Internet of Things-Assisted Vehicle Route Optimization for Municipal Solid Waste Collection

Abstract

The efficient collection of municipal solid waste poses a significant challenge for the prospective development of smart cities. Using Internet of Things (IoT) technology enables the detection of various kinds of waste-related information, facilitating the implementation of a comprehensive plan for efficient waste collection. In this paper, an innovative waste collection mechanism leveraging the IoT sensors and widely recognized Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), a robust multi-criteria decision analysis method is introduced. Recognized for its ability to yield optimal solutions amidst multiple influencing parameters, TOPSIS proves particularly advantageous when confronted with diverse factors affecting decision making. A TOPSIS-based algorithm for optimal route selection is developed to collect waste using metrics such as toxicity, volume, and time duration of the waste while minimizing the route distance. To demonstrate the efficiency of our proposed algorithm, a comparative analysis with existing algorithms that are dependent on and optimized for single parameters is conducted. Through rigorous evaluation, it is shown that our proposed algorithm reduces the total distance traveled to collect the waste from all the bins by $14\%$ by effectively considering multiple criteria and optimizing waste collection routes.

1. Introduction

The upsurge in urban population correlates with a heightened demand for municipal services, placing additional stress on waste management facilities. The increase in city residents invariably leads to a proportional rise in the generation of municipal solid waste, prompting the need for the development of supplementary waste disposal sites to accommodate the amplified volume [1].

The environmental consequences of mounting municipal solid waste (MSW) are substantial, playing a significant role in the exacerbation of climate change [2]. Inadequate waste disposal practices lead to the release of significant quantities of greenhouse gases, particularly methane, as organic waste decomposes in landfills. Moreover, the energy-intensive processes involved in waste treatment and disposal contribute to an increased carbon footprint, intensifying the overall environmental impact. Addressing these challenges through the adoption of sustainable waste management practices is imperative to mitigate adverse environmental effects and reduce the contribution to climate change.

Typical waste collection processes in metropolitan cities involve several key stages [3]. Residents generate waste through daily activities, resulting in the production of household waste comprising various materials. Waste bins or containers are strategically placed in residential areas, commercial districts, and public spaces to facilitate convenient waste disposal. Waste collection schedules are established, specifying the days and times when waste collection vehicles will visit designated areas for pickup. Specialized waste collection vehicles, such as garbage trucks, move through predetermined routes to collect waste from designated bins. In some cases, residents are required to separate their waste into different categories, such as recyclables and non-recyclables. Waste collectors may also perform additional sorting. Collected waste is transported to transfer stations or intermediate facilities, where it may undergo further sorting and processing. Waste is then transported to landfills or recycling facilities, depending on its nature. Recyclables are sent to recycling plants, while non-recyclables may be disposed of in landfills. The final step involves the proper disposal of waste, adhering to environmental regulations and waste management policies. Overall, an effective waste collection process in metropolitan cities integrates strategic planning, scheduled collections, sorting, and proper disposal to ensure the efficient management of diverse types of waste generated by a densely populated urban environment [4].

Advancements in sensors and wireless communications have paved the way for the integration of Internet of Things (IoT) networks in numerous smart city applications. Waste management can also harness the power of IoT to ascertain the quantity and composition of waste, transmit these data to waste collection organizations, and formulate optimized routes for efficient waste collection. Indeed, IoT can automate and improve the entire waste collection process [5].

In the context of MSW, the predominant use of road transport emerges as a notable environmental issue, accounting for a substantial portion exceeding 95% in both oil and fossil fuel consumption. This results in a considerable carbon dioxide (CO₂) footprint, marking it as a significant contributor to the emission of greenhouse gases. According to [6], In Europe, the transportation sector contributes to over 27% of the overall CO₂ emissions. Specifically, within this sector, road transport stands out as the most significant source of pollution. This alarming statistic underscores the pivotal role of road transport in environmental pollution, with tangible health implications such as lung cancer, asthma, allergies, and various respiratory problems, highlighting the pressing necessity for the adoption of sustainable waste management practices. Addressing this challenge in urban planning is imperative, necessitating strategic measures to effectively handle growing municipal waste and minimize adverse environmental effects [1].

Numerous studies have investigated both cost and route optimization problems to enhance the performance of operational efficiency. Cost optimization in solid waste management involves identifying and implementing strategies to minimize expenses while maintaining effective waste collection and disposal services. The first step is designing collection routes that minimize travel distances, reduce fuel consumption, and optimize the use of collection vehicles. Next, optimal allocating resources are required, such as personnel, vehicles, and equipment, effectively to enhance operational efficiency and reduce idle time. Another important factor in cost optimization is the implementation of technology, such as route optimization software, sensors, and monitoring systems, to streamline operations and identify areas for cost savings. Waste can also be efficiently sorted at the residential areas so that waste collection and processing cost can be reduced.

Vehicle route optimization is important part of solid waste management and requires the designing of efficient and cost-effective paths for waste collection. There are many important factors that should be considered while designing vehicle routes for waste collection. These include consideration of geographical layout of the city area, population of the area, traffic density, and current distribution of waste bins around the city [7]. Furthermore, vehicle routes should be dynamic and change with real-time data to maximize the waste collection efficiency.

The optimization process extends to vehicle capacity planning, ensuring that collection vehicles are assigned routes aligning with their capacity to minimize unnecessary trips and vehicle idling. Predictive analytics play a crucial role by anticipating changes in waste generation, allowing for proactive adjustments to collection routes and schedules. Furthermore, the integration of advanced technology, including GPS tracking, sensors, and communication systems on collection vehicles, facilitates ongoing monitoring of route performance, vehicle status, and adherence to planned routes. Valuable insights are also drawn from customer feedback, enabling the identification of areas for route adjustments based on shifts in waste generation or specific collection requirements. This holistic approach to route optimization aims to enhance the overall effectiveness, efficiency, and sustainability of waste collection operations.

In this study, our primary focus revolves around addressing the route optimization problem within the domain of solid waste management. Recognizing the multifaceted nature of decision-making in this context, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm is employed [8]. TOPSIS proves invaluable in situations where decision makers are confronted with the need to evaluate alternatives based on multiple criteria, each carrying varying degrees of importance.

The key features of the proposed algorithm and major contributions of the work are as follows:

• An IoT- and TOPSIS-based solution is provided to improve the waste collection process and route optimization of waste vehicles.
• Several key waste-related metrics are considered to design an effective route optimization algorithm for waste collection. These metrics include waste toxicity, waste volume, duration of waste in the bins, and distance of bins from other bins in the area.
• The TOPSIS technique is utilized to consider multiple factors in order to select routes that maximize the collection of old, highly toxic, and large-volume waste and minimize the travel distance of vehicles.
• Extensive simulations are performed to show that the proposed technique outperforms other techniques to maximize the efficiency of waste collection.

2. Related Work

Several works in the literature have worked on the problem of optimizing the route of vehicles for municipal waste collection. The primary objective is to devise optimal route designs for vehicle fleets, minimizing the total travel distance and, consequently, reducing overall driving costs [9,10]. Effective routing is pivotal in the planning and definition of paths for waste collection trucks, and the absence of technology in route selection can result in inefficient and costly collection systems [10,11,12].

In developing countries, the scheduling of trucks for the collection of waste often lacks organization and systematic planning, relying on intuitive methods and practical experiences with several negative consequences, as pointed out by [13]. To address these challenges, numerous studies [12,14,15,16] have delved into optimizing solid waste collection through the application of Geographical Information System (GIS)-based techniques. These approaches aim to ensure better management of resources and reduce negative impacts on the environment. GIS emerges as a valuable tool for determining cost-effective solid waste collection solutions, as emphasized by [14]. GIS solutions utilize topological information as well as waste-related data, such as amount of waste and size of available bins. Authors in [12] utilized GIS-based analysis of land elevation and slope for route optimization to achieve fuel savings, and [17] applied GIS in the urban setting for transport route optimization.

Stochastic vehicle routing, as applied by [18,19] models the problem considering randomness in the network. In the context of MSW collection, the stochastic approach does not consider various critical parameters, such as user numbers for a bin, social behaviors, demographic contexts influencing waste generation, and other pertinent factors. On the other hand, capacitated vehicle routing imposes constraints based on vehicle capacity in terms of weight and volume of waste and considers it for vehicle trip planning [20].

Additionally, the vehicle routing with time windows introduces defined time periods or windows during which waste should be collected. Time windows are crucial in ensuring that vehicles adhere to a fixed schedule with predetermined start and finish timings during the workday [21]. Studies have also explored optimal routing for solid waste collection trucks, employing sensors such as a Global Positioning System (GPS) sensor, a volume and flow sensor, and a Radio Frequency Identification (RFID) sensor. GIS, a widely adapted software, facilitates automated collection by tracking bin and vehicle locations and collection times. However, it falls short in estimating bin statuses and waste levels [22].

Further research has focused on mathematical programming using heuristic approaches to address the complexity of conventional methods. Such approaches include Particle Swarm Optimization (PSO) [23], the Genetic Algorithm (GA), the Nearest Neighbourhood Search Algorithm [24], and Artificial Neural Networks (ANN) [25]. Researchers highlight the benefits of efficient MSW collection vehicle routing through the development of mathematical algorithms to address optimization challenges. The authors in [15] employed a mixed-integer programming model, reducing the total collection system distance by 23.47 percent. The work in [26] formulated the MSW collection route problem into a mixed-integer program, achieving a reduction of over 30% in the overall length of the garbage collecting path.

In [27], a waste collection problem incorporating a midway disposal pattern is addressed. A hybrid artificial bee colony (ABC) algorithm is proposed, demonstrating superior optimum-seeking performance compared to other metaheuristics. The study validates the effectiveness of the hybrid approach, emphasizing that the midway disposal pattern reduces carbon emissions by up to 7.16% in practical instances. Similarly, the study in [28] addresses a complex recyclable waste collection problem, extending the vehicle routing problems with intermediate facilities. It introduces a unique combination of a fixed fleet, flexible depot assignment, and various constraints inspired by a real-world application. The proposed MILP model with enhanced valid inequalities faces challenges for larger instances, prompting the development of a multiple neighborhood search heuristic. The heuristic proves effective, achieving optimality on small instances, competitive performance for special cases, and significant savings in practical applications, notably in waste collection in Geneva, Switzerland. In [29], the pressing challenges of municipal solid waste management are addressed in rapidly urbanizing and developing markets. Introducing a coordinated framework for the vehicle routing problem, the research incorporates financial, environmental, and social considerations to achieve sustainability goals. The adaptive memory social engineering optimizer is introduced as a novel and superior optimization tool, outperforming simulated annealing and the social engineering optimizer. The findings emphasize practical solutions aligned with sustainability objectives in coordinated solid waste management, highlighting potential cost savings through increased recycling across multiple logistics echelons. The work in [30] addresses a real-life waste collection vehicle routing problem with time windows (VRPTW), incorporating multiple disposal trips and drivers’ lunch breaks. The extended Solomon’s insertion algorithm aims not only to minimize the number of vehicles and total traveling time, but also emphasizes route compactness and workload balancing—critical aspects in practical applications. To enhance these factors, a capacitated clustering-based waste collection VRPTW algorithm is introduced and successfully implemented in real-life waste collection problems. The study also provides a set of waste collection VRPTW benchmark problems.

In this investigation, our central focus centers on tackling the route optimization challenge in the realm of solid waste management. Acknowledging the intricate nature of decision-making within this context, the TOPSIS algorithm is employed. TOPSIS proves to be instrumental in scenarios where decision makers grapple with the evaluation of alternatives across multiple criteria, each carrying diverse degrees of significance. This algorithm provides a methodical and quantitative approach to rank and select alternatives, gauging their overall performance. It takes into consideration the preferences and priorities of decision makers, ensuring a comprehensive and well-informed decision-making process.

In the specific context of waste collection, TOPSIS is used to optimize routes by meticulously considering a range of factors. These factors encompass the volume of waste slated for collection, the toxicity levels associated with distinct waste types, the time efficiency inherent in each route, and the overall distance covered. By seamlessly integrating TOPSIS into our route optimization framework, our objective is to augment the efficiency of waste collection operations. The algorithm empowers us to make judicious decisions regarding the most efficient routes based on a nuanced understanding of diverse criteria. This involves prioritizing routes that minimize travel distance, maximize the collection of high-volume waste, reduce the time required for collection, and account for the environmental impact of toxic waste.

3. System Model

In this section, the system model for our proposed waste collection algorithm is introduced. Our system comprises n bins strategically distributed across a region, interconnected by e bin-to-bin paths, as illustrated in Figure 1. Each bin is equipped with IoT sensors to capture volume (V), toxicity ($\nu$), and the duration the trash has been in the bin (t). The volume of waste can be measured using ultrasonic sensors [31]. The toxicity of waste measures how hazardous the waste can be for the human health [32,33]. Typically, gas sensors can be used to measure the toxicity level of a waste [34]. The duration of trash in the bin can be measured using the time the bin was last collected. These sensor readings are communicated to a centralized location responsible for executing the route selection mechanism. Subsequently, vehicles are dispatched along the chosen routes based on the information gathered from the sensors.

In normal route selection for the waste collection, certain parameters, such as toxicity, are used, and the route is selected that maximizes the waste collection based on toxicity, and hence, an accumulated toxicity value will be maximized.

4. Proposed Technique

In our proposed mechanism, multiple parameters related to waste is considered such that the route is selected keeping in mind all those parameters. For that, TOPSIS, known as the Technique for Order of Preference by Similarity to Ideal Solution, is used. It is a multi-criteria decision analysis method. TOPSIS is useful in situations where decision makers need to consider multiple criteria with varying importance. It provides a systematic approach to rank and select alternatives based on their overall performance, taking into account the preferences of decision makers. In waste collection, TOPSIS is utilized to choose the most efficient route by considering factors like volume, toxicity, time, and distance. The detailed algorithm is presented in Algorithm 1.

Algorithm 1 Route Selection Algorithm using TOPSIS

Inputs: A graph $G=(n,e)$ with nodes n and edges e Data regarding waste attributes as weights of G (toxicity $\nu$, volume V, time t, d) Algorithm Steps: Step 1: Normalize the data for each waste attribute ($\nu$, V, t, d) between 0 and 1. The goal is to maximize $\nu$, V, and t while minimizing d.      $\mathrm{Normalized}\mathrm{Value}=\frac{\mathrm{Actual}\mathrm{Value}}{\sqrt{\sum \mathrm{Actual}{\mathrm{Value}}^2}}$ Step 2: Calculate the weighted normalized values for each route based on the waste attributes.      WeightedValue = $(\nu \times W_{\nu })+(V\times W_V)+(t\times W_t)+(d\times W_d)$      where $W_{\nu }$, $W_V$, $W_t$, and $W_d$ are the assigned weights. Step 3: Determine the ideal and negative-ideal solutions for each attribute.      Ideal solution: Maximum normalized value for toxicity, volume, and time; minimum normalized value for distance.      Negative-ideal solution: Minimum normalized value for toxicity, volume, and time; maximum normalized value for distance. Step 4: Calculate the proximity of each path to the ideal and negative-ideal solutions using a distance measure.     - Calculate the distance of each path from the ideal solution and the negative-ideal solution.      $D_i^{+}=\sqrt{{\sum }_{j=1}^m{({\mathrm{NormalizedValue}}_{ij}-{\mathrm{IdealSolution}}_j)}^2}$      $D_i^{-}=\sqrt{{\sum }_{j=1}^m{({\mathrm{NormalizedValue}}_{ij}-{\mathrm{NegativeIdealSolution}}_j)}^2}$ Step 5: Compute the TOPSIS score for each path:      $TOPSI{S}_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$ Step 6: Rank the paths based on their TOPSIS scores.      The routes with higher accumulated TOPSIS scores are more favorable for waste collection as they match the criteria of higher toxicity, volume, time, and lower distance. Output: The prioritized route(s) for waste collection based on TOPSIS scores.

Algorithm 1 provides the steps involved in determining the prioritized routes in a graph G, with nodes n representing the bins and edges e representing the paths between the nodes. The aim is to calculate or obtain a path between starting and ending nodes that is optimum for all the waste attributes that we are considering as weights of the edges. The data are normalized for each waste attribute (toxicity, volume, time and distance) individually to ensure that each attribute is on the same scale for a fair comparison. The normalization is performed as given below:

$$\mathrm{Normalized}\mathrm{Value}=\frac{\mathrm{Actual}\mathrm{Value}}{\sqrt{\sum \mathrm{Actual}{\mathrm{Value}}^2}}$$

(1)

Next, the algorithm calculates the weighted normalized values for each path. The weighted value is obtained by multiplying each normalized attribute (toxicity, volume, time, and distance) by its assigned weight and summing these values. The formula is given by:

$$\mathrm{WeightedValue}=(\nu \times W_{\nu })+(V\times W_V)+(t\times W_t)+(d\times W_d)$$

(2)

where, $W_{\nu }$, $W_V$, $W_t$, and $W_d$ are the weights assigned for toxicity, volume, time, and distance, respectively. Then, in the next step, the ideal and negative-ideal solutions for each attribute are identified. The ideal solution represents the maximum normalized value for toxicity, volume, and time, and the minimum normalized value for distance. The negative-ideal solution is the opposite. These solutions are crucial for calculating the proximity of each route. The proposed algorithm uses a Euclidean distance measure to calculate the proximity of each path to the ideal and negative-ideal solutions. The distances ($D_i^{+}$ and $D_i^{-}$) are calculated for each path, considering the normalized values of toxicity, volume, time, and distance.

The TOPSIS score for each path of the adjacent bins is computed using the distances obtained in Step 4 given by:

$${\mathrm{TOPSIS}}_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$$

(3)

The overall rankings of the end-to-end routes is determined based on their cumulative TOPSIS scores. These scores are calculated by summing up the TOPSIS scores for each path within all possible routes. A higher cumulative TOPSIS score for a specific route signifies that the route is more advantageous for waste collection in relation to the considered parameters. An illustrative route, starting from node 1 and concluding at node 7 (highlighted in red), is depicted in Figure 2. The TOPSIS score for each node-to-node segment is aggregated along the route, resulting in an accumulated TOPSIS score of 3.447 in this particular case.

5. Results

In this section, some of the results that will show the importance/strength of our proposed method of route selection for the garbage collection is presented. The typical value of each parameter has been used for simulations and is given as follows unless stated otherwise. The no. of bins is represented by n, which is chosen from the set $\{8,12,16,20\}$. The total number of point-to-point paths is represented by e, which is kept at twice the value of n in the figure from Figure 3, Figure 4, Figure 5 and Figure 6. The value of toxicity $\nu$ ranges from 0–1, and the volume of the bin V ranges from 600–1200 litres. The distance of the point-to-point path d ranges from 10 to 200 m, and the time elapsed t for garbage in the bin ranges from 1–100 h. The vehicle capacity for the waste collection is set to 5000 L.

It can be seen from Figure 3 that the proposed TOPSIS-based route selection method approaches the result of the algorithm that is solely based on toxicity. The volume- and the time-based algorithms perform worst in terms of accumulated toxicity value as they are aimed at maximizing the corresponding parameters. The proposed TOPSIS-based algorithm considers all parameters, enabling it to select a route that balances performance across the considered parameters. Figure 3 illustrates this consistent pattern across various bin values denoted by n.

Similar to Figure 3, it can be seen in Figure 4 that the proposed scheme performs better in terms of collecting the waste that has seen more time in the bin. The purple bar will be maximum, as it is an upper bound on the waste collected based on time. The time-based algorithm is designed to maximize the waste collected based on time, and hence, it will give a lower score in the other parameters, as can be seen from Figure 3. Similarly, the trend is followed for various values of n.

The data depicted in Figure 5 illustrate a consistent pattern across all algorithms, except for the volume-based algorithm, which attains the maximum threshold of 5000. This value represents the vehicle’s capacity limit. The volume threshold is a factor in all algorithms, resulting in the proximity of all outcomes to the 5000 threshold. However, only the volume-based algorithm effectively reaches and approaches the 5000 value.

Finally, as evident from Figure 6, our proposed algorithm successfully attains the objectives illustrated in Figure 3, Figure 4 and Figure 5 by covering the shortest distance when compared to the other algorithms. This achievement can be attributed to the fact that our proposed algorithm takes distance into account as one of the parameters. Figure 6 underscores the effectiveness of the TOPSIS-based algorithm, which consistently delivers balanced results across all parameters.

In the second set of results, data are displayed where the parameter n is fixed at 12, and the number of direct routes, denoted as e, between the bins is varied from 12 to 20. This demonstrates the influence of having more available routes on the efficiency of garbage collection. As shown in Figure 7, it is evident that the total toxic load of the collected waste increases with the rise in the number of routes. The value of 12 signifies the presence of 12 direct paths among the ’n’ bins, which remains constant for the subsequent figures. Consequently, the total count of end-to-end routes diminishes, resulting in fewer routes available for waste collection, as observed from Figure 7, Figure 8, Figure 9 and Figure 10.

Moreover, as indicated in Figure 7, it is clear that the proposed waste collection approach demonstrates a performance level comparable to the toxicity-based algorithm, which sets the upper limit for accumulated toxicity. The volume-based and distance-based algorithms exhibit lower toxicity levels. This outcome is reasonable, given that these algorithms are optimized to maximize their respective parameters: volume for the volume-based method and distance for the distance-based approach.

Similarly, by examining Figure 8, it is observed that the proposed system demonstrates improved performance, particularly in collecting waste that has been in the bin for an extended period, exemplified by the 200 h mark. This figure represents waste that has accumulated in the bins over a 200 h duration in total i.e., the sum of the number of hours in all the bins in the selected route for the value of $e=12$. For a different value of e, i.e., 20, this duration increases to approximately 330 h for the proposed system. The reason behind this extension is the increased availability of collection routes. Our specific route selection, among all available options, generates results that surpass both the volume-based and toxicity-based algorithms. The time-based algorithm yields the highest value since its purpose is to collect waste based on the duration it has spent in the bin. Consequently, it serves as the upper limit in this context.

A similar trend can be seen in Figure 9, where it can be seen that the proposed algorithm performs at par with the volume-based algorithm. and secondly, as the number of routes are increased, the overall combined volume is increased.

Figure 10 shows the distance traveled by each of the schemes for collecting waste according to their desired parameter, and it can be seen that the proposed TOPSIS-based algorithm performs better than all of the other schemes as it gives the lowest distance among all. This figure shows the power of the TOPSIS-based algorithm, similar to Figure 6, as it shows that in a shorter distance, it can collect waste that is better in terms of all the parameters i.e., volume, toxicity, and time. This is because of the fact that the TOPSIS-based algorithm also considers distance, toxicity, volume, and time as parameters, and provides the best solution in terms of all the parameters, unlike the other schemes, which are optimized on a single parameter.

Table 1. Parameters values for $n=8$ and $e=20$.

Scheme	Volume V	Toxicity $\mathit{\nu }$	Time t	Distance d
TOPSIS-Based	4700	3.2	330	505
Volume-Based	5000	2.5	320	585
Toxicity-Based	4650	3.4	310	575
Time-Based	4700	2.5	390	580

shows the values of various parameters from Figure 3 to Figure 6 into a single table for $n=8$ and $e=20$. Here, it can be clearly seen that the TOPSIS-based scheme performs better in all aspects, as it gives the second best result in each of the parameter.

When the number of bins is increased from 8 to 12, it can be seen from

Table 2. Parameter values for $n=12$ and $e=20$.

Scheme	Volume V	Toxicity $\mathit{\nu }$	Time t	Distance d
TOPSIS-Based	4800	3.5	340	510
Volume-Based	5000	2.6	325	585
Toxicity-Based	4750	3.6	315	580
Time-Based	4800	2.7	400	585

, that the values of various parameters jump slightly. It is understandable as the number of choices for waste collection increases.

Unlike in Table 2, a slight decline in the parameter values as the bins is increased from 12 to 16 in

Table 3. Parameter values for $n=16$ and $e=20$.

Scheme	Volume V	Toxicity $\mathit{\nu }$	Time t	Distance d
TOPSIS-Based	4750	3.5	340	515
Volume-Based	4950	2.65	325	580
Toxicity-Based	4750	3.55	322	575
Time-Based	4750	2.7	392	570

can be seen. Although the number of bins has increased, which should provide more options of collecting waste, the trend starts to decrease because of the fact that the number of routes connecting those bins have not increased. It means that the 16 bins are connected through $e=20$ bin-to-bin connecting paths.Therefore, the total end-to-end paths are now lower compared to the earlier cases. That is why a decline in the various parameters can be seen.

This trend of decline in the waste parameters extends further, as the number of bins is increased to 20, as can be seen in

Table 4. Parameter values for $n=20$ and $e=20$.

Scheme	Volume V	Toxicity $\mathit{\nu }$	Time t	Distance d
TOPSIS-Based	4650	3.35	330	515
Volume-Based	4900	2.65	325	580
Toxicity-Based	4550	3.45	320	575
Time-Based	4650	2.7	380	570

. Again, it is important to understand that the 20 bins are connected through 20 paths i.e., there are 20 bin-to-bin connections among the 20 bins, so the overall end-to-end paths decrease further, and hence, a declining trend can be seen.

6. Conclusions

This paper proposes an optimal waste collection mechanism employing the robust TOPSIS method for multi-criteria decision analysis. The proposed technique considers key waste-related metrics, including toxicity, volume, time duration of the waste, and distance between the bins, to optimize the vehicle route for waste collection. Simulation results show that the proposed algorithm reduces the total distance traveled by the waste collection vehicle by $14\%$ compared to other algorithms that only consider a single parameter for route optimization. The proposed TOPSIS-based scheme achieves this performance while collecting the most critical waste in terms of volume, toxicity, and time duration.