
1	41.3965470	27.3746385	100 (Rub.)	1100 (Rub.)	1100 (Rub.)	2600 (Rub.)
2	41.3934534	27.3569651	100 (M.O.)	100 (M.O.)	100 (M.O.)	1100 (G.W.)
3	41.3983778	27.3427843	100 (Rub.)	1100 (Rub.)	100 (P.W.)	100 (P.W.)
4	41.4045958	27.3767424	100 (Rub.)	900 (Rub.)	1900 (Rub.)	1900 (Rub.)
5	41.3824355	27.3610047	100 (Rub.)	100 (G.W.)	200 (P.W.)	200 (P.W.)
6	41.3870425	27.3932412	100 (M.O.)	100 (M.O.)	1100 (Rub.)	1500 (G.W.)
7	41.3839122	27.3744872	100 (V.O.)	100 (V.O.)	100 (M.O.)	100 (Rub.)
8	41.3871556	27.3444506	100 (Rub.)	900 (Rub.)	1900 (Rub.)	1900 (Rub.)
9	41.3900190	27.3453489	100 (Rub.)	900 (G.W.)	200 (P.W.)	900 (P.W.)
10	41.4100243	27.3578250	100 (V.O.)	100 (V.O.)	1000 (Rub.)	2500 (Rub.)

,

Table 2. Waste locations, types and quantities of 20 notifications.

Locations of 20 Notifications
Waste Locations	Location’s Latitude	Location’s Longitude	Waste Quantities and (Types) in Scenarios (kg)
			S1	S2	S3	S4
Repository	41.4588092	27.3872315	-	-	-	-
1	41.3965470	27.3746385	100 (V.O.)	1000 (G.W.)	1000 (Rub.)	1000 (G.W.)
2	41.3934534	27.3569651	100 (Rub.)	1100 (Rub.)	1100 (Rub.)	1100 (Rub.)
3	41.3983778	27.3427843	300 (Rub.)	100 (Rub.)	1100 (Rub.)	1100 (Rub.)
4	41.4045958	27.3767424	100 (Rub.)	500 (Rub.)	1000 (Rub.)	1000 (Rub.)
5	41.3824355	27.3610047	200 (Rub.)	200 (Rub.)	200 (Rub.)	200 (G.W.)
6	41.3870425	27.3932412	200 (V.O.)	200 (M.O.)	200 (M.O.)	200 (G.W.)
7	41.3839122	27.3744872	200 (M.O.)	100 (V.O.)	100 (Rub.)	100 (Rub.)
8	41.3871556	27.3444506	200 (M.O.)	500 (Rub.)	800 (Rub.)	800 (G.W.)
9	41.3900190	27.3453489	100 (V.O.)	200 (M.O.)	200 (M.O.)	200 (G.W.)
10	41.4100243	27.3578250	100 (V.O.)	1100 (Rub.)	1100 (Rub.)	1100 (Rub.)
11	41.4141052	27.3548341	500 (Rub.)	100 (V.O.)	100 (Rub.)	100 (Rub.)
12	41.4199962	27.3432308	200 (Rub.)	100 (Rub.)	100 (Rub.)	2100 (Rub.)
13	41.4081865	27.3290329	200 (Rub.)	100 (Rub.)	100 (Rub.)	1100 (Rub.)
14	41.4061865	27.3250330	100 (M.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
15	41.4027809	27.3446722	200 (M.O.)	100 (Rub.)	100 (Rub.)	1100 (Rub.)
16	41.3854258	27.3451406	100 (V.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
17	41.3808565	27.3624735	600 (Rub.)	100 (M.O.)	100 (M.O.)	100 (G.W.)
18	41.3951295	27.3810322	300 (Rub.)	100 (V.O.)	100 (P.W.)	100 (P.W.)
19	41.3953395	27.3846133	300 (Rub.)	100 (G.W.)	100 (P.W.)	100 (P.W.)
20	41.4267475	27.3724537	300 (V.O.)	1100 (G.W.)	100 (P.W.)	100 (P.W.)

and

Table 3. Waste locations, types and quantities of 40 notifications.

Locations of 40 Notifications
Waste Locations	Location’s Latitude	Location’s Longitude	Waste Quantities and (Types) in Scenarios (kg)
			S1	S2	S3	S4
Repository	41.4588092	27.3872315	-	-	-	-
1	41.3965470	27.3746385	100 (Rub.)	300 (M.O.)	100 (M.O.)	200 (G.W.)
2	41.3934534	27.3569651	100 (Rub.)	100 (Rub.)	500 (Rub.)	500 (Rub.)
3	41.3983778	27.3427843	100 (Rub.)	100 (Rub.)	400 (Rub.)	400 (Rub.)
4	41.4045958	27.3767424	100 (Rub.)	300 (Rub.)	300 (Rub.)	300 (Rub.)
5	41.3824355	27.3610047	100 (Rub.)	100 (M.O.)	100 (M.O.)	200 (G.W.)
6	41.3870425	27.3932412	100 (M.O.)	100 (M.O.)	100 (M.O.)	100 (G.W.)
7	41.3839122	27.3744872	100 (V.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
8	41.3871556	27.3444506	100 (Rub.)	200 (M.O.)	200 (M.O.)	200 (G.W.)
9	41.390019	27.3453489	100 (Rub.)	200 (M.O.)	200 (M.O.)	200 (G.W.)
10	41.4100243	27.3578250	100 (Rub.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
11	41.4141052	27.3548341	100 (M.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
12	41.4199962	27.3432308	100 (Rub.)	100 (Rub.)	1100 (Rub.)	2100 (Rub.)
13	41.4081865	27.3290329	100 (Rub.)	100 (Rub.)	100 (Rub.)	1100 (Rub.)
14	41.4061865	27.3250330	100 (Rub.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
15	41.4027809	27.3446722	100 (M.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
16	41.3854258	27.3451406	100 (Rub.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
17	41.3808565	27.3624735	100 (M.O.)	100 (Rub.)	100 (Rub.)	100 (G.W.)
18	41.3951295	27.3810322	100 (V.O.)	100 (V.O.)	100 (P.W.)	100 (P.W.)
19	41.3953395	27.3846133	100 (V.O.)	100 (V.O.)	100 (P.W.)	100 (P.W.)
20	41.4267475	27.3724537	100 (V.O.)	100 (V.O.)	100 (P.W.)	100 (P.W.)
21	41.4630619	27.3963241	100 (Rub.)	300 (Rub.)	300 (Rub.)	300 (G.W.)
22	41.4693557	27.3971262	100 (Rub.)	200 (Rub.)	200 (Rub.)	500 (Rub.)
23	41.4463374	27.3832809	100 (Rub.)	100 (Rub.)	400 (Rub.)	400 (Rub.)
24	41.4117605	27.4063042	100 (Rub.)	300 (Rub.)	300 (Rub.)	300 (Rub.)
25	41.3905818	27.3924887	100 (Rub.)	200 (Rub.)	200 (Rub.)	200 (G.W.)
26	41.3566706	27.4291384	100 (M.O.)	200 (Rub.)	200 (Rub.)	200 (G.W.)
27	41.3523540	27.3975527	100 (V.O.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
28	41.3653997	27.3888838	100 (V.O.)	100 (Rub.)	400 (Rub.)	400 (G.W.)
29	41.3379846	27.3916304	100 (V.O.)	100 (V.O.)	100 (P.W.)	200 (G.W.)
30	41.3473927	27.4499952	100 (M.O.)	1100 (G.W.)	100 (P.W.)	100 (Rub.)
31	41.3637570	27.4791347	100 (V.O.)	600 (G.W.)	100 (P.W.)	100 (Rub.)
32	41.4483645	27.3698753	100 (Rub.)	100 (Rub.)	100 (Rub.)	2100 (Rub.)
33	41.4655074	27.3571723	100 (Rub.)	100 (Rub.)	1100 (Rub.)	1100 (Rub.)
34	41.4816813	27.3351568	100 (Rub.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
35	41.4657647	27.3215955	100 (Rub.)	100 (Rub.)	100 (Rub.)	100 (Rub.)
36	41.4497155	27.3512071	100 (Rub.)	400 (Rub.)	400 (Rub.)	100 (Rub.)
37	41.4882397	27.3367875	100 (Rub.)	100 (G.W.)	100 (P.W.)	100 (G.W.)
38	41.3739503	27.4092938	100 (Rub.)	100 (G.W.)	100 (P.W.)	100 (P.W.)
39	41.3613894	27.3799826	100 (Rub.)	100 (G.W.)	100 (P.W.)	100 (P.W.)
40	41.3564933	27.3211027	100 (Rub.)	500 (G.W.)	100 (P.W.)	100 (P.W.)

. Table 1 contains 10 notifications, Table 2 contains 20 notifications, and Table 3 contains 40 notifications, which also include waste types and quantities in four different scenarios (S1, S2, S3 and S4). The irregular waste types used in the study include construction rubble (Rub.), mineral oil (M.O.), vegetable oil (V.O.), packaging waste (P.W.) and garden waste (G.W.).

The types and capacities of the vehicles in the waste collection fleet are given in

Table 4. Collection vehicles and capacities for each type of waste.

Waste Type	Vehicle Types and Capacities
	Vehicle-0	Vehicle-1	Vehicle-2	Vehicle-3	Vehicle-4
Rubble	5 tons	3 tons
Mineral Oil			1000 L
Vegetable Oil			1000 L
Garden Waste				3 tons
Packaging Waste					2 tons

. Vehicle-0 and vehicle-1 are designed to collect only construction rubble, vehicle-2 has a tank divided into two separate compartments and collects mineral oil and vegetable oil wastes, vehicle-3 collects garden waste, and finally, vehicle-4 collects packaging waste. To reduce waste collection costs and increase efficiency, the shortest route covering all locations is minimized, while simultaneously optimizing the vehicle according to the type and quantity of waste.

In order to test the success of the methodology we developed and the optimization method we used, which are presented in the following sections, four waste collection scenarios were created. Each of these scenarios is tested by applying it to waste collection routes and vehicle optimizations consisting of 10, 20, and 40 locations. The vehicles used in all scenarios are those whose capacities are specified in Table 4. The total waste amounts for the created scenarios are given in

Table 5. Waste quantities for each waste type, according to the scenarios.

Waste Type	Scenario 1	Scenario 2	Scenario 3	Scenario 4
Rubble	x < 3 tons	x = 4 tons	x > 5 tons	8 < x < 10 tons
Mineral Oil	x < 1000 L	x < 1000 L	x < 1000 L	0
Vegetable Oil	x < 1000 L	x < 1000 L	0	0
Garden Waste	0	x < 3 tons	0	x < 3 tons
Packaging Waste	0	0	x < 1 ton	x < 2 tons

. In addition to determining the shortest route, these scenarios will test:

• Whether the appropriate vehicle was selected for the type of waste at each location;
• Whether the total amount of waste of the same type exceeds the vehicle capacity;
• Whether the vehicle with the lowest capacity that can collect the total amount of waste of the same type was selected.

4. Methodology

The proposed study consists of the following steps: first, collecting waste coordinates and waste information from citizens via an application running on mobile devices. Second, calculating the distance matrix between wastes using the Google Distance Matrix API based on the waste coordinates and information recorded in the database. Third, defining a constraint-based waste collection model for a large number of wastes and collection vehicles. Lastly, performing route minimization and vehicle optimization using GA and DE algorithms under the same parameters and analyzing the results.

4.1. Notification of Waste via a Mobile Application

With an irregular waste mobile application we developed in this study, individuals can report their waste information to the municipality for collection. The application includes an authentication process using the user’s email and password. User information is saved to the municipal database after the user confirms a verification code sent to their email address. Thus, a minimum level of user verification security will be provided.

Users locate the waste on the mobile application’s map using a pin symbol, as shown in Figure 1. If the waste is nearby, they pinpoint its current location; if not, they pinpoint the location of the waste. After pinpointing the waste location on the map, a new page appears, as shown in Figure 2, where users can select waste types such as rubble, vegetable oil, mineral oil, packaging, and garden waste. A field is also defined here for entering the quantity of waste along with its type. These fields are essential for route minimization and vehicle optimization. Optionally, users can save a photo of the waste to the database, either by taking a picture with their mobile device’s camera or selecting from their gallery. They complete the waste notification by clicking the “Submit Notification” button. Users can view their submitted waste notifications on the map, and by clicking on the pinpoints, they can view the waste information and image. The date and type of waste are also displayed. The mobile application allows users to delete a previously submitted notification by double-clicking the pinpoint and confirming.

4.2. Distance Matrix Generation

Each node represents a real geographic location notified by a user via the mobile application, which are GPS coordinates. The repository is indexed as node 0, and all vehicle routes start from and end at the repository.

In order to obtain realistic vehicle routes and distances, the Google Distance Matrix API (driving mode) was used. Thus, distances are obtained according to the real road network instead of Euclidean distances. The resulting distance matrices are stored locally in a .pkl file to avoid unnecessary API requests and ensure experimental consistency. All optimization processes use the same distance matrix in experiments with GA and DE algorithms.

4.3. Constraint-Based Irregular Waste Collection Model

In this section, a constraint-based fitness function (total cost) is proposed for a large number of irregular wastes and collection vehicles. The fitness function consists of the total distance between waste locations and constraint penalties. The total distance is the distance covered in one full trip, from the waste collection vehicle leaving the repository, completing its route, and returning to the repository. One objective of this study is to minimize the distance of this route. Another objective is vehicle optimization. A penalty is added to the total distance if a constraint is violated. Constraints are used to ensure waste–vehicle type matching. The fitness and constraints in the proposed model are given in Equation (1) below:

$$\mathrm{m}\mathrm{i}\mathrm{n}\left(f\right)=D+P_{type}+P_{capacity}+P_{operation}$$

(1)

where f is the fitness (km), D is the total distance (km) between waste locations, P_type is the penalty (km) for vehicle and waste type mismatch, P_capacity is the penalty (km) for waste quantity exceeding vehicle capacity, and P_operation is the penalty (km) for selecting the right vehicle type but wrong capacity. The total distance is the sum of the distances of the routes starting from and ending at the repository for all vehicles.

4.3.1. Penalty of Waste–Vehicle Type Mismatch

If a waste collection vehicle is assigned to a location containing a different type of waste than its own on any route, a fixed penalty (C1) of 500 km is added to that route, thus discouraging the infeasible assignments while allowing for new discoveries during the search. This penalty is calculated by Equation (2) below.

$$P_{type}=N_m\times 500$$

(2)

where N_m is the number of type mismatch.

4.3.2. Penalty for Exceeding the Vehicle Capacity

For any type of waste, a capacity penalty (C2) is applied if the total amount of waste on the route exceeds the vehicle’s capacity. For vehicle-2 only, this rule consists of two independent constraints. The capacity of the vehicle-2’s mineral oil and vegetable oil compartments are checked separately. The penalty is calculated by Equation (3) below.

$$P_{capacity}=N_c\times 500$$

(3)

where N_c is the number of capacity exceedings.

4.3.3. Penalty of Operational Rules

In addition to the capacity constraint mentioned above, a strategic fleet usage rule is applied to prevent any vehicle from being overloaded or underloaded. Let R represent the total amount of waste of rubble, two strategic rules are defined within this scope:

• If Rub. < 3 tons, vehicle-0 (5-ton truck) should not be used,
• If 3 ≤ Rub. < 5 tons, vehicle-0 must be used.

This penalty is calculated by Equation (4) below.

$$P_{operation}=N_R\times 2000$$

(4)

where N_R is the number of rules unsatisfied. Violation of a condition results in a penalty (C3) of 2000 km. The operation of this mechanism prevents the unnecessary use of high-capacity vehicles for small loads, thus ensuring economically rational fleet usage.

Penalty parameters for waste–vehicle type mismatch and for exceeding the vehicle capacity constraints are chosen as 500, and those for operational rule constraints are chosen as 2000 in the study. The only criterion considered in choosing these parameters is that they must be greater than the maximum route distance. Since operational rule parameters take precedence over type mismatch and vehicle capacity parameters, they should be larger, for example, at least twice as large.

4.4. Genetic Algorithm and Differential Evolution Algorithms

The study employs GA and DE algorithms for route minimization and vehicle optimization in the benchmark problem presented in Section 3. Below, we provide brief explanations of these algorithms.

4.4.1. Genetic Algorithm

Genetic algorithms (GAs) are heuristic optimization methods inspired by the mechanism of natural selection. First described by John Holland in 1975, these algorithms aim to reach solutions by mimicking biological evolution and using biological principles such as natural selection, crossover, and mutation [20,21]. GAs are frequently preferred for finding the optimum solution in large and complex solution spaces. These algorithms are used particularly in the field of the traveling salesman problem (TSP), vehicle routing, job and machine scheduling, and artificial intelligence. GAs consist of the following basic steps:

Initial Population: An initial population is created from individuals (chromosomes) randomly or according to a specific distribution in the solution space. Each individual represents a possible candidate solution.

Fitness Evaluation: The fitness value of each individual is calculated using a fitness function that measures the individual’s success in solving that problem. In the case of TSP, the fitness value is usually the inverse of the total path length.

Selection: Individuals with high fitness values within the population are selected with a high probability to pass on their genes to the next generation. Selection methods include tournament selection, roulette wheel selection, or sequential selection.

Crossover: The goal is to produce offspring with better fitness values than their parents by crossing over the genes of selected parent individuals. This means searching for better solutions than the current ones for the problem.

Mutation: Genetic diversity is ensured by randomly changing some genes in offspring individuals with a certain probability. This means distributing existing solutions that are gathered in one region to other points in the search space [22].

Elitism: In the crossover, it is possible to produce worse offspring, even though the aim is to produce offspring that are better than their parents. In this case, the selected parents are passed on to the next generation instead of the undesirable offspring, ensuring the continuity of solution quality.

Termination Criterion: The algorithm terminates when a certain number of generations is reached or when the solution quality no longer improves.

For the proposed method, GA and DE were implemented using the formulas given in Section 4.3 and the pseudocode given in below.

Inputs:     Notifications(Waste_coordinate, Waste_type, Waste_amount),

Vehicles(Waste_type, Capacity), Distance_matrix(Depot_coordinate, Waste_coordinate)

N_vehicle: Number of vehicles, N_location: Number of locations, N_pop: Number of population,

N_gen: Number of generations.

*/ Initial Population

for p = 1: N_pop

for i = 1: N_location

Node(i) = {rand(l), rand(v)}  |  l, v $\in$ Z, l: unique, l $\in$ (1, N_location), v $\in$ (0, N_vehicle)

Population(p) = {Node(1), Node(2), … Node(N_location)}

*/Loop of generations

for x = 1: N_gen

for p = 1: N_pop

*/ Decomposition of nodes according to vehicles

for i = 1: N_location

for v = 0: N_vehicle

if Vehicle_type(Node(i)) = v append Node(i) to set of Vehicle(v){}

*/ Distance calculations based on vehicles.

for v = 0: N_vehicle

Node(0) = Depot

i = number of nodes in set of Vehicle(v){}

D(v) = Distance_matrix([Node(0), Node(1)]) + … + Distance_matrix([Node(i), Node(0)])

Distance = sum(D(0: N_vehicle))

*/ Penalty calculations.

P_type = 0, P_capacity = 0, P_operation = 0

for i = 1: N_location

if Waste_type(Node(i)) ≠ Vehicle_type(Node(i)) then P_type = P_type +1

for v = 0: N_vehicle

Amount(v) = sum(Waste_amount(Node(1):Node(i)))   |   nodes in set of Vehicle(v){}

if Amount(v) > Capacity(Vehicle(v)) then P_capacity= P_capacity +1

if (Amount(v = 0) + Amount(v = 1) ≤ 3tons) & (Amount(v = 0) > 0) then P_operation = 1

if (Amount(v = 0) + Amount(v = 1) > 3tons) & (Amount(v = 0) = 0) then P_operatio n= 1

Fitness(p) = Distance + 500 × P_type + 500 × P_capacity + 2000 × P_operation

*/  Apply GA operators        or       */  Apply DE operators

Selection                            Mutation

Crossover                          Crossover

Mutation                           Evaluation

Elitism                               Selection

end.

Outputs: Best_routes, vehicle assignments, D(1:v)

4.4.2. Differential Evolution

The DE algorithm is an evolutionary optimization method that generates new solutions using difference vectors between individuals in a population and is effectively used in continuous optimization problems [23]. This method provides a directed exploration in the search space by using the differences between individuals in the existing population during the generation of new candidate solutions. In this respect, it differs from classical random mutation approaches and has the capacity for faster convergence and efficient solution generation. DE, by providing the advantage of the differential mutation strategy in global exploration, shows superiority over other heuristic methods by avoiding strong local optima, although the algorithm can sometimes converge slowly [24]. Furthermore, DE works efficiently in large-scale and nonlinear searches without needing gradient information. This presents the algorithm as a strong option [25]. The parameters of the algorithm are population size, the mutation factor, and the number of generations. The DE algorithm creates a randomly initialized population in the feasible solution space. Similar to GA it uses mutation, crossover, and selection parameters.

5. Results and Discussion

This study, unlike those in the literature, focuses not on regular waste generated as a result of normal daily activities, but on developing a methodology for collecting irregular waste. In order to test the success of the methodology we developed and the optimization methods we used, presented in Section 4, we applied it to the test problem we developed in Section 3. In the benchmark there is only one waste collection repository and numerous waste locations. The 10 notification locations given in Table 1, the 20 notification locations given in Table 2, and the 40 notification locations given in Table 3 were used in the optimizations. Collection vehicles start from the repository, visit all waste notification locations, and finish the route back at the waste collection repository.

Waste types and quantities, along with the geographical locations (latitude–longitude) of the wastes, are taken from Table 1, Table 2 and Table 3. Waste collection vehicles with maximum capacities given in Table 4 were used in the four waste collection scenarios given in Table 5. Each of these scenarios was tested by applying it to waste collection routes and vehicle optimizations consisting of 10, 20, and 40 locations. Notification data was recorded in a database, and daily planning was carried out using this data. GA and DE algorithms were used for vehicle routing and vehicle type optimization. In addition to determining the shortest route, optimization also considered whether the appropriate vehicle was selected for the type of waste at each location, whether the amount of waste on the route exceeded the vehicle’s capacity, and whether an unnecessarily large-capacity vehicle was selected for a low amount of waste. To achieve this, the waste–vehicle type mismatch, exceeding the vehicle capacity and operational rule constraints and penalty coefficients described in Section 4.3 were used.

Preliminary trials and analyses were conducted to determine the parameters to be used in the algorithms; these parameters include population size, mutation rate, and number of generations. The results of these preliminary trials are given in

Table 6. Best distances according to population size and mutation rates.

Population Size	Generation Number	Mutation Rate	Best Distance
20	200,000	0.001	175.41
		0.005	172.47
		0.010	171.17
		0.020	174.54
		0.050	198.51
50	200,000	0.001	166.04
		0.005	166.45
		0.010	161.82
		0.020	172.16
		0.050	186.00
100	200,000	0.001	192.41
		0.005	164.01
		0.010	165.83
		0.020	176.13
		0.050	176.04
200	200,000	0.001	186.11
		0.005	168.81
		0.010	164.01
		0.020	169.63
		0.050	195.38

. According to analysis of these results, the population size was determined to be 50, the mutation rate 0.01, and the number of generations 200,000, and the study was continued using these parameters. Figure 3 shows the change in best cost at different mutation rates when the number of locations is 40 and the population size is 50 for scenario 1.

For the stability test, both GA and DE algorithms were run 10 times with different seed numbers, and the best, worst, and mean route fitnesses, standard deviations, and mean run times were recorded in

Table 7. Stability of GA and DE algorithms for 10 locations.

Seed Numbers	GA					DE
	D (km)	Penalties (km)			f (km)	D (km)	Penalties (km)			f (km)
		C1	C2	C3			C1	C2	C3
1	90.06		500		590.06	90.09		500		590.09
2	90.52		500		590.52	90.88		500		590.88
3	85.78		500		585.78	93.60		500		593.60
4	90.52		500		590.52	90.62		500		590.62
5	85.78		500		585.78	86.20		500		586.20
6	90.06		500		590.06	90.42		500		590.42
7	85.78		500		585.78	90.62		500		590.62
8	85.78		500		585.78	89.18		500		589.18
9	90.52		500		590.52	90.06		500		590.06
10	89.77		500		589.77	85.18	500	500		1085.18
Mean Fitness					588.46					639.68
Std. Dev.					2.32					156.54
Best Fitness					585.78					586.20
Worst Fitness					590.52					1085.18
Mean Time (s)					12.41					22.99

. In the table, the distance of D is excluding expected infeasibility penalties and the fitness of f is including all penalties. The test was performed with 10 waste locations for scenario 4. In the first nine seed numbers, both GA and DE algorithms failed to satisfy one constraint each, resulting in an approximately 585 km fitness, with an additional penalty of 500 km added to the pure route distance of approximately 85 km. However, the DE algorithm failed to satisfy two constraints in the 10th seed number, resulting in an additional penalty of 1000 km to the pure 86.20 km route distance. From a robustness perspective, GA has a standard deviation of 2.32 km compared to 156.4 km in DE; GA appears more robust. Feasibility rate, the percentage of runs that avoid extra violations beyond the expected infeasibility situation, is 100% in GA, compared to 90% in DE. Figure 4 shows the performance of GA and DE according to different seed numbers.

The routes obtained as a result of route minimization and vehicle optimization performed with GA for 10 locations are shown separately for each scenario in Figure 5. Figure 6a, Figure 6b, Figure 6c, and Figure 6d show the routes for the first, second, third, and fourth scenarios, respectively. Although the routes shown in the figures are plotted as Euclidean distances, the distances between locations are street distances taken from the Google Distance Matrix API; however, route minimization is realized by GA. It was observed for 10 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 85.78 km. The total amount of rubble in Scenario 4 is due to exceeding the combined capacity of the two vehicles allocated for rubble collection, and this is not a failure of the algorithm. For all scenarios, operational constraints were satisfied because the amount of waste along the route was lower than that of the lowest-capacity vehicles allocated in the same type. This results in a positive outcome in terms of both fuel costs and carbon emissions.

The routes obtained as a result of optimization with DE for 10 locations are shown for scenarios 1 to 4 in Figure 6, respectively. It was observed for 10 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 85.78 km. The total amount of rubble in scenario 4 is due to exceeding the combined capacity of the two vehicles allocated for rubble collection, and this is not a failure of the algorithm. In all scenarios, operational constraints were also satisfied in the DE algorithm.

The routes obtained as a result of optimization with GA for 20 locations are shown for scenarios 1 to 4 in Figure 7, respectively. It was observed for 20 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 102.68 km. The total amount of rubble in Scenario 4 is due to exceeding the combined capacity of the two vehicles allocated for rubble collection, and again this is not a failure of the algorithm. In all scenarios, operational constraints were also satisfied in the GA.

The routes obtained as a result of optimization with DE for 20 locations are shown for scenarios 1 to 4 in Figure 8, respectively. It was observed for 20 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 100.71 km. The total amount of rubble in scenario 4 is due to exceeding the combined capacity of the two vehicles allocated for rubble collection, and again this is not a failure of the algorithm. In scenario 1, it was observed that operational constraint (C3) was not satisfied, and a 2000 km penalty was added to the distance of 71.51 km. This was due to the allocation of a 5-ton vehicle instead of a 3-ton vehicle, which was more suitable for the amount of waste.

The routes obtained as a result of optimization with GA for 40 locations are shown for scenarios 1 to 4 in Figure 9, respectively. It was observed for 40 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 283.22 km. In scenario 1, it was observed that operational constraint (C3) was not satisfied, and a 2000 km penalty was added to the distance of 211.84 km. This was due to the allocation of a 5-ton vehicle instead of a 3-ton vehicle, which was more suitable for the amount of waste.

The routes obtained as a result of optimization with DE for 40 locations are shown for scenarios 1 to 4 in Figure 10, respectively. It was observed for 40 locations that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied, and a 500 km penalty was added to the distance of 272.49 km. In scenario 1, it was observed that operational constraint (C3) was not satisfied, and a 2000 km penalty was added to the distance of 217.40 km. This was due to the allocation of the wrong vehicle.

Table 8. Optimization results with GA and DE based on scenarios and number of locations.

Scenarios	Locations	GA Fitness f (km)	DE Fitness f (km)	GA Penalties (km)			DE Penalties (km)			GA D (km)	DE D (km)	Difference Between the Ds (%)
				C1	C2	C3	C1	C2	C3
S1	10	50.96	50.96	0	0	0	0	0	0	50.96	50.96	0.0
	20	72.77	2071.51	0	0	0	0	0	2000	72.77	71.51	1.8
	40	2211.84	2217.40	0	0	2000	0	0	2000	211.84	217.40	−2.6
S2	10	76.37	76.37	0	0	0	0	0	0	76.37	76.37	0.0
	20	84.52	85.28	0	0	0	0	0	0	84.52	85.28	−0.9
	40	274.64	264.24	0	0	0	0	0	0	274.64	264.24	3.9
S3	10	93.57	93.57	0	0	0	0	0	0	93.57	93.57	0.0
	20	100.92	102.20	0	0	0	0	0	0	100.92	102.20	−1.3
	40	262.63	254.68	0	0	0	0	0	0	262.63	254.68	3.1
S4	10	585.78	585.78	0	500	0	0	500	0	85.78	85.78	0.0
	20	602.68	600.71	0	500	0	0	500	0	102.68	100.71	2.0
	40	783.22	772.49	0	500	0	0	500	0	283.22	272.49	3.9
Average												0.8

shows the route lengths and whether the constraints are violated in each scenario for the 10, 20, and 40-location problems as a result of optimizations performed with GA and DE. According to the results, it was observed that our penalty-based model significantly prevented constraint violations. It was observed that the waste–vehicle type mismatch constraint (C1) was satisfied in all scenarios and for all numbers of locations. In scenario 4, it was observed that exceeding the vehicle capacity constraint (C2) was not satisfied for all numbers of locations, and a 500 km penalty was added to the distance. This result is not due to algorithm failure but rather because the total amount of rubble given in scenario 4 (8 < x < 10 tons) exceeded the total capacity (8 tons) of the vehicles allocated for rubble collection. This scenario was intentionally included among the other scenarios to demonstrate the success of the developed methodology. In scenario 1, it was observed that the operational constraint (C3) was not satisfied for optimizing 20 locations with DE and 40 locations with both GE and DE. This meant that a 5-ton-capacity vehicle was unnecessarily allocated, even though there was less than 3 tons of rubble waste in total along the route.

In all scenarios for 10 locations, both GA and DE found the same routes with minimum distances and allocated the same vehicles. GA has better results than DE in scenario 1 with 40 locations, scenario 2 with 20 locations, and scenario 3 with 20 locations. DE has better results than GA in scenario 1 with 20 locations, scenario 2 with 40 locations, scenario 3 with 40 locations, and scenario 4 with 20 and 40 locations. This shows that GA and DE can generally find routes of equal or similar length and select appropriate vehicle types according to the type and capacity of the waste. If we compare the performance of GA and DE, DE is found to be on average 0.8% better. This does not seem like a very significant difference.

Table 9. Optimizations with GA based on Euclidean distances and Distance Vector API distances.

Scenarios	Locations	Optimization with Euclidean Distance D1 (km)	Converting Euclidean Distance to Distance Matrix API D2 (km)	Optimization with Distance Matrix API D3 (km)	Differences Between D2 and D3 (%)
S1	10	41.26	50.96	50.96	0.0
	20	54.86	75.62	72.77	3.8
	40	126.36	263.32	211.84	19.6
S2	10	60.47	78.47	76.37	2.7
	20	79.51	104.62	84.52	19.2
	40	160.10	291.95	274.64	5.9
S3	10	74.73	95.39	93.57	1.9
	20	83.56	109.35	100.92	7.7
	40	156.25	280.95	262.63	6.5
S4	10	72.11	93.62	85.78	8.4
	20	80.04	102.35	102.68	−0.3
	40	172.01	300.65	283.22	5.8
Average					6.8

and

Table 10. Optimizations with DE based on Euclidean distances and Distance Vector API distances.

Scenarios	Locations	Optimization with Euclidean Distance D1 (km)	Converting Euclidean Distance to Distance Matrix API D2 (km)	Optimization with Distance Matrix API D3 (km)	Differences between D2 and D3 (%)
S1	10	43.26	50.96	50.96	0.0
	20	74.46	103.00	71.51	30.6
	40	129.81	266.86	217.40	18.5
S2	10	60.47	78.41	76.37	2.6
	20	68.78	90.61	85.28	5.9
	40	156.26	298.53	264.24	11.5
S3	10	74.73	94.91	93.57	1.4
	20	85.21	110.70	102.20	7.7
	40	153.50	276.25	254.68	7.8
S4	10	57.58	75.88	85.78	−13.0
	20	82.20	110.09	100.71	8.5
	40	172.52	316.78	272.49	14.0
Average					8.0

show the results of optimizations performed with GA and DE, respectively, using Euclidean distances and the Google Distance Matrix API. First, optimizations were performed using Euclidean distances. Then, distances between the waste locations forming the route sequence were obtained from the Google Distance Matrix API and converted into actual road distances. These were compared with the optimization results obtained from the actual road distances. Optimizations performed with actual road distances were found to be 6.8% and 8.0% more successful than optimizations performed with Euclidean distances. The distances shown in both tables are pure route distances only and do not include penalty distances added due to violated constraints.

This shows us that if route planning is carried out without using actual road distances in any method, that is, in cases where the driver makes completely arbitrary decisions without a plan, the total distance will be long. Therefore, municipalities must collect irregular waste by using actual road lengths and making a plan. They should have vehicles with compartments in different combinations to reduce vehicle type mismatch. In addition, they should have vehicles with different capacities for the most commonly collected waste types. However, municipalities generally use standard types and capacities of vehicles, which leads to higher waste collection costs.

In the study, the low-capacity rubble collection vehicle, which collects less than 3 tons of rubble (vehicle-1) and consumes 14 L of fuel per 100 km, and the high-capacity rubble collection vehicle, which collects 5 tons of rubble (vehicle-0) and consumes 20 L of fuel per 100 km, were used. To prevent the assignment of an unnecessarily large vehicle, the P_operation (C3) constraint is used for route planning. This constraint supports the assignment of the most suitable vehicle to the route, thus reducing fuel consumption and consequently emissions. The emissions are calculated in accordance with the ISO-14083 standard [26] using Equation (5).

$${emission\_CO}_2=(D\times C)/100)\times 2.64$$

(5)

where D is the distance (km), C is the fuel consumption (L), and 2.64 is the diesel emission factor. In

Table 11. A comparison example for emissions.

Scenarios	Locations		D (km)	Fuel Consumption (L)	CO2 Emission (Kg CO2)
S1	20	GA	72.77	10.19	26.90
		DE	71.51	14.30	37.76

, a comparison example for emissions is shown. In scenario 1, for 20 locations, GA chose the correct vehicle by avoiding the C3 constraint, resulting in a total fuel consumption of 10.19 L and total CO₂ emissions of 26.90 kg. In contrast, DE chose an incorrect, larger vehicle, resulting in a fuel consumption of 14.30 L and total CO₂ emissions of 37.76 kg. These results demonstrate a 28.74% improvement in fuel consumption and a 28.76% improvement in total CO₂ emissions. These findings show that properly optimized routes and correct vehicle allocation can make significant contributions to environmental sustainability.

6. Conclusions

Unlike household waste, which is extensively studied in the literature, we focused on the collection of irregular waste that arises unexpectedly or unusually. In this study, a complete system encompassing irregular waste notification, vehicle allocation, and route planning was developed for municipalities to use in irregular waste collection services within the scope of smart cities. While household waste is collected periodically by a single vehicle following a fixed route within a region, irregular waste collection requires route and vehicle planning for different types and quantities of waste. We used a constraint-based cost function for a large number of irregular wastes and collecting vehicles. We minimized the route length between waste locations and optimized vehicle allocation according to the type of waste. Since we could not find a benchmark problem in the literature to test our developed method, we created a test problem with four different scenarios containing 10, 20, and 40 locations, five waste types, and five vehicle types. We used GA and DE algorithms for these scenarios and discussed their success. We observed that both algorithms were able to allocate vehicles 100% appropriately to the waste type and could allocate vehicles with capacity corresponding to the amount of waste. Although the difference was not very significant, we noted that DE has 0.8% better results than GA. However, GA seems more robust and has a higher feasibility rate than DE. We also found that optimizations performed with GA and DE algorithms by using actual road distances were 6.8% and 8.0% more successful than optimizations performed with Euclidean distances, respectively.