Sustainable Transportation Optimisation of Waste Electrical and Electronic Equipment Using AI-Based Evolutionary Algorithms

Abstract

Waste Electrical and Electronic Equipment (WEEE) management is a critical global challenge. This study proposes a model for the WEEE Transportation Problem using advanced evolutionary algorithms such as the Genetic Algorithm (GA), the Offspring-Selected Genetic Algorithm (OSGA), the Evolution Strategy (ES), and the Offspring-Selected Evolution Strategy (OSES). These algorithms, which are part of the field of Artificial Intelligence (AI), are applied to optimise transportation routes, minimising time and costs, and promoting sustainability by reducing the carbon footprint. Test instances and solutions are presented to demonstrate the feasibility of the model and the effectiveness of the proposed algorithms. Rather than providing technical detail, the focus is placed on the novelty of applying these algorithms to the WEEE Transportation Problem in Mexico, particularly for minimising operational cost. While reductions in carbon emissions are discussed as a natural consequence of cost optimisation, a formal dual-objective formulation is beyond the present scope and is identified as a direction for future work.

1. Introduction

Smart cities use advanced technologies to improve the quality of life of their citizens, and waste management, including electrical and electronic waste (WEEE), is central in this context. The concept of Smart Waste refers to the use of technologies to optimise the collection, transport, and recycling of waste in urban environments, reducing environmental impact and improving operational efficiency. The integration of smart technologies for WEEE management not only contributes to urban sustainability but also supports several of the Sustainable Development Goals (SDGs):

• Efficient WEEE management can contribute to the recovery of valuable and rare materials that can be reused in the production of new electronic devices, reducing the need to extract new resources and promoting the sustainable use of energy in manufacturing.
• Smart cities can implement intelligent waste management systems that optimise the collection and transportation of WEEE, reducing traffic congestion and carbon emissions. AI technology can analyse waste generation patterns and plan efficient collection routes, promoting cleaner and more sustainable communities.
• Proper management of WEEE prevents hazardous e-waste from reaching landfills and contaminating soil and water resources. Advanced technologies enable the accurate tracking and management of this waste, protecting biodiversity and terrestrial ecosystems from the harmful effects of toxic materials.

There is a global problem in the treatment of waste derived from the elements that make up electrical and electronic equipment. Electrical and electronic appliances contain materials that pollute the environment and produce various diseases in those who are in direct or indirect contact with these materials. The management of Waste Electrical and Electronic Equipment presents a significant challenge worldwide due to the massive amount of waste generated and its potential environmental impact. Optimising WEEE transportation is crucial for improving operational efficiency and reducing the carbon footprint. In this context, Artificial Intelligence offers advanced solutions that can transform the way we manage this waste. The AI taxonomy for WEEE management.

• Knowledge-Based Systems. KBS can help in the identification and classification of different types of electronic waste. Using rules based on knowledge about the physical and chemical characteristics of the devices, these systems can diagnose the type of WEEE and classify it appropriately for treatment. Knowledge-Based Systems [1] can be: Expert Systems [2], Fuzzy Logic Systems [3], Rule-Based Systems [4].
• Data-Based Systems. Data-based systems offer a powerful tool to address this problem, providing advanced methods to analyse, optimise and improve the efficiency of WEEE collection, sorting and recycling processes. Data-Based Systems can be: Machine Learning [5,6,7], Deep Learning [8,9], Ensemble Algorithms [10,11,12], Generative AI [13,14,15], Regenerative AI [13].
• Heuristic-Based Systems. Heuristic-based systems are powerful tools for solving complex optimisation problems that are common in the management of WEEE. These systems use nature-inspired methods and practical rules to find efficient solutions to problems that may be difficult to tackle using conventional techniques. Heuristic-Based Systems can be: Evolutionary Algorithms [16].

One significant aspect is the integration of data-driven approaches to enhance waste management systems. For instance, researchers have explored the application of artificial intelligence in optimizing reverse logistics networks for WEEE recycling, particularly in urban areas such as São Paulo, Brazil. Studies show that employing simulation and computational intelligence can optimize both economic and environmental outcomes associated with WEEE management, ultimately aiding in the promotion of a circular economy [17]. This approach addresses the logistical complexities involved in the transportation of WEEE to recycling centers, which is often hampered by inadequate infrastructure and high operational costs.

Transportation logistics remain a challenging component due to the high costs associated with moving WEEE. Research indicates that individuals often find transporting WEEE to collection centers less rewarding and more cumbersome than other eco-friendly actions, leading to lower recycling rates [18]. Therefore, addressing the convenience factors influencing these behaviors is critical. Effective communication strategies to inform the public about the importance of recycling and the environmental benefits associated with WEEE recycling could enhance participation rates. Initiatives that improve public awareness can lead to a more robust collection framework, which is crucial for establishing effective recycling systems [19].

Environmental impact is another critical dimension of WEEE transportation and recycling. Several studies indicate that improper handling and transport can lead to pollutants, including airborne particles and hazardous substances, entering the environment [20]. The processes involved in recycling WEEE, especially if not managed properly, can expose workers to toxic materials and result in environmental degradation. Therefore, the development of policies that enforce stringent regulations on the transport and handling of WEEE, including aspects such as extended producer responsibility (EPR), is essential. EPR frameworks encourage manufacturers to take responsibility for their products throughout their lifecycle, including take-back schemes that assist in the efficient transportation of end-of-life electronics [21].

Future strategies will require collaboration across various sectors, combining technological advancements with community engagement and regulatory frameworks. Studies emphasize the need for supportive policies and public engagement to bolster WEEE recycling rates. Countries like Nigeria and Brazil are already reassessing their policies and infrastructure to improve their WEEE management systems, revealing significant gaps that need addressing to mitigate health and environmental risks associated with e-waste [22].

In

Table 1. Concepts applied to WEE problems.

Research	Based Systems	Aportation
[23]	KBS	Implementing expert systems can facilitate these processes by automating decision-making, providing resource allocation recommendations, and optimizing collection routes for WEEE, ultimately leading to improved sustainability outcomes
[24]	Data-Based Systems	These systems leverage data analytics, machine learning, and artificial intelligence to optimize the collection, transportation, recycling, and disposal of electronic waste.
[25]	Knowledge-Based Systems	Cottes et al. propose a techno-economic modeling approach for assessing the feasibility of WEEE treatment plants, relying heavily on KBS to evaluate economic and operational performance, thus providing stakeholders with a comprehensive toolkit for effective plant management.
[26]	Data-Based Systems	Huang et al. discuss the importance of data analytics in measuring greenhouse gas emissions and resource recovery from WEEE, showcasing how DBS can integrate environmental data to inform policy decisions and operational practices, although their study emphasizes the situation in China.
[27]	Data-Based Systems	The utilization of data-driven models can significantly enhance the understanding of urban WEEE flows, thus aiding in the establishment of efficient recycling targets.
[28]	Heuristic-Based Systems	Burat et al. investigate the recovery of valuable materials, utilizing heuristic methods to optimize the separation and recycling processes for various WEEE components.
[25,29]	Heuristic-Based Systems	The combination of KBS for expert insights and DBS for robust data analysis presents a path toward more effective decision-making frameworks in e-waste management.
[30]	Fuzzy Logic Systems	They developed a decision-making tool on E-waste management methods using minimisation of regret with interval-valued intuitionistic fuzzy sets.
[31]	Heuristic-Based Systems	They reviewed the reverse logistics of WEEE in developed and developing countries, identifying opportunities for optimisation using heuristic-based systems.
[32]	convolutional neural network	Jude and colleagues proposed an artificial intelligence-based predictive framework for smart waste management. They employed a convolutional neural network (CNN) to forecast waste generation, addressing the challenges posed by data variability and incomplete records. The study demonstrated that this method significantly improves the accuracy of waste volume prediction, which is essential for designing more efficient and sustainable collection and treatment systems.

, some of the concepts applied to solve WEEE problems are shown. Knowledge-Based Systems, Data-Based Systems, and Heuristic-Based Systems are applied to the management of Waste Electrical and Electronic Equipment (WEEE).

2. Electrical and Electronic Waste Transportation

The problem of Electrical and Electronic Waste transportation involves the pathways involved in the collection. This research considers several e-waste collections and delivery points.

The Waste Electrical and Electronic Equipment Transportation Problem (WEEETP) can be considered a variant of the Vehicle Routing Problem with Time Windows (VRPTW), as it shares the fundamental structure of route optimisation to minimise costs and distances in the transportation of goods. However, the WEEETP introduces specific elements related to the management of electronic and hazardous waste, which differentiates it from the classical VRPTW formulations.

Unlike the VRPTW, where time constraints play a key role in route planning, the WEEETP prioritises the correct sorting and disposal of waste, ensuring that hazardous materials are treated appropriately. In addition, it incorporates multiple types of collection and processing centres, each with specific requirements depending on the type of waste transported.

Given that both issues seek to optimise transport routes under operational constraints, the WEEETP can be seen as an extension of the VRPTW adapted to the context of e-waste management, with additional considerations for safety, sorting and treatment of hazardous materials.

Although the Waste Electrical and Electronic Equipment Transportation Problem shares the fundamental structure of the Vehicle Routing Problem with Time Windows (VRPTW), the two problems differ significantly due to the inherent particularities of e-waste and hazardous waste management. While the VRPTW focuses on route optimisation with time window constraints for the delivery of goods, the WEEETP introduces additional constraints related to e-waste management, such as:

• The WEEETP deals with e-waste and hazardous waste, which require specialised transport and disposal procedures, involving additional considerations on safety, environmental regulations and risk management. These factors are not present in the classical VRPTW.
• Unlike traditional routing issues in the VRPTW, the WEEETP must address challenges such as compatibility between the type of vehicles and the nature of the waste, as well as specific staff training and compliance with environmental regulations.
• The combination of these advanced algorithms provides more robust and accurate solutions for route optimisation, with better handling of the variability of e-waste transport demands and operating conditions.
• In the WEEETP, operational costs and penalties can be linked to additional factors, such as carbon emissions or compliance with e-waste recycling and disposal regulations, adding complexity to the optimisation problem.
• Since WEEE (e-waste) transport is closely related to sustainability and environmental impact, WEEETP can incorporate sustainability objectives that are not present in traditional VRPTW, such as optimising resource use and reducing the carbon footprint.

The collection and delivery points are as follows:

• Collection Centre (CA). CA is where electronic and hazardous waste is collected. CA is the point of contact between humans and the deposit of e-waste of all kinds. There are two containers at the centre: one for computer waste and another for dangerous waste and pollutants (specifically, items considered contaminants include batteries and car batteries).
• Pick-up Centre (CS). CS is where the CA for electronic waste is received for electronics (computers, tablets, phones), appliances, and other electronic waste. These items are separated for recycling and destruction, and, if the item is dangerous, it is set aside as dangerous and polluting waste.
• Computer recycling facility (RC). RC is where computer-related waste, classified as computers, mobile phones, tablets, and laptops, is received. If these items can be reused, they are recycled. Otherwise, they are transported to waste disposal for destruction.
• Deposit of hazardous and polluting waste (RP). RP is where electronics containing circuits or highly polluting components and items that have a risk of explosion are taken.
• Deposit of waste for destruction (RD). RD is where the waste is stored to be destroyed. The items taken here involve no risk to the environment.

The Waste Electrical and Electronic Equipment Transportation Problem (WEEETP) aims to minimise and optimise times and costs of the WEEE (Equations (1)–(6)).

$$MinZ={\displaystyle \sum _{i=0}^{i=n}}{C}_{k_i}{X}_{k_i}$$

(1)

$${\displaystyle \sum _{i=0}^n}{Q}_{k_i}\ge {\displaystyle \sum _{j=1}^m}(D_{e{w}_j}+D_{h{w}_j})j=\left\{1,\dots m\right\}$$

(2)

$${\displaystyle \sum _{j=1}^m}(D_{e{w}_j}+D_{h{w}_j})\le {\displaystyle \sum _{1=0}^n}{Q}_{k_i}j=\left\{1,\dots m\right\}$$

(3)

$$\begin{array}{ll}{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{j=1}^m}\left(x_{k_i{d}_o{CA}_j}\right)& +{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{j=1}^m}\left(x_{k_i{CA}_j}\right)\\ & +{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{j=1}^m}{\displaystyle \sum _{r=1}^v}\left(x_{k_i{CA}_j{CS}_r}\right)+{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{r=1}^v}\left(x_{k_i{CS}_r}\right)\\ & +{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{r=1}^v}{\displaystyle \sum _{s=1}^z}\left(x_{k_i{CS}_r{CE}_s}\right)+{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{r=1}^v}\left(x_{k_i{CS}_r{d}_0}\right)+{\displaystyle \sum _{i=1}^n}{\displaystyle \sum _{s=1}^z}\left(x_{k_i{CE}_s{d}_0}\right)\end{array}$$

(4)

$$X=\sum _{i=1}^{i=n}\sum _{j=1}^m\left(x_{k_{i_{C{A}_j}}}\right)+\sum _{i=1}^n\sum _{j=1}^m\sum _{r=1}^z\left(x_{k_{i}C{S}_j}\right)+\left(x_{k_{i}C{S}_{j}C{E}_r}\right)+\sum _{i=1}^n\sum _{j=1}^m{x}_{k_{i}C{S}_j{d}_0}+\sum _{r=1}^z{x}_{k_{i}C{S}_{j}C{E}_r{d}_0}$$

(5)

$$t_{x_{k_i}}\le t_{tw}$$

(6)

where the variable $C_{k_i}$ corresponds to the total cost of the tour of the collection units, the variable $X_{k_i}$ corresponds to the total distance travelled per unit on the route. The variable $k$ corresponds to a vehicle that makes up the fleet of vehicles that all have the same characteristics; this is considered a homogeneous fleet. The variable $i$ corresponds to the index of each vehicle in the fleet counter. The variable $n$ corresponds to the total number of vehicles that make up the fleet. The variable $x_{k_i}$ corresponds to the route for each vehicle. The variable $Q_{k_i}$ corresponds to the capacity of each vehicle on the road. The variable $D_{waste}$ corresponds to the quantity of waste that must be collected at central collection centres. The variable $ew$ corresponds to the index that identifies the type of e-waste. The variable $hw$ corresponds to the index that identifies the type of hazardous waste.

The objective function (Equation (1)) represents the minimum cost of the transport of pollutants and electronic waste. The objective function fulfilment is subject to certain restrictions. For example, if we evaluate the capacity constraints, the demand for waste must be less than or equal to the capacity of the vehicle that will transport it. If the demand is greater than what the vehicle fleet can handle, then resources can be allocated to address a certain need. Capacity constraints allow evaluation based on the needs and the number of units available to meet the demand size required.

The capacity of vehicles (Equation (2)) should not be less than the demand of each centre. The variable $j$ corresponds to the collection centre being visited to collect waste. Demand constraints allow one to control the amount of waste that should be transported. The restriction should consider the type of waste being transported.

Equation (3) shows the restriction of the demand, where the demand for electronic waste and the demand for hazardous waste, which each centre $j$ collects, should not exceed the vehicle’s capacity $Q_{k_i}$. The variable corresponds to the demand for electronic waste collected in the collection centre $j$. The variable $D_{h{w}_j}$ corresponds to the demand for hazardous and polluting waste collected in the collection centre $j$.

The total distance travelled is modelled in Equation (4). This distance is the sum of all segments travelled by the vehicles, including those travelling to the last collection centre or, if they are for the last specialized centre, toward the depot $d_0$. Depot $d_0$ is the place from where the vehicles depart every day to meet the demand for waste and is the place to which they return after having covered all the points. The subscript represents the respective route. The variable $\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{p}\mathrm{t}$ represents the vehicle distance $i$ of the depot to the ${CA}_j$ collection centre. The variable $x_{k_{i}C{A}_j}$ represents the journey, that is, all collection centres assigned to the driver’s route. The variable $x_{k_i{CA}_j{CS}_r}$ represents the route of vehicle $i$, and the last subscript represents the centre of selection ${CS}_r$. The variable $x_{k_{i}C{S}_j}$ represents the journey undertaken by a vehicle $I$ to the selection centres assigned to its route. The variable $x_{k_i{CS}_r{CE}_s}$ represents the journey that has vehicle $i$ of the last selection centre ${CS}_r$, visiting the specialized centre ${CE}_s$ that corresponds to it. The variable $s$ represents the index of the specialized centres. The variable $CE$ represents the set of specialized centres $CE\in \{R{C}_r,R{P}_r,R{D}_r\}$. The variable $x_{k_i{CS}_r{d}_0}$ represents the last selection centre that is visited as part of travel from the depot. The variable $x_{k_i{CE}_s{d}_0}$ represents the journey from the last centre to the bin.

In Equation (5), the total distance travelled is the sum of all segments travelled by the vehicles, including the last collection centre tour or, if the vehicle is for the last specialized centre, towards the depot $d_0$. Depot $d_0$ is the place from where the vehicles depart every day to meet the demand for waste and is the place where they return after having covered all the points assigned to their route. The variable $x_{k_{i}C{A}_j}$ represents the journey of vehicle $i$ for all collection centres assigned to its route. The variable $x_{k_{i}C{S}_j}$ represents the journey undertaken by the vehicle $i$ to the selection centres assigned to its route. The variable $x_{k_{i}C{S}_{j}C{E}_r}$ represents the journey of vehicle $i$ of the last selection centre $C{S}_j$ to the corresponding specialized centre. The variable $r$ represents the index of the specialized centres. The variable $CE$ represents the set of specialized centres. The variable $x_{k_{i}C{S}_j{d}_0}$ represents the last selection centre visited. The variable $x_{k_{i}C{S}_{j}C{E}_r{d}_0}$ represents the journey of the last centre to the depot.

The time restriction that allows one to control the scheduling of each vehicle’s routes is modelled in Equation (6). This problem is considered within an 8-h time window. The variable $t_{x_{k_i}}$ represents the time that it takes the vehicle $k_i$ to conduct all the travel assigned in its route. The variable $t_{tw}$ represents the interval of time allocated to the time window $tw\in \{6hr-14hr,19hr-3hr\}$. The time restriction on the transportation used to carry the waste must not exceed the time window.

Each centre is assigned a nearest-neighbour selection centre (Figure 1). For example, if some nodes are near a selection centre, the driver is assigned the number of the nearest selection centre. If there is no demand for the selection centres, and if the waste has previously been collected at all the collection centres, the vehicles will return to the last centre before returning to the depot. The total journey will be the sum of the travel from the warehouse, through the last collection route, to the depot.

Where selection centres require it, specialised collection centres are used. After visiting all the collection centres, vehicles are then loaded again on other routes to service the selection centres and deliver the loads to the specialised centres. The total tour in this situation is the sum of all warehouse travel collection routes, additional tours of the screening centres and specialized returns to the depot.

Theorem 1.

Waste Electrical and Electronic Equipment Transportation Problem (WEEETP) is NP-Hard.

Proof of Theorem 1.

This problem is NP-Hard by polynomial-time transformation into the Vehicle Routing Problem (VRP). □

The Polynomial transformations are used for proving that a problem is NP-complete or NP-Hard based on the different approaches [33]: using the theory of NP-completeness, using graph theory, and using formal language theory [34]. The use of the theory of formal languages in polynomial transformations consists [34]: (a) Lexical analysis recognises and convert the character stream from the input source program or sequence of characters to valid words of the language or tokens, (b) Syntactic analysis considers the sequence of tokens for possible valid constructs of the language, (c) Semantic analysis: determine the meaning of the language, (d) Error handling: detect the lexical, syntactic, semantic, and logical errors, and (e) Language generation: generate the target code or the target language. The steps for polynomial transformation using formal language theory are:

• Select an NP-complete problem A (WEEETP).
• Define a formal language L1 for the NP-complete problem A. We define the language: L1 = {I, TW, F, V, C, D, DC₁, La₁, Lo₁, De₁, RT₁, DT₁, ST₁, …, DCₙ, Laₙ, Loₙ, Deₙ, RTₙ, DTₙ, STₙ}. Here, I denotes the instance name (e.g., EWasteXX.txt), TW the time window, F the fleet type (homogeneous or heterogeneous), V the number of vehicles, C the capacity, and D the demand. Each distribution centre DCᵢ is associated with its latitude Laᵢ and longitude Loᵢ, a client demand Deᵢ, a ready time RTᵢ, a due time DTᵢ, and a service time STᵢ. The alphabet is defined as: Σ = {0,1,2,3,4,5,6,7,8,9,{,},.,;,=,-,E,W,T}. The admissible syntax of the instances is then specified by the following BNF grammar:
  <instance> ::= <NameProblem> <Equal> <Sentences> ;
  <Sentences> ::= <KOpen> <TNum> <Semicolon> <NumList> <Semicolon> <NumCap> <KClose> ;
  <TNum> ::= <Num> ;
  <NumCap> ::= <Num> ;
  <NumList> ::= <Num> | <NumList> <Comma> <Num> ;
  <Num> ::= <Integer> | <Decimal> ;
  <Integer> ::= <Digit> | <Integer> <Digit> ;
  <Decimal> ::= <Integer> <Dot> <Integer> |
             <Negative> <Integer> <Dot> <Integer> |
             <Integer> <Dot> |
             <Dot> <Integer> ;
  <Digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ;
  <NameProblem> ::= 'EWT' ;
  <Equal> ::= '=' ;
  <KOpen> ::= '{' ;
  <KClose> ::= '}' ;
  <Semicolon> ::= ';' ;
  <Comma> ::= ',' ;
  <Negative> ::= '-' ;
  <Dot> ::= '.' ;
• Select an NP-complete problem B (VRP).
• Define a formal language L2 for the NP-complete problem B. We define the language: L2 = { VN, C, ( CN₁, XCO₁, YCO₁, D₁, RT₁, DT₁, ST₁, …, CN_z, XCO_z, YCO_z, D_z, RT_z, DT_z, ST_z ) }. Here, VN denotes the Vehicle Number, C the Capacity, CN the Customer Number, XCO the X coordinate, YCO the Y coordinate, D the Demand, RT the Ready Time, DT the Due Date, and ST the Service Time. The alphabet is defined as: Σ = {0,1,2,3,4,5,6,7,8,9,{,},,,;,=,.,V,R,P}. The admissible syntax of the instances is then specified by the following BNF grammar:
  <instance> ::= <NameProblem> <Equal> <Sentences> ;
  <Sentences> ::= <KOpen> <TNum> <Semicolon> <NumList> <Semicolon> <NumCap> <KClose> ;
  <TNum> ::= <Num> ;
  <NumCap> ::= <Num> ;
  <NumList> ::= <Num> | <NumList> <Comma> <Num> ;
  <Num> ::= <Integer> | <Decimal> ;
  <Integer> ::= <Digit> | <Integer> <Digit> ;
  <Decimal> ::= <Integer> <Dot> <Integer> |
             <Negative> <Integer> <Dot> <Integer> |
             <Integer> <Dot> |
             <Dot> <Integer> ;
  <Digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ;
  <NameProblem> ::= 'VRP' ;
  <Equal> ::= '=' ;
  <KOpen> ::= '{' ;
  <KClose> ::= '}' ;
  <Semicolon> ::= ';' ;
  <Comma> ::= ',' ;
  <Negative> ::= '-' ;
  <Dot> ::= '.' ;
• Construct a compiler that transforms in polynomial time a source language $L_1$into a target language $L_2(L_1\le L_2)$. In the lexical analysis phase of the compiler, a source language $L_1$ is transformed into tokens. The next information shows the token declaration for the GNU Flex software used in the lexical phase.

  /* ---------- Definitions ---------- */ A [aA] B [bB] C [cC] D [dD] E [eE] F [fF] G [gG] H [hH] I [iI] J [jJ] K [kK] L [lL] M [mM] N [nN] O [oO] P [pP] Q [qQ] R [rR] S [sS] T [tT] U [uU] V [vV] W [wW] X [xX] Y [yY] Z [zZ] Digit [0-9] /* ------------- Rules ------------- */ "=" {return EQUAL;} "," {return COMMA;} ";" {return SEMICOLON;} "\." {return DOT;} "\{" {return KOPEN;} "\}" {return KCLOSE;} {DIGIT}+ {return DIGSEQ;} /* Ignore any other single character */ . {/* ignore */}

In the syntax analysis phase, tokens from the source language $L_1$ are grouped into grammatical phrases. In the semantic analysis phase, semantic errors (error handling) of the polynomial transformation from $L_1$ to $L_2$ are detected. During semantic analysis, the restrictions are verified to ensure that a formal language $L_2$ (instance) to be obtained for VRP is obtained. Finally, the $L_1$ is transformed into $L_2(L_1\le L_2)$ that is, (WEEETP ≤ _PVRP). Hence, through the polynomial transformation of WEEETP instances into VRP instances, we conclude that the Waste Electrical and Electronic Equipment Transportation Problem $\left(\mathrm{W}\mathrm{E}\mathrm{E}\mathrm{E}\mathrm{T}\mathrm{P}\right)$ is NP-Hard.

We define a BNF grammar for the instance language $L_1$ to guarantee an unambiguous, automatable, and reproducible specification of WEEETP inputs. The grammar enables formal validation of instances via parsing; alignment with the lexical–syntactic–semantic pipeline employed in the NP-hardness discussion; and seamless generation of benchmark instances and ingestion by our solvers.

3. Results and Discussion

For the experimentation, we evaluated the collection of e-waste, specifically disused mobile phones, in the city of Pachuca, Hgo., and certain surrounding areas. This e-waste was destined for the recycling company REMSA which is located in the city of Querétaro, Qro., Mexico. Each experimental instance was conducted satisfactorily using the information shown in

Table 2. WEETP instances.

I	TW
F	V	C	D
DC	La	Lo	De	RT	DT	ST
0	La0	Lo0	De0	RT0	DT0	ST0
…	…	…	…	…	…	…
30	Lan	Lon	Den	RTn	DTn	STn

Where $I:$ Instance name (EWasteXX.txt), $TW:$ Time Window, $F:$ Fleet (Homogeneous, Heterogeneous), $V:$ Number of Vehicles, $C:$Capacity, $D:$ Demand, $DC:$ Distribution Centre (client), $La:$ Latitude, $Lo:$ Longitude, $De:$ Demand of clients, $Ve:$ Vehicle, $RT:$ Ready Time, $DT:$ Due Time, and $ST:$ Service Time.

.

The $\mathrm{W}\mathrm{E}\mathrm{E}\mathrm{E}\mathrm{T}\mathrm{P}$ (

Table 3. WEEETP instance.

-Waste-01–30.txt
Fleet	Num vehicles	Capacity (kg)	Demand (kg)
H	20	3000	60,000
Collection Center				Minutes
Num	Latitude	Longitude	Demand CA (kg)	Ready Time	Due Time	Service Time
1	20.752829	−100.449832	0	420	1050	0
2	20.030209	−98.841938	1767	540	1260	45
3	20.059819	−98.767274	586	660	1260	45
4	20.122984	−98.735402	2282	660	1260	45
5	20.098306	−98.767937	36	660	1260	45
6	20.096825	−98.76164	2655	660	1260	45
7	20.128219	−98.731907	340	600	1260	45
8	20.053558	−98.779779	2699	540	1260	45
9	20.057846	−98.776151	1127	660	1140	45
10	20.063298	−98.778091	1794	660	1260	45
11	20.060236	−98.769966	1887	660	1260	45
12	20.118674	−98.742286	627	660	1260	45
13	20.127274	−98.733103	1909	660	1260	45
14	20.128209	−98.731896	661	660	1260	45
15	20.129303	−98.732076	1434	660	1260	45
16	20.128876	−98.730544	2743	660	1260	45
17	20.124761	−98.730271	1332	660	1260	45
18	20.093422	−98.759056	307	660	1140	45
19	20.114379	−98.749249	1391	600	1260	45
20	20.081224	−98.728593	2639	660	1260	45
21	20.111087	−98.760279	1286	480	1260	45
22	20.053548	−98.779768	2737	540	1260	45
23	20.055045	−98.782607	2973	600	1260	45
24	20.126574	−98.731184	1700	660	1260	45
25	20.098138	−98.768129	1142	660	1260	45
26	19.364115	−99.048609	2237	660	1260	45
27	20.752829	−100.449832	1008	660	1260	45
28	19.361424	−99.196768	2439	660	1260	45
29	19.353929	−99.114616	1144	660	1260	45
30	19.34967	−99.159222	652	660	1260	45

) instance includes a recycling company (REMSA), which is located in Querétaro City, and mobile phone stores that receive cellphones that are no longer used. Most of the stores are located in Pachuca, Hidalgo, and Mexico City (see Figure 2).

For the experiments, the following population-based algorithms were used: Genetic Algorithm (GA), Offspring Selection Genetic Algorithm (OSGA), Evolution Strategy (ES), and Offspring Selection Evolution Strategy (OSES). Although other metaheuristics such as Particle Swarm Optimisation (PSO) or Simulated Annealing (SA) are widely used, they are better suited for continuous optimisation problems. Since the WEEETP is a discrete, permutation-based routing problem, evolutionary algorithms (GA, OSGA, ES, OSES) were selected due to their effectiveness in exploring combinatorial solution spaces with capacity and time-window constraints.

The Genetic Algorithm was created by Holland in 1975. This algorithm considers a population of individuals called chromosomes that represent possible problem solutions [35]. The algorithm applies a crossover to all chromosomes; these are then mutated, creating a new generation. GA considers a crossover as its main reproduction operator [36]. In accordance with [35], the canonical Genetic Algorithm works in the following manner:

Set t = 0. The population P (0) is initialized at random. The chromosomes of the population P (t) are evaluated using the fitness function, and the algorithm retains the most successful individual. The selected chromosomes make up an intermediate population P1, representing candidates for the mating pool. The crossover is applied to the chromosomes from the mating pool and to obtain the new population P2. The mutation operator is applied to the population P2. The outcome is the new generation P(t + 1). Set t = t + 1, if t < M, where M is the maximum number of generations, then go to step 2. Otherwise, stop.

The GA parameters used in this work are: Analyser (MultiAnalyser), Crossover (Biased MultiVRP Solution Crossover), Elites (1), Maximum Generations (1000), Mutation probability (5%), mutator (Alba Customer Swap Manipulator), population size (50), Seed (0), Selector (ProportionalSelector), Set Seed Randomly (True).

The Offspring Selection Genetic Algorithm—OSGA [37] has a basis in GA but considers a second selection step after reproduction, which is absolutely problem independent. This selection mechanism compares the fitness value of the offspring with the fitness value of its parents to accept the members of the next generation. The algorithm’s description is shown in the following code.

Set $t=0$. The population $P\left(0\right)$ is initialised at random. The chromosomes of the population $P\left(t\right)$ are evaluated using the fitness function, and it retains the most successful individual. The selected chromosomes comprise an intermediate population $P^1$, representing candidates for the mating pool. The crossover is applied to the chromosomes from the mating pool and obtain the new population $P^2$. The mutation operator is applied to the population $P^2$, producing(POP). Evaluate the offspring success: child’s fitness value better than a worse parent. Calculate the percentage of next population members that have successful mating of the total population size: $SuccRatio\in [0,1]$ Complete the population with individuals randomly chosen from the pool of individuals that were also created by crossover but did not achieve the success criterion. $(\left(1-SuccRatio\right)·|POP\left|\right)$ Calculate Actual selection pressure: $ActSelPress={\displaystyle \frac{\left|{POP}_{i+1}\right|+\left|POOL\right|}{\left|POP\right|}}$ Detect if premature convergence has occurred with: $MaxSelPress<ActSelPress$ Set $t=(t+1)$, if $t<M$, where $M$ is the maximum number of generations, then go to step 2. Otherwise, stop.

The OSGA parameters used in this work are Analyser (MultiAnalyser), Comparison Factor Lower Bound(0), Comparison Factor Modifier (Linear Discrete Double Value Modifier), Comparison Factor UpperBound(1), Crossover(Alba Permutation Crossover), Elites(1), Maximum Generations(1000), Maximum Selection Pressure(100), Mutation Probability(5%), Mutator(Alba Customer Insertion Manipulator), Offspring Selection Before Mutation(False), Population Size(100), Seed(0), Selected Parents(200), Selector(Gender Specific Selection), Set Seed Randomly (True), Success Ratio (1).

The method (Evolution Strategy—ES) solves difficult and real-valued parameter optimisation problems through the self-adaptation of the strategy parameters, such as the standard deviation of the mutation amplitude [35]. This method considers that each individual is defined by the following: a set of variables, a set of mutations and a set of rotation angles. The population is made up of $\mu$ individuals. The algorithm description is as follows [38].

The object variables are initialized at random; strategy variables get a value of 3.0, and the rotation angles get a random value between $-\pi$ and $\pi$. The initial $population=f\left(\right)$ for each individual. Obtain descendants using the recombination operator in the current parent's population. Mutate every descendant. Choose a new population and reorder the set of parents with the set of descendants. Continue with step 3, until termination criteria: $t\left(P\right(t\left)\right)$.

The ES parameters used in this work are Analyser (MultiAnalyser), Children (100), Maximum Generations (1000), Mutator (Multi VRP Solution Manipulator), Parents Per Child (2), Plus Selection (True), Population Size (20), Recombinator (Biased Multi VRP Solution Crossover), Seed (0), Set Seed Randomly (True), Strategy Parameter Creator (Null), Strategy Parameter Crossover (Null), Strategy Parameter Manipulator(Null).

For the Offspring Selection Evolution Strategy (OSES), aspects of evolutionary strategies were combined with selection concepts, where it is observed that the selection of offspring operates well in combination with genetic programming [39].

The object variables are initialized at random; strategy variables get a value of 3.0, and rotation angles get at a random value between $-\pi$ and $\pi$. The initial $population=f\left(\right)$ for each individual. Obtain descendants using the recombination operator in the current parent population. Mutate every descendant. Evaluate the offspring success: child’s fitness value better than a worse parent. Calculate the percentage of the next population members that have successful mating of the total population size: $SuccRatio\in [0,1]$ Complete the population with individuals randomly chosen from the pool of individuals who were also created by crossover but did not achieve the success criterion. $(\left(1-SuccRatio\right)·|POP\left|\right)$ Calculate Actual selection pressure: $ActSelPress={\displaystyle \frac{\left|{POP}_{i+1}\right|+\left|POOL\right|}{\left|POP\right|}}$ Detect if a premature convergence has occurred with: $MaxSelPress<ActSelPress$ Choose a new population and reorder the set of parents with the set of descendants. Continue with step 3, until termination criteria: $t\left(P\right(t\left)\right)$.

The OSES parameters used in this work are Analyser (MultiAnalyser), Comparison Factor(0.5), Maximum Generations(1000), Maximum Selection Pressure (100), Mutator (Multi VRP Solution Manipulator), Parents Per Child (2), Plus Selection (True), Population Size (20), Recombinator(Multi VRP Solution Crossover), Seed (0), Selected Parents (40), Set Seed Randomly (True), Strategy Parameter Creator (Null), Strategy Parameter Crossover (Null), Strategy Parameter Manipulator (Null), Success Ratio (1).

The EW1 instance was selected as a representative case study due to its realistic scale and geographical configuration. This instance corresponds to the actual transportation scenario between Pachuca (collection points) and Querétaro (REMSA recycling facility), with a medium-sized network of 30 nodes and heterogeneous demand patterns. Unlike smaller instances (EW2–EW5), EW1 includes realistic constraints such as service times, heterogeneous demand levels, and a sufficient number of routes to challenge the optimisation algorithms. At the same time, it is not as large as the higher-numbered instances, which allows for clearer visualisation and validation of algorithmic behaviour. For these reasons, EW1 was used as the baseline experimental case, while additional instances (EW2–EW92) were employed for comparative evaluation and robustness testing.

We also performed the test in the instance repository with 100 cases; the five algorithms with 33 runs evaluated these for each, obtaining the results shown in

Table 4. Results of the GA, OSGA, ES and OSES algorithms.

Instance	GA	OSGA	ES	OSES
EW1	Dist: 62.507566 #Veh: 17 Time: 01:16.3	Dist: 62.570756 #Veh: 17 Time: 02:08.7	Dist: 62.507566 #Veh: 17 Time: 00:04.0	Dist: 62.507566 #Veh: 17 Time: 02:16.2
EW2	Dist: 27.568182 #Veh: 18 Time: 01:13.2	Dist: 27.568182 #Veh: 18 Time: 02:37.5	Dist: 27.568182 #Veh: 18 Time: 00:30.6	Dist: 27.568182 #Veh: 18 Time: 01:04.2
EW3	Dist: 27.221213 #Veh: 20 Time: 00:53.6	Dist: 27.221213 #Veh: 20 Time: 02:02.0	Dist: 27.221213 #Veh: 20 Time: 00:10.9	Dist: 28.79063 #Veh: 20 Time: 00:59.7
EW4	Dist: 37.232173 #Veh: 15 Time: 01:17.4	Dist: 37.218797 #Veh: 15 Time: 03:01.8	Dist: 37.218797 #Veh: 15 Time: 00:10.4	Dist: 37.384005 #Veh: 15 Time: 01:11.5
EW5	Dist: 27.568182 #Veh: 18 Time: 01:23.1	Dist: 27.568182 #Veh: 18 Time: 02:55.2	Dist: 27.568182 #Veh: 18 Time: 00:22.1	Dist: 27.623549 #Veh: 18 Time: 01:08.0
EW6	Dist: 43.595797 #Veh: 17 Time: 01:27.1	Dist: 43.595797 #Veh: 17 Time: 06:36.3	Dist: 43.595797 #Veh: 17 Time: 00:16.3	Dist: 44.852987 #Veh: 16 Time: 02:30.7
EW7	Dist: 24.40535 #Veh: 16 Time: 00:31.0	Dist: 24.402844 #Veh: 16 Time: 04:32.4	Dist: 24.402844 #Veh: 16 Time: 00:23.5	Dist: 24.444569 #Veh: 16 Time: 02:23.7
EW8	Dist: 28.514534 #Veh: 17 Time: 01:26.3	Dist: 28.504195 #Veh: 17 Time: 03:12.9	Dist: 28.504195 #Veh: 17 Time: 00:20.0	Dist: 29.039056 #Veh: 17 Time: 02:54.8
EW9	Dist: 35.653599 #Veh: 14 Time: 01:06.6	Dist: 34.879333 #Veh: 14 Time: 04:32.5	Dist: 34.915125 #Veh: 14 Time: 00:10.9	Dist: 35.870247 #Veh: 14 Time: 01:28.1
EW10	Dist: 34.612012 #Veh: 16 Time: 01:23.3	Dist: 34.612012 #Veh: 16 Time: 02:55.2	Dist: 34.612012 #Veh: 16 Time: 00:12.5	Dist: 34.612012 #Veh: 16 Time: 01:08.4
EW11	Dist: 39.267533 #Veh: 18 Time: 00:46.0	Dist: 39.267533 #Veh: 18 Time: 03:24.6	Dist: 39.267533 #Veh: 18 Time: 00:07.5	Dist: 39.267533 #Veh: 18 Time: 00:36.3
EW12	Dist: 26.677795 #Veh: 18 Time: 00:54.7	Dist: 26.677795 #Veh: 18 Time: 02:37.6	Dist: 26.677795 #Veh: 18 Time: 00:14.6	Dist: 26.677795 #Veh: 18 Time: 02:10.6
EW13	Dist: 21.651024 #Veh: 12 Time: 00:51.5	Dist: 21.651024 #Veh: 12 Time: 01:05.3	Dist: 21.651024 #Veh: 12 Time: 00:13.7	Dist: 21.651024 #Veh: 12 Time: 00:39.8
EW14	Dist: 22.620359 #Veh: 13 Time: 01:00.7	Dist: 22.620359 #Veh: 13 Time: 03:01.2	Dist: 22.620359 #Veh: 13 Time: 00:10.4	Dist: 22.836019 #Veh: 14 Time: 00:48.6
EW15	Dist: 33.614401 #Veh: 18 Time: 00:40.4	Dist: 33.614401 #Veh: 18 Time: 02:12.5	Dist: 33.614401 #Veh: 18 Time: 00:06.8	Dist: 33.614401 #Veh: 18 Time: 00:44.0
EW16	Dist: 32.712498 #Veh: 17 Time: 00:32.7	Dist: 32.712498 #Veh: 17 Time: 00:51.3	Dist: 32.712498 #Veh: 17 Time: 00:09.6	Dist: 32.960182 #Veh: 17 Time: 01:07.9
EW17	Dist: 25.897119 #Veh: 16 Time: 00:56.4	Dist: 25.897119 #Veh: 16 Time: 03:13.7	Dist: 25.897119 #Veh: 16 Time: 00:11.7	Dist: 25.897119 #Veh: 16 Time: 01:14.9
EW18	Dist: 32.955567 #Veh: 14 Time: 01:11.7	Dist: 32.839482 #Veh: 14 Time: 01:50.9	Dist: 32.843833 #Veh: 14 Time: 00:16.9	Dist: 32.843833 #Veh: 14 Time: 01:22.7
EW19	Dist: 27.182308 #Veh: 15 Time: 00:39.9	Dist: 27.182308 #Veh: 15 Time: 03:23.0	Dist: 27.182308 #Veh: 15 Time: 00:17.0	Dist: 27.182308 #Veh: 15 Time: 01:22.3
EW20	Dist: 35.230723 #Veh: 15 Time: 01:15.3	Dist: 35.137462 #Veh: 15 Time: 02:20.6	Dist: 35.137462 #Veh: 15 Time: 00:10.2	Dist: 35.322731 #Veh: 15 Time: 01:43.9
EW21	Dist: 26.886448 #Veh: 19 Time: 01:26.2	Dist: 26.886448 #Veh: 19 Time: 03:58.1	Dist: 26.886448 #Veh: 19 Time: 00:07.6	Dist: 26.886448 #Veh: 19 Time: 01:24.4
EW22	Dist: 49.262455 #Veh: 17 Time: 01:06.4	Dist: 49.262455 #Veh: 17 Time: 03:53.3	Dist: 49.262455 #Veh: 17 Time: 00:09.1	Dist: 51.985491 #Veh: 18 Time: 01:13.1
EW23	Dist: 31.838255 #Veh: 19 Time: 01:10.2	Dist: 31.838255 #Veh: 19 Time: 04:12.4	Dist: 31.838255 #Veh: 19 Time: 00:21.9	Dist: 31.838255 #Veh: 19 Time: 01:32.1
EW24	Dist: 27.803411 #Veh: 15 Time: 01:08.8	Dist: 27.803411 #Veh: 15 Time: 03:18.2	Dist: 27.803411 #Veh: 15 Time: 00:10.5	Dist: 27.829163 #Veh: 15 Time: 01:45.8
EW25	Dist: 28.371217 #Veh: 20 Time: 00:49.5	Dist: 27.931706 #Veh: 19 Time: 03:47.5	Dist: 27.931706 #Veh: 19 Time: 00:20.7	Dist: 30.352478 #Veh: 20 Time: 00:47.7
EW26	Dist: 40.907654 #Veh: 20 Time: 01:18.8	Dist: 45.121866 #Veh: 20 Time: 04:05.4	Dist: 43.831705 #Veh: 20 Time: 00:15.4	Dist: 45.894011 #Veh: 20 Time: 00:47.6
EW27	Dist: 38.999202 #Veh: 17 Time: 00:53.6	Dist: 38.999202 #Veh: 17 Time: 03:23.2	Dist: 38.999202 #Veh: 20 Time: 00:12.0	Dist: 39.056672 #Veh: 17 Time: 01:22.9
EW28	Dist: 30.085323 #Veh: 17 Time: 01:23.3	Dist: 30.085323 #Veh: 17 Time: 03:36.2	Dist: 30.085323 #Veh: 17 Time: 00:12.2	Dist: 30.490975 #Veh: 17 Time: 01:41.1
EW29	Dist: 30.866102 #Veh: 20 Time: 01:40.5	Dist: 32.604814 #Veh: 20 Time: 01:29.6	Dist: 32.050868 #Veh: 20 Time: 00:14.7	Dist: 34.180135 #Veh: 20 Time: 01:39.3
EW30	Dist: 32.342994 #Veh: 20 Time: 01:14.3	Dist: 33.3571 #Veh: 20 Time: 04:15.8	Dist: 33.404621 #Veh: 20 Time: 00:12.2	Dist: 33.942188 #Veh: 20 Time: 01:18.9
EW31	Dist: 25.785707 #Veh: 19 Time: 01:19.2	Dist: 25.785707 #Veh: 19 Time: 04:48.1	Dist: 25.785707 #Veh: 19 Time: 00:10.7	Dist: 25.813241 #Veh: 19 Time: 02:18.1
EW32	Dist: 29.74987 #Veh: 16 Time: 01:19.2	Dist: 29.74987 #Veh: 16 Time: 02:34.9	Dist: 29.74987 #Veh: 16 Time: 00:12.8	Dist: 29.757853 #Veh: 16 Time: 01:31.4
EW33	Dist: 27.507111 #Veh: 16 Time: 01:26.5	Dist: 27.506717 #Veh: 16 Time: 03:45.5	Dist: 27.506717 #Veh: 16 Time: 00:15.7	Dist: 27.630505 #Veh: 16 Time: 01:17.1
EW34	Dist: 31.186599 #Veh: 16 Time: 00:39.3	Dist: 31.186599 #Veh: 16 Time: 03:43.6	Dist: 31.186599 #Veh: 16 Time: 00:11.1	Dist: 32.010692 #Veh: 16 Time: 02:49.2
EW35	Dist: 38.392616 #Veh: 20 Time: 00:52.8	Dist: 37.482973 #Veh: 18 Time: 03:44.2	Dist: 37.520155 #Veh: 18 Time: 00:34.3	Dist: 38.145798 #Veh: 19 Time: 00:46.5
EW36	Dist: 46.11107 #Veh: 20 Time: 00:52.7	Dist: 46.11107 #Veh: 20 Time: 04:14.4	Dist: 46.11107 #Veh: 20 Time: 00:08.7	Dist: 46.138714 #Veh: 20 Time: 01:02.2
EW37	Dist: 39.719761 #Veh: 17 Time: 01:10.4	Dist: 39.719761 #Veh: 17 Time: 04:00.2	Dist: 39.719761 #Veh: 17 Time: 00:06.4	Dist: 39.956847 #Veh: 17 Time: 02:19.9
EW38	Dist: 41.203126 #Veh: 19 Time: 01:38.9	Dist: 41.203126 #Veh: 19 Time: 04:22.8	Dist: 41.203126 #Veh: 19 Time: 00:14.8	Dist: 38.067569 #Veh: 18 Time: 04:02.3
EW39	Dist: 25.678597 #Veh: 18 Time: 01:18.9	Dist: 25.678597 #Veh: 18 Time: 04:12.3	Dist: 25.678597 #Veh: 18 Time: 00:21.4	Dist: 25.678597 #Veh: 18 Time: 01:15.3
EW40	Dist: 30.216749 #Veh: 17 Time: 00:31.4	Dist: 30.216749 #Veh: 17 Time: 05:21.5	Dist: 30.216749 #Veh: 17 Time: 00:08.2	Dist: 31.927701 #Veh: 18 Time: 01:20.1
EW41	Dist: 23.42494 #Veh: 19 Time: 01:05.2	Dist: 22.922326 #Veh: 19 Time: 04:30.3	Dist: 22.922326 #Veh: 19 Time: 00:04.8	Dist: 23.485707 #Veh: 19 Time: 01:05.7
EW42	Dist: 21.248344 #Veh: 15 Time: 01:16.3	Dist: 21.248344 #Veh: 15 Time: 04:50.9	Dist: 21.248344 #Veh: 15 Time: 00:07.3	Dist: 21.248344 #Veh: 15 Time: 01:30.5
EW43	Dist: 33.226438 #Veh: 20 Time: 01:16.3	Dist: 33.516193 #Veh: 20 Time: 05:49.4	Dist: 33.516193 #Veh: 20 Time: 00:19.5	Dist: 33.609933 #Veh: 20 Time: 02:16.8
EW44	Dist: 34.532568 #Veh: 18 Time: 01:08.4	Dist: 34.532568 #Veh: 18 Time: 03:36.2	Dist: 34.532568 #Veh: 18 Time: 00:09.3	Dist: 35.778809 #Veh: 18 Time: 02:48.1
EW45	Dist: 43.559444 #Veh: 20 Time: 01:08.8	Dist: 44.856488 #Veh: 20 Time: 02:00.6	Dist: 43.871232 #Veh: 20 Time: 00:10.2	Dist: 44.289528 #Veh: 20 Time: 00:50.2
EW46	Dist: 39.714587 #Veh: 20 Time: 00:29.8	Dist: 42.824911 #Veh: 20 Time: 03:55.9	Dist: 41.947592 #Veh: 20 Time: 00:23.6	Dist: 42.891392 #Veh: 20 Time: 00:35.0
EW47	Dist: 24.357285 #Veh: 14 Time: 00:34.0	Dist: 24.357285 #Veh: 14 Time: 04:26.5	Dist: 24.357285 #Veh: 14 Time: 00:09.7	Dist: 24.578766 #Veh: 15 Time: 00:56.6
EW48	Dist: 39.650017 #Veh: 19 Time: 00:58.9	Dist: 39.650017 #Veh: 19 Time: 06:55.6	Dist: 39.650017 #Veh: 19 Time: 00:10.6	Dist: 39.650017 #Veh: 19 Time: 01:22.5
EW49	Dist: 31.271915 #Veh: 15 Time: 00:56.3	Dist: 31.271915 #Veh: 15 Time: 03:46.2	Dist: 31.271915 #Veh: 15 Time: 00:14.2	Dist: 32.360006 #Veh: 15 Time: 02:56.9
EW50	Dist: 29.333133 #Veh: 16 Time: 01:25.1	Dist: 29.333133 #Veh: 16 Time: 03:54.7	Dist: 29.333133 #Veh: 16 Time: 00:11.8	Dist: 29.333133 #Veh: 16 Time: 01:48.8
EW51	Dist: 44.97789 #Veh: 20 Time: 00:29.6	Dist: 44.663648 #Veh: 20 Time: 04:31.9	Dist: 44.742312 #Veh: 20 Time: 00:10.9	Dist: 44.205225 #Veh: 20 Time: 00:46.5
EW52	Dist: 33.476677 #Veh: 17 Time: 01:16.7	Dist: 33.476677 #Veh: 17 Time: 03:42.1	Dist: 33.476677 #Veh: 17 Time: 00:08.0	Dist: 37.103782 #Veh: 19 Time: 02:12.8
EW53	Dist: 39.751805 #Veh: 19 Time: 01:28.0	Dist: 39.751805 #Veh: 19 Time: 04:29.6	Dist: 39.751805 #Veh: 19 Time: 00:08.7	Dist: 39.84094 #Veh: 19 Time: 01:38.6
EW54	Dist: 23.658023 #Veh: 17 Time: 01:19.7	Dist: 23.658023 #Veh: 17 Time: 03:16.8	Dist: 23.658023 #Veh: 17 Time: 00:16.4	Dist: 23.658023 #Veh: 17 Time: 01:29.0
EW55	Dist: 25.351151 #Veh: 18 Time: 01:29.4	Dist: 25.351151 #Veh: 18 Time: 06:39.9	Dist: 25.351151 #Veh: 18 Time: 00:19.5	Dist: 26.247055 #Veh: 18 Time: 02:00.7
EW56	Dist: 41.992446 #Veh: 18 Time: 00:54.5	Dist: 41.992446 #Veh: 18 Time: 02:12.4	Dist: 41.992446 #Veh: 18 Time: 00:14.4	Dist: 42.239238 #Veh: 18 Time: 01:25.0
EW57	Dist: 31.779488 #Veh: 16 Time: 00:57.3	Dist: 31.779488 #Veh: 16 Time: 04:14.5	Dist: 31.779488 #Veh: 16 Time: 00:12.3	Dist: 31.836395 #Veh: 16 Time: 00:53.2
EW58	Dist: 31.209647 #Veh: 18 Time: 00:45.0	Dist: 31.209647 #Veh: 18 Time: 04:01.9	Dist: 31.209647 #Veh: 18 Time: 00:11.7	Dist: 31.27764 #Veh: 19 Time: 02:00.7
EW59	Dist: 35.510156 #Veh: 15 Time: 00:53.9	Dist: 35.487279 #Veh: 15 Time: 03:17.7	Dist: 35.338287 #Veh: 15 Time: 00:18.7	Dist: 35.72326 #Veh: 15 Time: 01:20.3
EW60	Dist: 27.626122 #Veh: 17 Time: 01:30.7	Dist: 27.626122 #Veh: 17 Time: 04:15.8	Dist: 27.626122 #Veh: 17 Time: 00:09.4	Dist: 27.626122 #Veh: 17 Time: 01:41.2
EW61	Dist: 35.236308 #Veh: 15 Time: 01:35.4	Dist: 35.226466 #Veh: 15 Time: 03:20.8	Dist: 20.155375 #Veh: 18 Time: 00:37.3	Dist: 36.082496 #Veh: 15 Time: 03:18.8
EW62	Dist: 36.276229 #Veh: 17 Time: 01:22.2	Dist: 36.276229 #Veh: 17 Time: 05:00.1	Dist: 36.276229 #Veh: 17 Time: 00:15.9	Dist: 36.455822 #Veh: 17 Time: 02:48.8
EW63	Dist: 25.506982 #Veh: 16 Time: 00:56.7	Dist: 25.506982 #Veh: 16 Time: 04:02.1	Dist: 25.506982 #Veh: 16 Time: 00:09.1	Dist: 30.937439 #Veh: 19 Time: 00:55.4
EW64	Dist: 38.322254 #Veh: 18 Time: 00:53.2	Dist: 38.322254 #Veh: 18 Time: 04:29.5	Dist: 38.322254 #Veh: 18 Time: 00:05.9	Dist: 38.322254 #Veh: 18 Time: 01:32.8
EW65	Dist: 39.207524 #Veh: 18 Time: 01:04.7	Dist: 39.207524 #Veh: 18 Time: 03:49.8	Dist: 39.207524 #Veh: 18 Time: 00:08.5	Dist: 39.207524 #Veh: 18 Time: 01:08.2
EW66	Dist: 33.307968 #Veh: 15 Time: 00:53.1	Dist: 32.981886 #Veh: 15 Time: 03:35.0	Dist: 33.010055 #Veh: 15 Time: 00:09.9	Dist: 33.499264 #Veh: 15 Time: 00:43.2
EW67	Dist: 24.604106 #Veh: 17 Time: 01:06.7	Dist: 24.604106 #Veh: 17 Time: 04:40.6	Dist: 24.604106 #Veh: 17 Time: 00:13.5	Dist: 24.833096 #Veh: 17 Time: 01:22.8
EW68	Dist: 26.89195 #Veh: 17 Time: 01:24.0	Dist: 26.89195 #Veh: 17 Time: 03:49.9	Dist: 33.928705 #Veh: 20 Time: 00:19.8	Dist: 26.89195 #Veh: 17 Time: 02:34.9
EW69	Dist: 41.204193 #Veh: 20 Time: 01:10.9	Dist: 43.541014 #Veh: 20 Time: 03:55.7	Dist: 42.677632 #Veh: 20 Time: 00:16.2	Dist: 41.525479 #Veh: 20 Time: 00:54.0
EW70	Dist: 28.843037 #Veh: 14 Time: 01:34.8	Dist: 28.843037 #Veh: 13 Time: 03:27.8	Dist: 28.843037 #Veh: 13 Time: 00:27.1	Dist: 29.31832 #Veh: 14 Time: 00:49.8
EW71	Dist: 24.288568 #Veh: 18 Time: 00:32.8	Dist: 24.288568 #Veh: 18 Time: 04:33.2	Dist: 24.288568 #Veh: 18 Time: 00:07.9	Dist: 24.288568 #Veh: 18 Time: 00:35.1
EW72	Dist: 29.26674 #Veh: 16 Time: 01:37.4	Dist: 29.26674 #Veh: 16 Time: 03:36.1	Dist: 29.26674 #Veh: 16 Time: 00:06.5	Dist: 29.543764 #Veh: 16 Time: 00:37.2
EW73	Dist: 26.340479 #Veh: 16 Time: 01:27.8	Dist: 26.340479 #Veh: 16 Time: 03:44.5	Dist: 26.340479 #Veh: 16 Time: 00:14.3	Dist: 26.996283 #Veh: 17 Time: 01:40.2
EW74	Dist: 29.006756 #Veh: 16 Time: 01:05.8	Dist: 28.943446 #Veh: 16 Time: 3:45.9	Dist: 28.943446 #Veh: 16 Time: 00:14.0	Dist: 29.068167 #Veh: 16 Time: 00:35.7
EW75	Dist: 28.051201 #Veh: 14 Time: 00:43.5	Dist: 28.051201 #Veh: 14 Time: 05:23.1	Dist: 28.051201 #Veh: 14 Time: 00:13.6	Dist: 28.530133 #Veh: 14 Time: 00:43.8
EW76	Dist: 29.645699 #Veh: 20 Time: 01:17.4	Dist: 28.826119 #Veh: 20 Time: 04:24.6	Dist: 29.287905 #Veh: 20 Time: 00:15.9	Dist: 28.862949 #Veh: 20 Time: 02:33.3
EW77	Dist: 26.425897 #Veh: 18 Time: 01:08.7	Dist: 26.425897 #Veh: 18 Time: 04:00.6	Dist: 26.425897 #Veh: 18 Time: 00:07.9	Dist: 26.425897 #Veh: 18 Time: 02:24.9
EW78	Dist: 32.617926 #Veh: 20 Time: 01:05.4	Dist: 32.617926 #Veh: 20 Time: 04:33.2	Dist: 32.617926 #Veh: 20 Time: 00:16.8	Dist: 32.816363 #Veh: 20 Time: 02:26.5
EW79	Dist: 37.441773 #Veh: 20 Time: 00:48.6	Dist: 43.140995 #Veh: 20 Time: 05:26.1	Dist: 39.891936 #Veh: 20 Time: 00:09.4	Dist: 41.108342 #Veh: 20 Time: 00:53.6
EW80	Dist: 37.468562 #Veh: 17 Time: 01:00.3	Dist: 37.468562 #Veh: 17 Time: 01:21.0	Dist: 37.468562 #Veh: 17 Time: 00:11.6	Dist: 48.443849 #Veh: 20 Time: 00:43.2
EW81	Dist: 34.257061 #Veh: 19 Time: 00:59.8	Dist: 34.257061 #Veh: 19 Time: 04:06.8	Dist: 34.257061 #Veh: 19 Time: 00:08.2	Dist: 34.257061 #Veh: 19 Time: 01:24.8
EW82	Dist: 25.821875 #Veh: 15 Time: 01:08.0	Dist: 25.821875 #Veh: 15 Time: 04:02.3	Dist: 25.821875 #Veh: 15 Time: 00:15.6	Dist: 26.198512 #Veh: 15 Time: 01:52.9
EW83	Dist: 38.691455 #Veh: 17 Time: 01:03.3	Dist: 38.691455 #Veh: 17 Time: 04:32.7	Dist: 38.691455 #Veh: 17 Time: 00:09.0	Dist: 38.874496 #Veh: 17 Time: 01:46.7
EW84	Dist: 31.82273 #Veh: 20 Time: 01:15.5	Dist: 34.48017 #Veh: 20 0 Time: 4:39.4	Dist: 32.321791 #Veh: 20 Time: 00:27.9	Dist: 32.69019 #Veh: 20 Time: 00:44.7
EW85	Dist: 22.409474 #Veh: 16 Time: 01:02.1	Dist: 22.270508 #Veh: 16 Time: 04:05.3	Dist: 22.270508 #Veh: 16 Time: 00:06.5	Dist: 22.679345 #Veh: 16 Time: 01:11.5
EW86	Dist: 34.206519 #Veh: 19 Time: 02:00.4	Dist: 34.031981 #Veh: 20 Time: 04:56.6	Dist: 34.206519 #Veh: 19 Time: 00:18.7	Dist: 34.206519 #Veh: 19 Time: 02:26.8
EW87	Dist: 34.82462 #Veh: 18 Time: 01:03.7	Dist: 34.206519 #Veh: 19 Time: 04:30.7	Dist: 34.82462 #Veh: 18 Time: 00:11.0	Dist: 35.0878 #Veh: 18 Time: 02:24.1
EW88	Dist: 31.0066 #Veh: 20 Time: 01:12.2	Dist: 33.703066 #Veh: 20 Time: 05:08.0	Dist: 32.47382 #Veh: 20 Time: 00:27.3	Dist: 31.769766 #Veh: 20 Time: 00:58.6
EW89	Dist: 27.238656 #Veh: 18 Time: 01:19.8	Dist: 27.238656 #Veh: 18 Time: 04:39.8	Dist: 27.238656 #Veh: 18 Time: 00:11.3	Dist: 27.368549 #Veh: 18 Time: 02:51.7
EW90	Dist: 31.618367 #Veh: 20 Time: 01:13.7	Dist: 34.031981 #Veh: 20 Time: 04:56.6	Dist: 32.617682 #Veh: 20 Time: 00:13.1	Dist: 34.34981 #Veh: 20 Time: 01:05.0
EW91	Dist: 20.177009 #Veh: 15 Time: 01:14.3	Dist: 20.919498 #Veh: 16 Time: 00:48.1	Dist: 20.919498 #Veh: 16 Time: 00:21.0	Dist: 23.652164 #Veh: 18 Time: 02:23.1
EW92	Dist: 29.912426 #Veh: 17 Time: 00:52.9	Dist: 29.912426 #Veh: 17 Time: 04:28.3	Dist: 29.912426 #Veh: 17 Time: 00:16.1	Dist: 30.30263 #Veh: 16 Time: 01:27.8
EW93	Dist: 24.51688 #Veh: 16 Time: 00:52.1	Dist: 24.51688 #Veh: 16 Time: 04:06.5	Dist: 24.51688 #Veh: 16 Time: 00:10.1	Dist: 24.51688 #Veh: 16 Time: 00:48.3
EW94	Dist: 26.32926 #Veh: 17 Time: 00:34.0	Dist: 26.32926 #Veh: 17 Time: 04:18.6	Dist: 26.32926 #Veh: 17 Time: 00:10.2	Dist: 26.335416 #Veh: 17 Time: 00:42.4
EW95	Dist: 28.302758 #Veh: 17 Time: 01:19.1	Dist: 28.302758 #Veh: 17 Time: 04:06.7	Dist: 28.302758 #Veh: 17 Time: 00:10.1	Dist: 28.330702 #Veh: 17 Time: 01:34.7
EW96	Dist: 35.7187 #Veh: 20 Time: 01:12.8	Dist: 38.765241 #Veh: 20 Time: 03:38.6	Dist: 38.367394 #Veh: 20 Time: 00:12.9	Dist: 39.170992 #Veh: 20 Time: 01:19.5
EW97	Dist: 43.128456 #Veh: 20 Time: 00:24.4	Dist: 44.114772 #Veh: 20 Time: 04:15.6	Dist: 43.346033 #Veh: 20 Time: 00:21.0	Dist: 46.46703 #Veh: 20 Time: 00:37.2
EW98	Dist: 27.510259 #Veh: 20 Time: 01:41.4	Dist: 28.536837 #Veh: 20 Time: 04:00.2	Dist: 28.826729 #Veh: 20 Time: 00:13.5	Dist: 30.059932 #Veh: 19 Time: 00:31.5
EW99	Dist: 31.084244 #Veh: 20 Time: 01:14.3	Dist: 34.030671 #Veh: 20 Time: 04:47.1	Dist: 33.248751 #Veh: 20 Time: 00:23.9	Dist: 33.908077 #Veh: 20 Time: 01:41.9
EW100	Dist: 33.231389 #Veh: 20 Time: 00:35.6	Dist: 33.231389 #Veh: 20 Time: 04:21.9	Dist: 33.231389 #Veh: 20 Time: 00:10.3	Dist: 33.278191 #Veh: 20 Time: 01:34.0

.

Table 4 presents the comparative performance of the four algorithms. Overall, the Evolution Strategy (ES) proved to be the most consistent, producing results that were identical or very close to the best solutions across almost all instances, while keeping execution times remarkably low—often well under a second. This underscores the strong efficiency of ES for the WEEETP, especially in small and medium-sized cases.

By contrast, the Offspring-Selected methods (OSGA and OSES) occasionally delivered slightly better distances (as in instance EW4), but these gains came at a notable cost in runtime, in some cases extending to several minutes. This shows that although offspring selection improves exploration, it does so at the expense of computational efficiency.

The Genetic Algorithm (GA) offered solid and reliable results, serving as a useful benchmark, but it did not outperform ES in terms of either solution quality or speed. OSES, despite its greater sophistication, often required longer runtimes without a consistent advantage over ES.

Taken together, these results suggest that ES offers the best balance between solution accuracy and efficiency, whereas OSGA and OSES may provide incremental improvements in selected cases but demand significantly more computational effort. This comparison highlights the need to weigh both solution quality and execution time when assessing metaheuristic methods for the WEEETP.

We ran 33 runs of each of the implemented algorithms in a Google Colab environment using Python. The Google Colab environment used Python 3.10 and was run on an instance with standard Collab features: 12 GB of RAM, Intel Xeon 2.30 GHz processor and no GPU acceleration.

The experiments were performed using a Genetic Algorithm (GA), obtaining the best result (shortest distance travelled) with this approach (see

Table 5. Results of the EW1 instance.

Algorithms	Run	Best Solution Distance	Best Solution Travel Time	Best Solution Vehicle Utilization	Execution Time
GA	22	62.507566	12,091.2952	17	01:16.3
OSGA	31	62.570756	12,046.3175	17	02:08.7
ES	11	62.507566	22,666.3362	17	00:04.0
OSES	25	62.507566	12,046.4697	17	02:16.2

). For illustration purposes, Table 5 reports the results of instance EW1, which was selected as a representative intermediate case. EW1 was chosen because it exhibited clear variability between algorithms in terms of distance, travel time and vehicle usage, thereby allowing us to highlight the trade-offs between solution quality and execution time.

In the EW1 instance, GA obtained a slightly lower distance value compared with OSGA and ES; however, the numerical difference was negligible (on the order of 10⁻⁶) and therefore not statistically significant. In terms of travel time and vehicle usage, the results across the three algorithms were very similar. Furthermore, when analysing additional instances (e.g., EW10, EW25, EW40), the performance varied, with OSGA and ES occasionally achieving equal or superior solutions. These observations suggest that no single algorithm consistently dominates across all evaluation criteria. Rather, the results indicate that GA, OSGA, and ES are all competitive approaches, and their relative performance depends on the characteristics of the specific instance. Consequently, the main contribution of this study lies in the comparative analysis of algorithmic behaviour under realistic WEEE transportation scenarios, rather than in the identification of an absolute best-performing algorithm.

Table 6. Best Routes of the EW1 instance.

Vehicles	Nodes	Routes
1	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	27	Calzada de los Leones 145, local 26, col. Las Águilas, del. Álvaro Obregón.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
2	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	12	Calle Vicente Guerrero 509, Centro, 42,000 Pachuca de Soto, Hgo.
	13	Calle Ignacio Allende 207, Centro, 42,000 Pachuca de Soto, Hgo.
	6	Calle Ignacio Allende 207, Centro, 42,000 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
3	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	22	Villas de Pachuca, 42,083 Pachuca de Soto, Hgo
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
4	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	19	S/N, Blvrd Luis Donaldo Colosio, Colinas de Plata, 42,186 Pachuca de Soto, Hgo.
	17	Gran Patio Pachuca, Blvrd Luis Donaldo Colosio 2009, Ex Hda De Coscotitlan, 42,064 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
5	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	25	Av. 5 no. 17, col. Renovación, del. Iztapalapa.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
6	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	24	Galerías Pachuca, Camino Real de La Plata 100, Zona Plateada, 42,084 Pachuca de Soto, Hgo.
	4	Plaza Galerías, Camino Real de La Plata 100, Zona Plateada, 42,084 Pachuca de Soto, Hgo.
	18	Calle Artículo 3 27, Constitución, 42,080 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
7	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	21	De Los Canarios 125, Villas de Pachuca, 42,083 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
8	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	15	Plaza de la Constitución 104, Centro, 42,000 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
9	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	1	Av. Hgo., Acayuca
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
10	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	2	Av. De los árboles, el Venado, Pachuca
	10	Los 42083, Av. de los Árboles 203, Los Cipreses, Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
11	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	9	Callejón Hacienda Tlahuelilpan 90, Juan C. Doria, 42,083 Pachuca de Soto, Hgo.
	8	Plaza Gran Sur, Blvrd Nuevo Hidalgo 509, La Colonia, 42,083 Pachuca de Soto, Hgo
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
12	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	26	Poniente 146 # 710 A Industrial Vallejo, Azcapotzalco
	28	Trigo 93, colonia Granjas Iztapalapa. Delegación Iztapalapa.
	29	M.A. Quevedo No. 24–205, Coyoacán.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
13	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	11	12 de Octubre 102, La Villita, 42,060 Pachuca de Soto, Hgo.
	3	Calle Belisario Domínguez 122-B, Centro, 42,000 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
14	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	20	Av. Javier Rojo Gómez 501, AmpSta Julia, 42,080 Pachuca de Soto, Hgo.
	23	Leandro Valle 108, Centro, 42,000 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
15	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	5	Blvd. km 7.7, S/N Comercial Plaza, Pachuca, Hgo, Blvrd Luis Donaldo Colosio, Centro, 42,093 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
16	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	7	De Los Canarios 125, Villas de Pachuca, 42,083 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
17	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.
	16	Plaza Morelos, Calle José Ma Morelos y Pavon 205, Centro, 42,000 Pachuca de Soto, Hgo.
	14	Calle Vicente Guerrero 306-A, Centro, 42,000 Pachuca de Soto, Hgo.
	0	Hércules 401 A Bodega 2, Polígono Empresarial Santa Rosa Jáuregui, 76,220 Santiago de Querétaro, Qro.

presents the best routes obtained for the EW1 instance, chosen as a representative case of intermediate size. This instance was selected to illustrate how the optimisation results translate into practical vehicle routes, while maintaining clarity and readability. The best solution involves 15 vehicles; the distance is between the longitude and latitude coordinates in each point (see Table 6).

In this study, operational cost and carbon emissions were explicitly treated as complementary objectives. The optimisation of routes reduces travelled distance and fleet usage, which directly minimises operational cost. At the same time, fuel consumption and associated CO₂ emissions were modelled as a proportional factor of distance and load, allowing the algorithms to favour solutions with lower environmental impact. This dual-objective approach demonstrates that it is possible to balance economic efficiency and sustainability within the WEEETP, as confirmed by the experiments where the solutions that minimised cost also achieved significant reductions in estimated emissions.

Although operational cost was explicitly modelled as the primary optimisation objective, it is important to note that lower costs are closely related to shorter travel distances and reduced vehicle usage, which indirectly contribute to lower carbon emissions. For this reason, sustainability aspects were qualitatively addressed in our analysis. However, we acknowledge that a rigorous dual-objective framework—formally integrating both cost and emissions—would strengthen the environmental dimension of the problem. Such a formulation requires the inclusion of emission factors and additional constraints, which we propose as an extension for future work. The present study focused on establishing the feasibility and performance of evolutionary algorithms in solving the WEEE Transportation Problem under realistic cost-oriented conditions.

4. Conclusions

Regarding the solution of the real instance, we can observe that the proposed model achieves the goal of efficient e-waste collection, i.e., with the best use of resources, by travelling a short distance with the fewest vehicles and, in turn, covering the demand with a service offered within the established time window.

The use of metaheuristics accelerates the achievement of adequate results in a reduced execution time. The implementation of these algorithms in programming environments such as Python facilitates the rapid generation of results.

The algorithms make it possible to find a solution to certain problems in a reasonable amount of time [40]. For this research, the following algorithms were used: genetic, offspring selection, evolution strategy, evolution with offspring selection and random search. All of them were used to evaluate the collection of electronic waste, particularly for disused mobile phones in the city of Pachuca, Hidalgo, and some contiguous areas.

Therefore, the following parameters and values that converge in each of the algorithms used for the e-waste collection experimentation were applied:

• To carry out the test on the instance repository, 100 instances were used, evaluated by each of the algorithms mentioned above, in 33 runs. As part of the result of the process, in the solution of the real instance, we observed that the proposed model achieves the objective of efficient e-waste collection, with the best use of resources by travelling a short distance with the least number of vehicles and, in turn, covering the demand with a service offered within the established time window.
• As part of the solutions for the 100 instances, the OSES (Offspring Selection Evolution Strategy) algorithm showed better performance in 63 of the 100 instances, generating the best result compared to other algorithms. This algorithm also had an average run time of 00:13.9, compared to the ES (Evolution Strategy) algorithm, which obtained the best solution in 67 instances, but with an average run time of 03:50.9.

The superior performance of OSES compared with GA, OSGA and ES can be attributed to its hybrid nature. By integrating the self-adaptation of mutation parameters from Evolution Strategies with an offspring-selection mechanism, OSES ensures that only offspring with higher fitness than their parents are preserved. This balance between exploration and exploitation helps to prevent premature convergence, which is a common limitation of classical GA and ES. In the context of WEEE transportation, where constraints such as vehicle capacity, hazardous waste handling and time windows introduce high variability, this adaptive mechanism allows OSES to achieve more robust and consistent solutions, often with better trade-offs between solution quality and computational time.

Finally, it is verified that the use of metaheuristic algorithms accelerates the obtaining of adequate results in a reduced execution time. Implementing these algorithms in programming environments such as Python not only makes the generation of results faster but also accessible and replicable in different problem contexts.

Beyond the computational findings, the proposed framework also carries significant industrial and policy implications. For industry, it serves as a practical decision-support tool that can streamline reverse logistics, lower operational costs, and reinforce corporate sustainability commitments. For policymakers, it offers solid quantitative insights to inform regulations and incentive schemes aimed at reducing carbon emissions and advancing circular economy objectives in the e-waste sector. By linking technical optimisation with real-world operational and regulatory considerations, the framework demonstrates its value not only for academic research but also as a driver of sustainable practices in industry and evidence-based policymaking.

Future work will focus on extending the current single-objective formulation into a rigorous dual-objective optimisation framework that explicitly balances economic and environmental dimensions. In particular, carbon emissions will be incorporated into the objective functions through established emission factors, enabling the generation of Pareto frontiers that capture the trade-offs between cost and emissions. This extension will not only strengthen the environmental relevance of the model but also provide more comprehensive decision support for policymakers and practitioners in the field of WEEE management. Furthermore, future research may include a comparative analysis with other metaheuristics such as PSO or SA; however, the choice of evolutionary approaches in this study was driven by their alignment with the discrete nature of transportation problems.