A multi-objective optimization based on genetic algorithms for the sustainable design of Warm Mix Asphalt (WMA)

ABSTRACT

In this research, a methodology was developed to optimize the design of Warm Mix Asphalt (WMA) with the inclusion of three recycled materials as partial replacement of natural aggregates (NAs), namely Crumb Rubber (CR), Reclaimed Asphalt Pavement (RAP), and Recycled Concrete Aggregate (RCA). The methodological proposal is composed of 4 sections denominated: (I) environmental module, (II) economic module, (III) decision-support module, and (IV) results report module. Initially, a Life Cycle Assessment (LCA) is carried out to quantify the environmental impacts associated with WMA production. Similarly, in the second module, a Life Cycle Costing (LCC) is performed to estimate the financial investment required by the process under evaluation. Meanwhile, a computational model based on genetic algorithms (GAs) is created in the decision-support module to execute multi-objective optimization (minimization of costs and contaminating potential). In the last module, the more accurate WMA designs are presented employing a Pareto front, ternary plot, composition pie chart, and statistical analysis of the influence of the CR, RAP, and RCA on the validation criteria. This study concludes that even under long hauling distances and huge prices, it is possible to design WMA with CR, RAP, and/or RCA additions that form sustainability benefits compared to conventional WMA.

KEYWORDS:

• Genetic algorithms (GAs)
• Warm Mix Asphalt (WMA)
• Life Cycle Assessment (LCA)
• Recycled Concrete Aggregate (RCA)
• Reclaimed Asphalt Pavement (RAP)
• Crumb Rubber (CR)

1. Introduction and scope of work

The road infrastructure connects the urban, rural, and productive centers, allowing commerce and conditions for the economic and social development of the communities (Abudinen et al., 2017; Fuentes et al., 2019; J. Santos, Ferreira, et al., 2017). Nonetheless, the construction of pavements demands large amounts of building materials and energy consumption which generates a huge environmental burden that compromises non-renewable and ecosystem resources for future generations (Plati, 2019; Sartori et al., 2021). The preceding shows a turning point because although the construction and maintenance of road infrastructure are crucial for the development of societies, these activities necessitate a high economic investment and generate a vast environmental impact that ends up affecting the communities that were intended to benefit (Bryce et al., 2017; Obazee-Igbinedion & Owolabi, 2018; Y. Zhao et al., 2021). This scenario has led to progress in developing novel sustainable materials for the road infrastructure industry (Norambuena-Contretas et al., 2020; Sun et al., 2020). One of these innovations is the Warm Mix Asphalt (WMA) with waste material content (Cao et al., 2019; Calabi-Floody et al., 2020; Monu et al., 2020; Z. Zhao et al., 2020).

WMA is a type of asphalt concrete produced at a temperature between 20–40 °C lower than traditional Hot Mix Asphalt (HMA) (D’Angelo et al., 2008; Abed et al., 2019; Sukhija & Saboo, 2021). The decrease in the mixing and compaction temperatures occasions a lower energy consumption and reduced greenhouse gas emissions (Stimilli et al., 2017; Jomoor et al., 2019; Guo et al., 2020). Consequently, it is a consensus in the state of the art that WMAs present environmental and economic benefits compared to HMA (Diab et al., 2016; Behnood, 2020; Cheraghian et al., 2020; Polo-Mendoza et al., 2022). Nevertheless, this is not entirely correct in all scenarios, as the WMA technologies required to reduce the production temperatures can result in higher monetary or environmental costs. There are four WMA technologies, chemical additives, organic additives, direct foaming (water-based processes), and indirect foaming (water-bearing additives); each of these alternatives presents its benefits and challenges (Rubio et al., 2012; Vaitkus et al., 2016; Stimilli et al., 2017; Xu et al., 2017). Due to the particularities of each WMA technology and the context of its application in a case study, it is necessary to use economic and environmental assessments that allow the supposed sustainable benefits to be confirmed. Regarding environmental evaluations, the Life Cycle Assessment (LCA) is undoubtedly the most widely employed procedure in state of the art and in the industry to analyze the environmental burdens generated by WMA (Capitão et al., 2012; Mohammad et al., 2014; Pasetto et al., 2017; Georgiou & Loizos, 2021). On the other hand, in economic terms, there is a higher diversity of techniques to estimate the profitability of this type of asphalt concrete; nonetheless, the Life Cycle Costing (LCC) is one of the most notorious in the road infrastructure industry (Alaloul et al., 2021; Moins et al., 2020; J. Santos, Flintsch, et al., 2017). LCA and LCC techniques are explored in-depth in later sections of this article.

Numerous researchers have examined approaches to increase the sustainability components in WMAs. One of the most promising ways is the incorporation of waste materials as a partial replacement for natural aggregates (NAs); among these supplemental materials, the most notable are crumb rubber (CR), reclaimed asphalt pavement (RAP) and recycled concrete aggregates (RCA) (Albayati et al., 2018; Wang et al., 2018; Goli & Latifi, 2020; Guo et al., 2020; Monu et al., 2020). CR is the material generated after shredding scrap tires obtained after the end of the useful life of worn vehicle wheels (Sienkiewicz et al., 2012; Frolova & Salaiová, 2017; Wang et al., 2018). RAP is the product of crushing asphalt mixtures or reprocessing asphalt pavement materials; hence, RAP is obtained mainly from asphalt pavement reconstruction, resurfacing and recycling projects (Copeland, 2011; Hoy et al., 2016; Saboo et al., 2020). Lastly, RCA is the waste material resulting from the demolition and crushing of Portland cement concrete from buildings and hydraulic paving slabs (Y. Ding et al., 2021; Pasandín & Pérez, 2015; Sanchez-Cotte, Pacheco, et al., 2020).

Although there is a vast state of the art in the design of WMA with contents of waste materials, few studies have focused on the study of WMA with simultaneous inclusion of several supplementary materials. This may be due to the difficulty of finding the optimal proportion of each component of the asphalt mixture. This complexity refers to the alterations in the mix design that occur after incorporating non-traditional materials (i.e., other than NAs and asphalt binder). In other words, each possible combination of supplementary materials to be added generates a change in the mix design that translates into a variation in the environmental burden caused and the associated monetary costs. This situation ends in a multi-criteria optimization problem, in which it is desired to determine the most suitable proportions settings of the materials that guarantee to minimize the environmental impacts and minimize the economic investment (or maximize profitability).

The problem exposed previously is the foundation of the present research effort. In this study, a multi-objective optimization method was developed to find the optimal amount of CR, RAP, and/or RCA to be incorporated into a WMA, assuring the maximum economic benefits while minimizing the environmental damage. In addition, considering some constraints (detailed throughout this manuscript), restrictions were applied to ensure that the mechanical properties of the asphalt concrete were not negatively affected. The approach towards environmental and economic aspects was carried out with the techniques of LCA and LCC, respectively. The LCA-LCC integration is a methodology widely used in the sustainable design of products and services in the engineering field; some application examples can be consulted in (Calado et al., 2019; A. Di Maria et al., 2018; Hoogmartens et al., 2014; Jocanovic et al., 2019; Y. Ma et al., 2018; R. Santos et al., 2019). On the other hand, it was decided to implement genetic algorithms (GAs) to solve the optimization problem. GAs were chosen because metaheuristic optimization algorithms commonly solve mixture proportion design problems for pavement materials (Fakhri et al., 2017; Lyu et al., 2019; Liang et al., 2021). Such is the versatility and potential of GAs that they have been used in other areas of road infrastructure to solve complex issues, such as pavement maintenance scheduling (Bressi et al., 2021; Naseri et al., 2020; J. Santos et al., 2019; B. Yu et al., 2015), indirect calculation of parameters for the design of pavement structures (Sadrossadat et al., 2018; Zhang et al., 2021), assessing recycled pavements (Plati et al., 2017), generation of deterioration models for urban roads (Chopra et al., 2018), prognostication of Marshall mix design parameters (Azarhoosh & Pouresmaeil, 2020), among others.

In this order of ideas, this investigation aims to provide the industry and literature with an innovative procedure to optimize the WMA mix design from a sustainability viewpoint. For this purpose, the authors publicly confer all the codes and data necessary for the replicability of the developed methodology. Subsequently, it is expected that this research effort will motivate builders, agencies, engineers, decision-makers, and other stakeholders to implement this novelty asphalt concrete (WMA with waste material contents) to construct new pavement structures and rehabilitate pavements already existing.

The sections of the rest of the document were structured as described below. Section 2 manifests the details of the proposed framework for multi-objective optimization. The LCA and LCC are developed in Section 3 and Section 4, respectively. Section 5 addresses the model formulation, solution approach, and features of the GAs implementation. Meanwhile, Section 6 illustrates the capabilities of the submitted method through a case study. Section 7 presents the main conclusions generated by this investigation. Finally, Section 8 exhibits recommendations regarding future research lines.

2. Methodology

Considering state of the art and current practice in the design of WMAs, this section describes the chief components contemplated by the proposed methodology for multi-objective optimization. The methodological framework focuses on four modules: (I) the environmental module, in which the environmental burdens are assessed applying the LCA technique; (II) the economic module, where production costs are estimated through the LCC; (III) the decision-support module, in which the most suitable design proportions for the WMA are determined from a multi-criteria GA; and (IV) results-report module, where the most sustainable WMA alternatives are detailed (comprehensive description of the compositions, associated environmental impacts, and necessary monetary investment). Figure 1 shows a flowchart outlining the procedure framework. These modules are explained and expanded in deep in the following sections of this manuscript.

Figure 1. Proposed framework for multi-objective optimization. Legend: HFO – heavy fuel oil.

3. Environmental module

This module is in charge of estimating the environmental burden imposed by the production of the WMA alternatives under evaluation. For these purposes, the LCA technique was implemented. According to current regulations from the International Organization for Standardization (ISO), i.e., ISO-14040 and ISO-14044, the execution of LCAs must be based on four phases: goal and scope definition phase, life cycle inventory (LCI) phase, life cycle impact assessment (LCIA) phase, and interpretation phase (ISO, 2006a, 2006b). Additionally, the recommendations proposed by the Federal Highway Administration (FHWA) in the ‘Pavement Life Cycle Assessment Framework’ were followed (Harvey et al., 2016). To carry out the LCAs, the SimaPro 9.1.1 software was utilized. This computational tool allows collecting, analyzing, evaluating, and monitoring the sustainability performance of a wide range of products and services (Starostka-Patyk, 2015). The potential and versatility of SimaPro have made it one of the leading software in the industry (Herrmann & Moltesen, 2015; Vidergar et al., 2021). Table 1 compiles various LCA studies developed for the evaluation of WMAs. In this table, it is evident that the most recurrent tool is SimaPro.

Table 1. Synthesis of investigations regarding LCA efforts on WMA.

Research	Location	Software	Objective	Results
(Vidal et al., 2013)	Spain	SimaPro	Compare an HMA against a WMA (foaming process). Various RAP contents were evaluated.	Regarding the HMA control, the production of a WMA with 15% RAP reduced between 13-14% of the climate change potential, consumption of fossil fuels, and energy consumption.
(Blankendaal et al., 2014)	The Netherlands	SimaPro	Analyze the efficiency of different sustainable alternatives for hydraulic and asphalt concretes (including WMAs).	WMAs generate less environmental impact than HMAs by approximately 33%.
(Anthonissen et al., 2015)	Belgium	SimaPro	Contrast the environmental impacts of WMAs (zeolite and wax) against an HMA.	HMA was more polluting than WMA made with organic additives but less than WMA made with zeolites.
(Giani et al., 2015)	Italy	SimaPro	Evaluate pavement rehabilitation alternatives. HMA and WMA (with and without RAP) were considered.	The WMA-RAP alternative decreased (compared to HMA without RAP) by 12% of CO2eq, 15% of energy consumption, and 15% of water consumption.
(Rodríguez-Alloza et al., 2015)	Australia	Not specified	Compare an HMA against a WMA. Various CR contents were evaluated.	Compared to HMA, WMA production reduces greenhouse gas emissions and energy consumption by 18% and 20%, respectively.
(J. Santos et al., 2018)	France	OpenLCA	Evaluate HMA and WMA (foaming process and chemical additive), varying the RAP content.	In most impact categories, WMAs turn out to be the alternatives with the lowest environmental burden (compared to the respective HMA).
(Cao et al., 2019)	PR China	Not specified	Evaluate HMA and WMA (foaming process, organic additive, and chemical additive), varying the CR content.	Energy savings are highly dependent on the type of technology used for the modification.
(Hamdar et al., 2020)	Lebanon	SimaPro	Measure the functional, mechanical, environmental, and economic performance of a WMA in a hot climate.	WMA has enormous environmental benefits over HMA in energy consumption and global warming potential.
(Hasan et al., 2020)	United Arab Emirates	SimaPro	Development of LCA to measure environmental contributions of RAP and blast furnace slag within the WMA design.	Low dosages of these materials managed to reduce CO2eq, energy consumption, NOxeq, PM2.5eq, acidification and land use by 34%, 48%, 24.4%, 21.53%, 21.2% and 10.4%, respectively.
(Vega, Martinez-Arguelles, et al., 2020)	Colombia	SimaPro	Comparison of an HMA against a WMA (chemical additive). Various RCA contents were evaluated.	RCA increases the optimal asphalt content; therefore, an excess of this material reduces the environmental benefits attributed to WMA-RCA, even becoming more polluting than a conventional mixture.

3.1. Goal and scope definition phase

3.1.1. GOAL

The chief objective of this research effort is to conceive an optimization method for the sustainable design of WMA with the inclusion of supplementary materials, namely CR, RAP, and RCA. In consonance, in this study case, the goal of the LCA is to estimate the potential environmental impacts generated by the production (in the asphalt mixing plant) of the WMA designs under evaluation. The final result of this module is the creation of a computational model that calculates the environmental burden associated with the manufacturing of WMA with CR, RAP, and/or RCA content. It is expected that the findings of this investigation allow to facilitate and motivate state agencies, pavement design engineers, private companies, and other stakeholders to implement these asphalt concrete innovations within highway construction projects.

3.1.2. System description and boundaries

The FHWA suggests four possible approaches to framing LCAs to be carried out in the road infrastructure industry, namely cradle-to-gate, cradle-to-site, cradle-to-laid, and cradle-to-grave (Harvey et al., 2016). Figure 2 shows the scope of each of the previous approaches schematically. In order to be consistent with the defined goal, it was decided to implement the cradle-to-gate approach. Consequently, three stages were established: materials production, materials transport to the asphalt mixing plant, and asphalt mix production. In addition, due to the CR, RAP and RCA coming from a recycling process, it was decided to use the ‘cut-off’ approach to model them. The cut-off approach implies that the environmental burdens associated with the recycled materials are only generated by the processes necessary for their incorporation into a new activity or product (in this case, within a WMA) (Aurangzeb et al., 2014; J. Santos et al., 2018; Schrijvers et al., 2016). Figure 3 shows the system under evaluation and the boundaries that delimit it.

Figure 2. Approaches proposed by the FHWA to carry out LCAs in the pavement industry.

Adapted from: (Harvey et al., 2016; Vega et al., 2019).

Figure 3. Boundaries contemplated for modeling the production of WMA in asphalt mixing plants. Legend: NA – natural aggregates.

3.1.3. Functional unit

The functional unit is one of the essential parts of an LCA because this forms the reference point to compare alternatives that maintain the same function and similar features (Inyim et al., 2016; J. Santos et al., 2018; Vega, Martinez-Arguelles, et al., 2020). This research selected the production of 1 ton (1000 kg) of WMA in an asphalt mixing plant as the functional unit. According to the investigations that precede this study, it was considered that: (i) the WMAs had a dense granulometry composed of 50% coarse aggregate and 50% fine aggregate; (ii) the WMA technology employed was a chemical additive based on fatty acids; and, (iii) for all the WMAs, the compaction temperature was 110°C (Sanchez-Cotte, Fuentes, et al., 2020; Vega, Martinez-Arguelles, et al., 2020; Vega, Santos, et al., 2020b; Polo-Mendoza et al., 2022).

3.1.4. Data source

The vast majority of the information used in this study corresponds to primary data, which were collected in previous research efforts. The primary data comprises the information concerning NAs extraction, truck loading of NAs, CR processing, RAP processing, RCA processing, materials transport to the asphalt mixing plant, and asphalt mix production. Except for the CR and RAP processing, the primary data are representative of the northern region of Colombia. Meanwhile, the data inventory for the asphalt binder and additive production was extracted from United States Life Cycle Inventory Database (USLCI) and Ecoinvent databases, respectively. As evidenced above, the secondary data source corresponds to the Ecoinvent and USLCI, two of the most comprehensive databases that SimaPro has (NREL, 2009; Weidema et al., 2013; Moreno Ruiz et al., 2020). Ecoinvent was created by the Swiss Center for Life Cycle Inventories, and the last version was liberated in 2020 (Weidema et al., 2013; Moreno Ruiz et al., 2020). USLCI was developed by the National Renewable Energy Laboratory of the United States Department of Energy (NREL, 2009).

3.2. Lci phase

Table 2 shows the LCI adopted for this research. This table presents the SimaPro Unit Processes (SPUP) used to model the stages and sub-stages that compose the system boundaries (Figure 3). The corresponding SPUP were modified to assemble them consistent with the data inventory collected. Table 2 explains that the material mixing sub-stage is defined by an SPUP that requires the thermal energy (TE) demand as input data. TE is calculated by Equation (1), which adopts an energy balance developed by (J. Santos et al., 2018). (1) $\begin{array}{rl}\mathrm{TE}& =\left[\begin{array}{c}\left(\left(\mathrm{Tmix}-\mathrm{to}\right)\ast \sum _{i=1}^{i=5}\mathrm{Mi}\ast \mathrm{Ci}\right)+\left(\mathrm{Cw}\ast \left(100-\mathrm{to}\right)\ast \sum _{i=1}^{i=4}\mathrm{Mi}\ast \mathrm{Wi}\right)+\\ \left(\mathrm{Cvap}\ast \left(\mathrm{Tmix}-100\right)\ast \sum _{i=1}^{i=4}\mathrm{Mi}\ast \mathrm{Wi}\right)+\left(\mathrm{Lv}\ast \sum _{i=1}^{i=4}\mathrm{Mi}\ast \mathrm{Wi}\right)\end{array}\right]\ast \left(1+\mathrm{CL}\right)\end{array}$(1) Note: the meaning of the acronyms is presented in Table 3.

Table 2. LCI adopted for this research.

LCA stage	LCA sub-stage	SPUP	Modified input data
			Parameters	References
Materials production	NAs extraction	Gravel, crushed {RoW}| production | Cut-off, U	7 lt of diesel / ton of aggregate 0.02 kg of lubricant / ton of aggregate	(Martinez-Arguelles et al., 2019)
	Truck loading of NAs	Loader operation, large, INW/RNA	Efficiency: 4.5 ton of aggregates / hour 7 lt of diesel / ton of aggregate 0.02 kg of lubricant / ton of aggregate
	CR processing	Waste, pneumatic tyres {GLO}| market for waste, pneumatic tyres | Cut-off, U	2.98 lt of diesel / ton of CR 0.1 kg of lubricant / ton of CR 383.33 kWh of electricity / ton of CR 220 kg of water / ton of CR	(Bressi et al., 2018a)
	RAP processing	Rock crushing {RER}| processing | Cut-off, U Excavation, skid-steer loader {RER}| processing | Cut-off, U Machine operation, diesel, ≥74.57 kW, high load factor {GLO}	184 ton of processing capacity / hour (Combined capacity including four activities: crushing, stacking, conveying, and screening)	(J. Santos, Flintsch, et al., 2019)
	RCA processing	Diesel, burned in building machine {GLO}| processing | Cut-off, U	Efficiency: 0.28 lt of diesel / ton of RCA 0.00069 kg of lubricant / ton of RCA 2.33 kWh of electricity / ton of RCA 100 kg of water / ton of RCA	(Vega, Martinez-Arguelles, et al., 2020)
	Asphalt binder production	Bitumen, at refinery/kg/US	"Does not apply.’
	Additive production	Fatty acid {GLO}| market for | Cut-off, U
Materials transport to the asphalt mixing plant	Aggregates transportation	Transport, freight, lorry 16-32 metric ton, EURO4 {RoW}| transport, freight, lorry 16-32 metric ton, EURO4| Cut-off, U	2.12 lt of diesel / tkm - 0.00942 kg of lubricant / tkm	(Vega, Martinez-Arguelles, et al., 2020)
	Asphalt binder transportation		15.78 lt of diesel / tkm - 0.07066 kg of lubricant / tkm
	Additive transportation		7.34 lt of diesel / tkm - 0.03295 kg of lubricant / tkm
Asphalt mix production	NAs processing	- Diesel, burned in building machine {GLO}| processing | Cut-off, U	Efficiency: 0.28 lt of diesel / ton of aggregate 0.00069 kg of lubricant / ton of aggregate 2.33 kWh of electricity / ton of aggregate - 100 kg of water / ton of aggregate
	Mixing process	- Heat, district or industrial, other than natural gas {RoW}| heat production, heavy fuel oil, at industrial furnace 1MW | Cut-off, U	Required thermal energy (MJ / ton of mixture), which is calculated using Equation 1.	(J. Santos et al., 2018; Vega, Santos, et al., 2020b)

Table 3. Parameters considered to calculate TE.

Abbreviation	Parameter	Unit	Value
TE	Thermal Energy	MJ/ton of mixture	Variable
Tmix	Mixing temperature	°C
M1	NAs mass	kg
M2	CR mass	kg
M3	RAP mass	kg
M4	RCA mass	kg
M5	Asphalt binder mass	kg
C1	Specific heat of NAs	KJ/kg/°C	0.74^a
C2	Specific heat of CR	KJ/kg/°C	2.01^c
C3	Specific heat of RAP	KJ/kg/°C	0.74^b
C4	Specific heat of RCA	KJ/kg/°C	0.74 ^a
C5	Specific heat of asphalt binder	KJ/kg/°C	2.09 ^a
W1	Water content of NAs	%*	3 ^a
W2	Water content of CR	%*	0^c
W3	Water content of RAP	%*	0 ^b
W4	Water content of RCA	%*	3 ^a
to	Ambient temperature	°C	25 ^a
Cw	Specific heat of water at 15°C	KJ/kg/°C	4.19 ^a
Cvap	Specific heat of water vapor	KJ/kg/°C	1.83 ^a
Lv	Latent heat of vaporization of water	KJ/kg	2256 ^a
CL	Casing loses factor	%/100	0.27 ^a

Notes: * By the mass of aggregates; ^a (Vega, Santos, et al., 2020b);^b Value taken from the literature (Vandewalle et al., 2020); ^c Typical value.

3.2.1. Influence of waste materials

This investigation analyzes the environmental-economic efficiency of designing WMA with the contents of three supplementary materials (CR, RAP, and RCA). It could be considered that by maximizing the inclusion percentage of these materials, sustainability benefits are generated since the sending of waste to landfills is avoided, and the exploitation of quarries is reduced; in other words, the non-renewable natural resources depletion is mitigated. Nevertheless, this is not entirely accurate because excessive CR, RAP, or RCA content has side effects that can even affect the mechanical properties of asphalt concrete (Pasandín & Pérez, 2013; Farina et al., 2017; Plati, 2019). The remainder of this subsection explains how the inclusion of CR, RAP, and RCA was modeled and constrained.

It is a consensus in the literature that the inclusion of CR in asphalt mixtures increases the required mixing temperature (Vignali et al., 2016; Bakheit & Xiaoming, 2019; Rodríguez-Fernández, Cavalli, et al., 2020; H. Yu et al., 2016). However, the exact temperature rise depends on various variables such as the viscosity of the virgin asphalt binder, the incorporation technology, the digestion time, and even the chemical composition of the CR (Lo Presti, 2013; Mashaan et al., 2014; Rodríguez-Fernández, Baheri, et al., 2020; Riekstins et al., 2021). This research decided to simplify this phenomenon, assuming that any amount of CR that is included generates an increase of 10 °C, as reported in experimental results found in the literature (Moreno et al., 2011; Yucel et al., 2021). Also, to limit the scope of this study, only the incorporation of CR by the dry process was considered; specifically, it was modeled the partial replacement of fine aggregate by CR up to 6%. This limitation is imposed according to typical dosages because higher percentages tend to affect the mechanical performance of asphalt concrete (Hassan et al., 2014; Farina et al., 2017).

Regarding RAP, this is one of the most popular waste materials in the pavement industry because its use as a partial replacement for NAs leads to reduce the content of virgin asphalt binder (Lu & Saleh, 2016; Guo et al., 2020; Habbouche et al., 2021). This phenomenon is due to the ‘re-activation’ process of the asphalt binder attached to the recycled asphalt mixture (Stimilli et al., 2015; Ingrassia et al., 2021). Although this alteration depends on various factors (primarily related to the chemical compatibility between materials), this study adopted a simplification. Figure 4 shows the mathematical model implemented to represent the reduction in virgin asphalt binder consumption, which is associated with RAP percentage that partially replaces NAs. This relationship was taken from the literature; the details of the original research can be consulted in (Lu & Saleh, 2016). Following the state-of-the-art recommendations, the substitution of RAP was limited to up to 30% of the NAs weight (Copeland, 2011; Miró et al., 2011; Van Dam et al., 2015; Plati, 2019).

Figure 4. Incidence of RAP and RCA in WMAs produced with chemical additives.

On the other hand, RCA has the opposite effect. Due to the presence of attached mortar, RCA has a higher porosity and absorption capacity than NAs, which translates into an increase in the demand for asphalt binder (Cassiani et al., 2021; Sanchez-Cotte, Pacheco, et al., 2020). The findings obtained from a previous investigation were used to describe this behaviour (Vega, Martinez-Arguelles, et al., 2020). Likewise, these data are shown in Figure 4. In addition, based on preceding studies, the incorporation of RCA was restricted to only replace the coarse aggregate up to 45% (in terms of weight) (Vega et al., 2019; Vega, Santos, et al., 2020a, 2020b). Although at a dosage of 45%, the asphalt mixtures produced demonstrated a notable deterioration in their mechanical and volumetric behavior, these samples developed properties quite close to the minimum limits required by Colombian standards (Vega, Martinez-Arguelles, et al., 2020; Vega, Santos, et al., 2020a, 2020b).

The above considerations are based on the fact that the supplementary aggregates have resistance and mechanical performance comparable to NAs. Therefore, to implement this multi-objective optimization in an engineering project, it is required that all the aggregates (natural and recycled) must satisfy the minimum quality standards that the applicable regulations impose.

3.3. LCIA Phase

The groups that classify the different environmental burdens are named Impact Categories (ICs) (Inyim et al., 2016; H. Mazumder et al., 2016; Ma et al., 2019). The set of specific ICs is called the Impact Assessment Method (IAM) (Hischier et al., 2010; Mohan, 2018). Choosing an appropriate IAM is a fundamental step in LCAs because each IAM presents its particular gaps or levels of uncertainties (Núñez et al., 2016; Pelletier et al., 2019). Such is the importance of this matter that it is even advisable to compare the information provided by different IAMs (Boulay et al., 2015). For this research, it was decided to use an IAM called ‘BEES+ v.4.08,’ which uses 13 ICs, namely acidification, eutrophication, ecotoxicity, global warming, habitat alteration, human health (HH) cancer, HH criteria air pollutants, HH noncancer, indoor air quality, natural resource depletion, ozone depletion, smog, and water intake (Lippiatt, 2007; Sackey & Kim, 2018).

‘Building for Environmental and Economic Sustainability’, also called BEES+, is a model created by the National Institute of Standards and Technology (NIST) to improve the procedures related to the LCA implementation (Curran et al., 2002; Suh & Lippiatt, 2012; Babaizadeh et al., 2015). The more notable difference between BEES+ and other IAM (as the Tool for Reduction and Assessment of Chemicals and Other Environmental Impacts -TRACI-) is that BEES+ allows the execution of the weighting process (Gloria et al., 2007). The weighting is an optional element within the interpretation phase of an LCA (ISO, 2006a, 2006b); which enables to combine of all ICs into a single score through the implementation of numerical factors (weights) at each type of environmental burden (ISO, 2006b; Gloria et al., 2007; Pizzol et al., 2017). The preceding mentioned serves as the main reason to employ the BEES+ model in this research. Furthermore, the multi-optimization process is simplified since the environmental optimization criteria are summarized by minimizing a whole number (instead of 13). In this way, a ‘many objectives optimization problem’ is avoided, thus reducing the complexity of the problem (Ishibuchi et al., 2015; Li et al., 2015; R. Ding et al., 2021; Rao & Lakshmi, 2021).

3.4. Interpretation phase

This phase presents the results generated by integrating the LCI and LCIA according to those defined in the goal and scope definition phase (ISO, 2006a). As a minimum, it is necessary to report the ‘characterization’ of the environmental burden, i.e., the individual quantification of each one of the different ICs that the adopted IAM contains (ISO, 2006b). The ISO standard proposes in a complementary way some optional procedures (normalization, grouping, weighting, and data quality analysis) to enhance the breadth of the LCA outputs (ISO, 2006a, 2006b). However, based on the established goal and scope definition phase, it is only necessary to carry out the weighting process.

3.4.1. Characterization results

Based on the LCI and LCIA phases, the unitary environmental impacts caused by each LCA sub-stage were determined. The units employed were MJ for the mixing process, tkm (i.e., ton*km) for transporting the materials, and ton for the other sub-stages (related to the production or processing of the materials). Table 4 shows the characterization results for the first stage. Meanwhile, Table 5 discloses the characterization results for the other stages (materials transport to the asphalt mixing plant and asphalt mix production).

Table 4. Characterization results for the materials production stage.

ICs [Unit]	NAs extraction (1 ton)	Truck loading of NAs (1 ton)	CR processing (1 ton)	RAP processing (1 ton)	RCA processing (1 ton)	AB production (1 ton)	CA production (1 ton)
Acidification [H+ mmole eq]	1450000	17000	31100	369	314	366000	467000
Ecotoxicity [g 2.4-D eq]	19600	36.7	650	7.59	9.28	4450	17800
Eutrophication [g N eq]	9270	17.9	150	3.11	1.6	249	19500
Global warming [g CO2 eq]	2790000	22200	104000	1340	873	508000	4400000
Habitat alteration [T&E count]	1.47E-11	0	9.69E-13	5.09E-15	8.25E-15	0	2.02E-11
HH cancer [g C6H6 eq]	17800	10.7	226	3.4	2.94	1750	6400
HH criteria air pollutants [microDALYs]	526	2.35	11.2	0.131	0.121	93	403
HH noncancer [g C7H7 eq]	20300000	8270	800000	7130	8760	1360000	25300000
Indoor air quality [g TVOC eq]	0	0	0	0	0	0	0
Natural resource depletion [MJ surplus]	42300	42.9	148	2.27	2.66	7050	925
Ozone depletion [g CFC-11 eq]	3.19	9.19E-7	0.00474	0.00015	0.000161	0.000151	0.0498
Smog [g NOx eq]	15300	485	261	8.18	3.62	4010	10100
Water intake [liters]	3470	0	1460	5.83	111	0	41700

Legend: AB - asphalt binder; CA - chemical additive.

Table 5. Characterization results for the for the second and third stage.

ICs [Unit]	Aggregates transportation (1 tkm)	AB transportation (1 tkm)	CA transportation (1 tkm)	NAs processing (1 ton)	Mixing process (1 MJ)
Acidification [H+ mmole eq]	177	22	509	314	31.1
Ecotoxicity [g 2.4-D eq]	2.74	14.1	7.07	9.28	0.29
Eutrophication [g N eq]	1.07	6.67	3.21	1.6	0.0513
Global warming [g CO2 eq]	442	118	1110	873	95.3
Habitat alteration [T&E count]	5.15E-15	1.38E-14	8.44E-15	8.25E-15	9.38E-17
HH cancer [g C6H6 eq]	2.02	12.5	6.04	2.94	0.131
HH criteria air pollutants [microDALYs]	0.0721	0.384	0.191	0.121	0.00923
HH noncancer [g C7H7 eq]	3180	14400	7470	8760	0.131
Indoor air quality [g TVOC eq]	0	0	0	0	0
Natural resource depletion [MJ surplus]	4.32	30	14.1	2.66	0.167
Ozone depletion [g CFC-11 eq]	0.000324	0.00226	0.00106	0.000161	125000
Smog [g NOx eq]	2.4	11.7	5.97	3.62	0.196
Water intake [liters]	0	0	0	111	0.0398

Legend: AB - asphalt binder; CA - chemical additive.

The analysis of the two previous tables permits the understanding of various features related to the contaminating potential of the WMA production. These are:

• The processing of the supplementary materials (CR, RAP, and RCA) impacts less on the environment than the production of NAs. The preceding is according to the magnitude of each of the ICs considered. Nevertheless, this behavior must be confronted with the side effects that these waste materials cause in the WMA design.

• In all ICs, the production of the chemical additive causes a higher environmental impact than the asphalt binder. The above could lead to conceiving that WMAs are more polluting than HMAs. Nonetheless, this fact must be contrasted with the typical additive doses, which are even less than 0.5% by asphalt binder weight (Diab et al., 2016; Behnood, 2020; Cheraghian et al., 2020; Sukhija & Saboo, 2021). Also, it is necessary to consider the reduction in the mixing and compaction temperatures.

• In each stage and sub-stages, the environmental impact associated with the generation of Total Volatile Organic Compounds (TVOC) is zero. Therefore, through chemical additive technology, the WMA production (with or without CR, RAP, and RCA contents) does not emit an appreciable amount of TVOC into the atmosphere.

From the data collected in Table 4 and Table 5, a mathematical model is proposed to estimate the environmental impacts associated with WMA production. The model was drafted under the scenario of implementing chemical additive technology and incorporating CR, RAP, and/or RCA as a partial replacement for NAs. The mentioned model is described by Equation (2). Besides, the subscripts of this equation represent each of the materials considered (i.e., NAs, CR, RAP, RCA, asphalt binder, and chemical additive). (2) $\mathrm{IC}=\left(\sum _{i=1}^n\mathrm{fi}\ast \mathrm{mi}\right)+\left(2\ast \sum _{i=1}^n\mathrm{si}\ast \mathrm{mi}\ast \mathrm{di}\right)+\left(t1\ast \mathrm{mNAs}+t2\ast \mathrm{TE}\right)$(2) Note: the meaning of the acronyms is presented in Table 6.

Table 6. Parameters that define Equation (2).

Acronyms	Description	Unit
IC	Estimation of the environmental impacts for each IC.	The one corresponding to each IC evaluated
fi	Unitary characterization results of material production stage determined for each material for each IC.
si	Unitary characterization results of material transport stage determined for each material for each IC.
t1	Unitary characterization results of NAs processing sub-stage determined for each IC.
t2	Unitary characterization results of mixing process sub-stage determined for each IC.
mi	Mass of each material required to produce 1 ton of WMA.	ton
mNAs	Mass of NAs required to produce 1 ton of WMA.
di	One-way transport distance of each material.	km
TE	Thermal energy required to produce 1 ton of WMA.	MJ
n	Number of materials employed for the WMA production.	-

3.4.2. Weighting process

Using Equation (2) it is possible to estimate each of the 13 ICs that compound the BEES+ model. Nonetheless, in LCAs, it is not common to analyze multiple ICs individually; on the contrary, it is suggested to use a weighting process to unify all environmental detriments in a single indicator (Tuomisto et al., 2012; Su et al., 2019). Hence, suitable weighting improves decision-making and reduces uncertainties and subjectivity (Du et al., 2019; Nikkhah et al., 2019; Miao et al., 2021). Therefore, it was decided to implement this additional step in the present investigation. Moreover, this procedure reduces the computational demand (in terms of time and requirements) that would generate the simultaneous minimization of all ICs by iterating the proportion of the materials (WMA mix designs). In other words, the weighting enhances the LCA and avoids many objectives optimization problems. The weights suggested by the U.S. Environmental Protection Agency (EPA) were employed; these numerical factors can be consulted in Table 7. The result of the weighting is identified as ‘points,’ abbreviated as ‘Pt’. Besides, this method is synthesized through Equation (3). (3) $\mathrm{Pt}={\displaystyle \frac{{\sum }_{j=1}^k\mathrm{ICj}\ast \mathrm{Wj}}{100}}$(3) Note: where ‘k’ is the number of IC considered by the IAM used.

Table 7. Numerical factors to perform the weighting process in the BEES+ model.

Source: SimaPro 9.1.1 and (Gloria et al., 2007).

IC	Unit	Weights (W)
Acidification	H+ mmole eq	5
Ecotoxicity	g 2.4-D eq	11
Eutrophication	g N eq	5
Global warming	g CO2 eq	16
Habitat alteration	T&E count	16
HH cancer	g C6H6 eq	5.5
HH criteria air pollutants	microDALYs	6
HH noncancer	g C7H7 eq	5.5
Indoor air quality	g TVOC eq	11
Natural resource depletion	MJ surplus	5
Ozone depletion	g CFC-11 eq	5
Smog	g NOx eq	6
Water intake	liters	3
TOTAL		100

4. Economic module

This module focuses on estimating the production costs of WMAs using LCC. The LCC is a technique applied for predicting and assessing the cost profitability of products, projects, and services over a specific period (either during the entire life cycle or during a part of it) (ISO, 2017; J. Santos, Flintsch, et al., 2017). When using the LCC to assess alternatives that have been environmentally evaluated through LCA, it is recommended to abide by the previously defined functional unit and system boundaries (Naves et al., 2019; Peña & Rovira-Val, 2020). Therefore, it has been defined that the WMA production has a cost equal to that defined in Equation (4). As in previous equations, the subscripts represent each of the required materials. (4) $\mathrm{PC}=\left(\sum _{i=1}^n\mathrm{mi}\ast P_{\mathrm{COSTi}}\right)+\left(\sum _{i=1}^n\mathrm{mi}\ast \mathrm{di}\ast T_{\mathrm{COSTi}}\right)+\left({\displaystyle \frac{\mathrm{TE}}{\mathrm{LHV}}\ast \mathrm{HF}{O}_{\mathrm{price}}}\right)$(4) Note: the meaning of the acronyms is presented in Table 8.

Table 8. Parameters that define Equation (4).

Acronyms	Description	Unit
PC	Production costs of 1 ton of WMA.	USD
P_COSTi	Production or processing costs of each material.	USD/ton
T_COSTi	Hauling costs of each material.	USD/ton/km
mi	Mass of each material required to produce 1 ton of WMA.	ton
di	One-way transport distance for each material.	km
TE	Thermal energy required to produce 1 ton of WMA.	MJ
HFO_price	Price of heavy fuel oil (typical fuel for asphalt mixing plants).	USD/kg
LHV	Lower heating value of heavy fuel oil.	MJ/kg
n	Number of materials employed for the WMA production.	-

Equation (4) presents three specific terms representing the stages within the defined system boundaries. These terms are explained below:

• The first term calculates the acquisition cost of the materials. This is the purchase price in the case of NAs, asphalt binder, and chemical additives. Meanwhile, for the supplementary materials (CR, RAP, and RCA) this is the cost of processing the solid wastes.

• The second term calculates the cost of transporting all the materials. In this instance, a simplification was adopted. It is considered that the distributor/supplier of the different materials cash out the totality of the one-way transport distance. The aforementioned is not entirely accurate because it is common in the industry that sellers of materials only charge the hauling activity when distances are higher than a specific limit.

• Finally, in the third term, the costs of the mixing process are estimated. Here another simplification was made; it was assumed that the cost of this process is equal to the price of the fuel necessary to achieve the required TE. To determine the fuel consumption (in kg of HFO), dividing the TE by the lower heating value is required (X. Chen & Wang, 2018; J. Santos et al., 2018). The lower heating value measures the quantity of heat obtained from the complete combustion of an energy source, usually associated with hydrocarbons (Basu, 2010; F. Di Maria & Lasagni, 2017; Posom & Sirisomboon, 2017). For this investigation, a typical value reported in the literature was used, that is, 42.18 MJ/kg (IEA, 2004; J. Santos et al., 2018; WNA, 2021).

LCCs are generally tailored to a particular case, including appropriate discount rates, analysis periods, and future costs (Hochschorner & Noring, 2011; Islam et al., 2015; Kambanou, 2020). However, all the WMA production costs are generated within a short time interval in this study. Hence, none of those mentioned above aspects was contemplated. Accordingly, only a cost estimation was performed in the ‘current year.’ In other words, economic indicators such as discounted payback period, internal rate of return, net present value, and profitability index were not calculated.

5. Decision-support module

5.1. Model formulation and solution approach

The objective function that constitutes the optimization process is expressed mathematically as follows: (5) $\begin{array}{rl}minF\left(x\right)& =\left[\begin{array}{c}\mathrm{Pt}\left(\mathrm{CR},\mathrm{RAP},\mathrm{RCA}\right),\\ \mathrm{PC}\left(\mathrm{CR},\mathrm{RAP},\mathrm{RCA}\right)\end{array}\right]\\ & \mathrm{subject}\mathrm{to}\{\begin{array}{c}0\le \mathrm{CR}\le 6\\ & 0\le \mathrm{RAP}\le 30\\ 0\le \mathrm{RCA}\le 45\\ & \mathrm{Pt}\le \mathrm{Pt}\left(\mathrm{CR},\mathrm{RAP},\mathrm{RCA}=0\right)\\ & \mathrm{PC}\le \mathrm{PC}\left(\mathrm{CR},\mathrm{RAP},\mathrm{RCA}=0\right)\end{array}\end{array}$(5) As mentioned throughout the paper, this research aims to develop a methodology for the sustainable design of WMA with supplementary material contents. Therefore, it is browsing for the optimal contents of CR, RAP, and/or RCA that manage to minimize two attributes, namely environmental impacts and production costs. For these purposes, Equation (3) and Equation (4) are defined as the objective functions (to be minimized). Also, the decision variables (or ‘genes’ as these are designated later) correspond to the proportion of alternative materials that achieve the proposed sustainability goal, i.e., generating less environmental burden and requiring smaller monetary investment than a traditional WMA. Consequently, the solution approach presents three constraints, which are:

• The inclusion of CR, RAP, and/or RCA could not generate an environmental impact higher than that associated with the control WMA (the case where these materials are not incorporated).

• The inclusion of CR, RAP, and/or RCA could not generate a higher production cost than the control WMA.

• Also, the maximum content for CR, RAP, and RCA is limited, as mentioned in Section 3.2.1.

5.2. Implemented gas

GAs are a group of metaheuristic optimization algorithms whose operating principle is inspired by the Darwinian evolution theory (Del Ser et al., 2019; Harini & Karthi, 2022). GAs perform their processes based on exploring search space and exploitation through genetic operators, namely selection, crossover, and mutation (Harini & Karthi, 2022; Venkata Lavanya et al., 2022). Although there are different types of GAs, each with its peculiarities, it is possible to identify the common aspects that serve as a general guideline for executing these techniques. According to some authors (Gutierrez et al., 2020; Hamida & Benjelloun, 2021), the typical steps are: (I) create the initial pseudo-random population (within certain thresholds); (II) apply the genetic operators (selection, crossover, and mutation) to the individuals that compose the initial population through specific algorithms to obtain a new population; (III) evaluate the current population using the objective function, optimization aims, constraints, and decision variables (genes); (IV) iterate the genes that constitute individuals utilizing genetic operators and an evolutionary algorithm until obtaining an adequate population in terms of fitness and convergence.

Figure 5 shows the implementation of GAs adopted in this research. This illustration exhibits that the proposed computational model is supported by the evolutionary algorithm called ‘eaSimple,’ as well as by other three algorithms, namely ‘selNSGA2,’ ‘cxOnePoint,’ and ‘mutUniformInt,’ which respectively correspond to the genetic operators for selection, crossover, and mutation. These canonical algorithms were executed through the Distributed Evolutionary Algorithms in Python (DEAP) library with the hyperparameter conditions presented in Table 9. DEAP is a framework for the Python programming language developed by the Vision and Numerical Systems Laboratory at the Laval University (Quebec, Canada) in 2012 (Fortin et al., 2012; Hamida & Benjelloun, 2021). The considerable collection of GAs included within DEAP (both strongly and loosely typed) makes this library a powerful tool for solving complex engineering problems (Kim & Yoo, 2019; Gutierrez et al., 2020). Based on (Fortin et al., 2012; Gutierrez et al., 2020), a brief description of each of the algorithms taken from DEAP is exposed below:

• eaSimple is one of the simplest versions of an evolutionary algorithm since the population size remains constant through the different iterations; therefore, results are obtained quickly.

• selNSGA2: creates an extended population, which is evaluated and classified according to their levels of dominance, then the individuals at lower levels pass to the following genetic operators.

• cxOnePoint: it randomly selects one gen from an individual to exchange the contained genetic information with another member of the population.

• mutUniformInt: it uses an independent probability to alter (within a specified range) the attributes associated with an individual.

  Figure 5. Optimization process through GAs proposed for this study.

  

  Table 9. Selected hyperparameter values to the proposed optimization process through GAs.

  Hyperparameter	Value
  Number of individuals	400
  Number of generations	80
  Crossover probability, Pcx	0.8
  Mutation probability, Pmut	0.2
  Independent probability for mutUniformInt	0.1

Figure 5 and Table 9 present the configuration of the computational model based on GAs that allowed to precisely optimize the sustainable design of WMA with the inclusion of supplementary materials as partial replacement of NAs. Notwithstanding, to reach the accurate set it was necessary to scan multiple combinations of hyperparameters and genetic operator algorithms (even some canonical GAs not present in DEAP were assessed). This experimentation procedure involved an extensive combinatorial search that permitted obtaining the most reliable possible performance in terms of accuracy, convergence, and execution time; that also conceived interesting aspects of the issue under evaluation. First, it is not mandatory to implement variable size population evolutionary algorithms. In this case study, minimalism turned out to be the most suitable option. Second, despite having short chromosomes (with only three (3) genes), the process of crossover by one point generated greater convergence than other algorithms. Third, it was more decisive to have a vast number of individuals than a large number of generations, which indicates that exploration of search space is more crucial than exploitation for this problem. Fourth, the adjustment of the probabilistic hyperparameters confirms the prevalence of exploration above exploitation. The preceding shows that the ideal balance between exploration and exploitation was found for the problem addressed in this investigation. Remarkably, not having an adequate harmony between exploration and exploitation criteria can lead to premature convergence concerns and the inability to find suitable solutions in GAs (Mirsaleh & Meybodi, 2018; Pelusi et al., 2020; Mohar et al., 2022). Thus, it was possible to establish a starting point to manage similar issues in future research efforts (Crepinsek et al., 2013; Singh & Deep, 2019; Chohan et al., 2021). On the other hand, intending to guarantee easy and free access to the proposed methodology, a simplified version of the computational model was uploaded (publicly available) to the GitHub repository: https://github.com/rpoloe/WMA-GAs-methodology.

The double criterion optimization proposed in this study ended with a Pareto front. Nevertheless, this information is presented in Section 6 to concentrate all the results in a single section of the article. A Pareto front is the graphical representation of the elite solutions associated with an optimization problem (Kurasova et al., 2013; Grygar & Fabricius, 2019). Pareto fronts allow identifying the behavior and trend of the set of optimal solutions, thus reducing complexity in decision making (Cibulski et al., 2020; Jafaryeganeh et al., 2020).

6. Case study and results report module

With the purpose to demonstrate the capabilities of the proposed computational model, a case study was developed to determine the optimal WMA designs in the context of the northern region of Colombia. Table 10 shows the features of the control mixture design, that is, without the addition of supplementary materials. Meanwhile, Table 11 exhibits the typical hauling distances for materials. There is no habitual hauling distance for the waste materials due to these can come from various places such as landfills, recycling plants, and demolition sites. Notwithstanding, it was decided to assume a critical scenario, i.e., consider that the one-way transport distance for the CR, RAP, and RCA is equal to twice that associated with NAs. Also, following Colombian National Roads Institutés recommendations, a price of 0.31 USD (per tkm) was adopted to transport all materials (INVIAS, 2021). In addition, Table 12 presents the typical acquisition costs of the different materials in the northern region of Colombia. This value represents the processing cost for the CR, RAP, and RCA. Likewise, there is no representative processing cost for the CR, RAP, and RCA. Hence, a severe condition was contemplated in which these values correspond to double the retail cost of the NAs.

Table 10. Composition and characteristics of the control WMA. Taken from: (Vega, Martinez-Arguelles, et al., 2020; Vega, Santos, et al., 2020a).

Item	Unit	Value
NAs	%^a	95.6
Asphalt binder	%^a	4.4
Chemical additive	%^b	0.3
Ambient temperature	°C	25
Mixing temperature	°C	120

Notes: ^a Percentage of total mixture weight; ^b Percentage of asphalt binder weight.

Table 11. Hauling distances adopted for this study. Taken from: (Vega, Santos, et al., 2020a).

Material	One-way transport distance (km)
Asphalt binder	592
Chemical additive	248
NAs	73

* Value assumed considering the worst possible scenario.

Table 12. Standard prices in the northern region of Colombia.

Material	Acquisition costs
	Unit	Value
Asphalt binder	USD/ton	115
Chemical additive	USD/ton	150
NAs	USD/ton	9.4
HFO	USD/kg	1.18

According to the methodology procedure described in Sections 5-6, the WMA design was optimized, resulting in the Pareto front presented in Figure 6. This graph manifests that multiple mix design alternatives minimize production costs and environmental impacts (expressed in units of Mega-Points, that is, Points/1000000). Figure 6 shows a trend following the theory of Pareto optimality, which mentions that it is not possible to improve one of the variables to be optimized without affecting the other (Kurasova et al., 2013; Rao & Lakshmi, 2021). Figure 7 displays the composition of two WMA forms part of the Pareto front, i.e., among the more fitting WMA designs. This illustration reveals that there are several possibilities to guarantee sustainability principles. This gives asphalt mix producers a wide range of options to operate. Figure 8 exposes a ternary chart of the unitary composition of the supplementary materials considered as genes. This triangle plot indicates that most viable mix designs (lower environmental burden and monetary investment than the control WMA) are composed of similar amounts of RAP and RCA, which suggests that these materials counteract each other's effects on asphalt binder consumption. Finally, Figure 9 examines CR, RAP, and RCA's influence on the optimization criteria. For this, the 500 most suitable (in compliance with fitness) WMA designs were analyzed. The evaluation above confirms that RCA is the least desired waste material in WMAs because the increment in the optimal asphalt content increases production costs. Nevertheless, as discussed previously, this counterproductive impact is neutralized when RCA is combined with appreciable quantities of RAP.

Figure 6. Pareto front obtained for the case study.

Figure 7. Percentage composition of the materials that compose two of the most suitable WMA designs. Legend: mAB – modified asphalt binder.

Figure 8. Ternary plot for the unitary composition of CR, RAP, and RCA in the viable mix designs.

Figure 9. Effect of supplementary materials on optimization criteria.

6.1. Analysis of the predominance of certain IC

Among the different factors that influence the achievement of optimal mixture designs, the IC weights are one of the most adaptable by the researcher according to the context and the particular environmental necessities of each project. For instance, if the environmental policies of a country or state only focus their guidelines on reducing CO2 emissions, then the only target IC would be Global Warming. The methodology proposed in this research is effortlessly and precisely adjustable for these unique requirements. It is only necessary to give 100% weight to the IC mentioned above, while the other impact categories are assigned 0% influence. Consequently, Figure 10 presents the mix designs that minimize the environmental burden associated with WMA production for each IC recognized in the BEES+ model. Thus, it is possible to show the predominance of the different IC over the optimization process. The case study data under consideration (Tables 9-12) were used for this analysis. It is clarified that the economic module is kept in concern for the execution of this assessment. The findings that emerge after the examination of Figure 10 are detailed below.

Figure 10. Optimal contents of supplementary materials considering a single IC. Acronyms: AC – acidification; EC – ecotoxicity; EU – eutrophication; GW – global warming; HA – habitat alteration; HHC – HH cancer; HHP – HH criteria air pollutants; HHN – HH noncancer; IAQ – indoor air quality; NRD – natural resource depletion; OD – ozone depletion; SM – smog; WI – water intake.

This figure makes it possible to determine that in cases in which the environmental criteria objective minimizes a single IC, the optimal WMA designs are highly variable. For instance, based on global warming, it is obtained that the best design is composed of 5.8, 25, and 27% of CR, RAP, and RCA, respectively. Meanwhile, the most suitable waste material dosage considering the ecotoxicity is only formed by 6 and 19% of CR and RAP, respectively. In 6 impact categories, namely ecotoxicity, eutrophication, HH cancer, HH noncancer, ozone depletion, and smog, the minimal environmental burden is generated when the maximum allowable amount (from a mechanical point of view) of CR is utilized. In the other ICs, the lowest environmental damage is achieved at great CR content. The above indicates that using this waste material to replace NAs is highly competitive from an economic-environmental perspective. Accordingly, it was demonstrated that the increase in mixing temperature caused by the CR does not reach to outshine the economic-environmental savings induced by mitigating the depletion of NAs.

Furthermore, Figure 10 exhibits that high contents of RAP generate the most significant environmental benefits. Even in the IC with greater restrictions (i.e., eutrophication), the optimal replacement dosage is 19% of the total NAs. This situation is associated with the reduction in demand for the asphalt binder that RAP causes and, consequently, the less requirement for chemical additives. In other words, the mitigation of the environmental impacts of the incorporation of RAP involves more than one component of the mix design. Figure 10 also shows that RCA is the waste material that generates the most negligible environmental benefits (concerning the other materials evaluated in this research). This is evidenced in three ICs, namely ecotoxicity, eutrophication, and indoor air quality, which produce the lowest environmental burdens when the RCA quantity is zero. Even in other IC (acidification, HH cancer, ozone depletion, and water intake), the optimal content of coarse RCA is less than 10%. This is occasioned by the additional environmental impact associated with the increase in the optimal asphalt content caused by the high porosity and absorption of RCAs.

6.2. Running time

The running time analysis is one of the most significant evaluations to measure the efficiency of optimization algorithms (Tirado & Valero, 2009; Early & Schellekens, 2013; Doan & Kalita, 2017). In the case of evolutionary algorithms, due to their stochastic component and associated uncertainties, the execution times are habitually long; therefore, this analysis is essential to understanding the explanatory capacity of the models (Gupta et al., 2015; Bian et al., 2020). Consequently, it was decided to measure the running time of the proposed optimization process (Figure 5). Pythońs native module called ‘TIME’ was implemented for these purposes. Further, data reported in Tables 9-12 were adopted. After executing 100 occasions the complete code (including the Pareto front generation) independently, it was possible to determine that the minimum, average and maximum time required were 9.8, 10.6, and 11.4 seconds, respectively. Figure 11 shows the detail of this analysis.

Figure 11. Record of the running time of the proposed methodology in 100 independent executions.

To establish a comparison point regarding the efficiency of the GAs implementation, the running time needed to solve this optimization problem was also assessed under traditional methods, i.e., through an extensive search. This type of procedure involves the evaluation of all conceivable scenarios. For these purposes, all possible combinations of waste materials were considered as follows: (6) $\mathrm{for}\{\begin{array}{c}0\le \mathrm{CR}\le 6\\ 0\le \mathrm{RAP}\le 30\\ 0\le \mathrm{RCA}\le 45\end{array}\mathrm{in}\mathrm{steps}\mathrm{of}0.1\text{\%}\stackrel{\mathrm{yields}}{\to }8280810\mathrm{scenarios}$(6) Consequently, optimization through extensive search led to calculating environmental impact and production costs repeated for the 8280810 possible scenarios. This procedure required approximately 490 seconds of running time (measured via the TIME module). Thus, the optimization methodology using GAs denotes a time saving of around 97-98%. Furthermore, this execution is relatively fast within the evolutionary computation context and can be associated with applying constant population sizes instead of a variable size population.

Undoubtedly, the execution time is affected by the characteristics of the development environment and the computer employed. Therefore, to simulate a non-advantageous case, non-professional everyday systems were used for this analysis. To be transparent, the specifications of these elements are listed below:

• Computer: Laptop with AMD Ryzen™ 7 3700U microprocessor, 8GB of DDR4 SDRAM, and a 512GB M.2 PCIe® NVMe™ solid-state drive.

• Development environment: an online tool with software acceleration disabled, i.e., neither graphics processing unit nor tensor processing unit was utilized.

7. Conclusions

In this study, a methodology based on GAs was developed to optimize the design of WMA from economic and environmental criteria with three supplementary material contents, namely CR, RAP, and RCA. As technical support, LCA and LCC procedures were employed. Also, influences on the mix design caused by the aforementioned waste materials were considered. The optimal configuration of GAs to solve this multi-objective optimization problem was achieved through the DEAP library. In addition, to guarantee free access to the methodology, the programmed codes were uploaded to the GitHub repository under an open license to the public. The main conclusions obtained from this research are listed below:

• The chemical additives production for WMAs generates more prominent contaminating potential than the asphalt binder production. Nonetheless, the reduction in the mixing and compaction temperatures that these agents cause makes the WMA a sustainable alternative compared to HMA.

• Remarkably, the production of chemical additive WMA technology (with or without supplemental materials) does not produce an appreciable quantity of TVOC.

• Although the supplementary materials processing generates less environmental impact than the NAs production, it is necessary to consider the influences that the CR, RAP, and RCA have on the mixture design. The results suggest that higher RCA contents could generate a more elevated environmental burden, but this is not entirely accurate because the simultaneous inclusion of RCA and RAP (in similar quantities) confers neutrality in the alterations concerning the optimal asphalt content.

• Even in the adverse scenario presented in the case study developed in this article, it was possible to detect multiple WMA designs with supplementary material content that generate a lower monetary investment and environmental impact than the control case.

• The best combination of GAs obtained to solve the multi-objective optimization problem posed in this paper was composed of the algorithms eaSimple, selNSGA2, cxOnePoint, and mutUniformInt, respectively, for the evolutionary algorithm, selection operator, crossover operator, and mutation operator.

• The optimal values determined for the number of individuals, the number of generations, and the probabilistic hyperparameters indicate that to find viable solutions to the multi-objective optimization problem posed, the exploration of search space is more decisive than the exploitation. Notably, it was unnecessary to use a procedure involving variable size populations. This enabled the development of a fast convergence computational model.

8. Future research lines

The formulation of the optimization model focuses on Equations (3)-(4). These mathematical expressions originate from an LCA and LCC, respectively. Consonantly, the proposed optimization process is internally based on an LCA-LCC integration. The above provides a remarkably robust analysis framework because combining these techniques facilitates decision-making from a multi-criteria perspective, even approaching an ultimate sustainability assessment (Jeswani et al., 2010; Bradley et al., 2018; Sackey & Kim, 2018; Calado et al., 2019). Although this type of methodology is not wholly novel (similar strategies have already been employed for the evaluation of hydraulic concretes (Kurda et al., 2019a, 2019b)), the contribution of this article to state of the art prevails in establishing the first base to recognize the feasibility of large-scale production of this type of asphalt concrete.

In particular, it is necessary to discuss two aspects of the proposed methodology: the weighting process and the social costs. Notably, the weighting of the environmental burdens performs an essential role in optimization efficiency (both conceptual and computational). Nevertheless, in this study, it was selected to use constant weights. In retrospect, dynamic weighting may have been of greater interest to the literature. Because in this way, it would be possible to obtain the most suitable alternatives in different time windows, namely in short-term, medium-term, and long-term planning (Su et al., 2017, 2019; Sohn et al., 2020). Likewise, considering the potential of the evolutionary algorithm system implemented, it would have been possible to minimize the social costs of the analysis. This may have been achieved through various techniques, for example, employing the environmental prices of the environmental impacts (Y. Coulombel et al., 2018; de Bruyn et al., 2018; Chen et al., 2021). Consequently, it might be feasible to obtain a more comprehensive sustainability analysis. It is expected to address the above aspects in future research efforts to increase the road infrastructure's eco-friendly attributes.

On the other hand, it is necessary to involve the experimental component more in-deep in future research. Specifically, it is essential to verify that the optimal WMA designs satisfy the minimum quality standards required for asphalt mixtures. Consequently, it is recommended to carry out laboratories test and evaluate trial sections. Furthermore, if the WMAs do not present acceptable mechanical and volumetric behavior, new restrictions or conditions for incorporating recycled materials must be determined to solve such inconvenience.

Acknowledgements and conflicts of interest

The authors express their gratitude to the Administrative Department of Science, Technology, and Innovation (COLCIENCIAS) and the Universidad del Norte for funding this study through ‘Research Project 745/2016, Contract 037-2017, No. 1215-745-59105.’ The authors declare no conflicts of interest.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Departamento Administrativo de Ciencia Tecnologia e Innovacion (COLCIENCIAS) [Grant Number 745/2016].