Multi-objective optimization for the green vehicle routing problem: A systematic literature review and future directions

Abstract This article aims to present research conducted on the literature regarding multi-objective optimization for routing problems with environmental considerations, referred to here as Multi-objective Optimization for the Green Vehicle Routing Problem (MOOGVRP). A Brazilian database, CAPES (Coordination for the Improvement of Higher Education Personnel), was used to collect articles of general application, case studies and reviews in English starting from, since 2012. The terms “green vehicle routing problem” (GVRP), “pollution routing problem” (PRP), “vehicle routing problem in reverse logistics” (VRPRL) and “multi-objective” were used in the research protocol. Consequently, this study obtained 1,744 research results that, following the application of the filtering criterion, resulted in a sample of 76 articles from 38 journals, for which a bibliometric data (bibliometric review) survey was conducted. The originality of this article lies in how the research is presented, highlighting the results and details obtained through the survey, which may be considered of great academic importance in the sense of guiding the trends for future research.


PUBLIC INTEREST STATEMENT
This article aims to present research conducted on the literature regarding multi-objective optimization for routing problems with environmental considerations. Here referred as Multi-objective Optimization for the Green Vehicle Routing Problem (MOOGVRP). Thus, through the bibliometric data we intend to present the directions for future research.

Introduction
In 2015, the UN (United Nations) proposed an agenda with 17 sustainable development goals to be implemented by all countries by the year 2030. The present study especially focuses on Goals 12 and 13 of this document. It addresses Goal 12 (Responsible consumption and production) by seeking an intelligent and optimized alternative to perform activities, and Goal 13 (Climate action) by seeking to reduce greenhouse gas emissions (ONUBR, 2015).
According to the report published by the United States Environmental Protection Agency (US EPA, 2018), the sources of greenhouse gas (GHG) emissions include five main sectors: Transportation; Electricity; Industry; Commercial and Residential; and Agriculture, as shown in Figure 1, which presents their respective percentages. In this study, the emphasis will be on the "share" related to Transportation (28.5%). Regarding this "share", we found the following results: CO 2 from Fossil Fuel Combustion (27.4%), Substitution of Ozone Depleting Substances (0.7%), Mobile Combustion (0.3%) and Non-Energy Use of Fuels (0.1%). Of these, this study will address the issues related to CO 2 from Fossil Fuel Combustion and Mobile Combustion.
The Vehicle Routing Problem (VRP), proposed by Dantzing and Ramser (1959), is highly significant for an efficient logistic distribution (Poonthalir & Nadarajan, 2018;Validi et al., 2015). The Green Vehicle Routing Problem (GVRP) directs routing activities through a perspective with environmental considerations (Toro et al., 2017a;Soleimani et al., 2018). Thus, a Multi-objective approach aids this process of complex decision-making in order to meet the objectives to be achieved (Ramos et al., 2014;Steiner et al., 2015;Steiner Neto et al., 2017).
In a complementary manner, the Triple Bottom Line of sustainability aids a real understanding of the application of Environmental Considerations to the VRP by addressing economic aspects through cost reductions, environmental considerations through GHG emissions and fuel consumption, and social considerations, such as work conditions and opportunities.
The aim of this study is to present research conducted on the literature regarding Multi-objective optimization (MOO) for vehicle routing problems with Environmental Considerations, referred to here as MOO for the Green Vehicle Routing Problem (MOOGVRP). Thus, this work aims to detect gaps in the literature for development and advances in this field of knowledge. This has been recognized as an important theme in a wide range of previous literature reviews, such as that of Demir et al. (2014a).
The originality of this article lies in how the research is presented, showing the results and peculiarities obtained through the content analysis (systematic review), with the bibliometric data collection (bibliometric review) regarding the published articles related to the analyzed problem from 2012 to 2018.
The present work is organized as follows. After this introductory section, the methodological procedures are presented in Section 2. Section 3 contains a brief presentation of the Multi-objective approach (the VRP approach) and its variations, as well as the VRP with Environmental Considerations. In Section 4, the results are explained and discussed. The conclusions of the study are summarized in Section 5.

Methodological procedures
For the methodology of this research, the following steps were established as a search protocol ( Figure 2 shows the flowchart of the review process methodology of this research): (1) First, the timeline cut, covering the period between 2012 and 2018, in order to identify the recent discussions analyzed by academia; (2) Database selection: the study used the Brazilian database of CAPES (Coordination for Improvement of Higher Education Personnel), which gathers and makes available international scientific content for educational and research institutions in Brazil, composed of 38,000 journals, 532 reference databases including Cambridge Journals Online, Emerald Insight Emerald, IEEE Xplore, Scopus (Elsevier), Science Direct, SpringerLink, Taylor & Francis, as well as books, encyclopedias, technical standards, statistics and audiovisual content (Szejka et al., 2017); (3) The English language was adopted to select the articles; (4) Only journals (articles) were searched; (5) The keywords, as well as the logical operators used were: "green vehicle routing problem" OR "pollution routing problem" OR "vehicle routing problem in reverse logistics", which were necessarily linked to "multiobjective" OR "multi-objective" OR "bi-objective". The possible suffix variations in the terms used were also taken into account. The terms related to routing with Environmental Considerations were obtained from the literature review proposed by Lin et al. (2014); Figure 2. Flowchart of the review process methodology.
(6) As an acceptance criterion, it was established that: (i) the research result should present the "green vehicle routing problem", "pollution routing problem" or "vehicle routing problem in reverse logistics", all of them being "multi-objective". For this purpose, the titles and abstracts were assessed, as exemplified in Figure 2; (ii) they could be literature "review", "general" application (mathematical modeling and/or algorithm improvement articles), as well as "case" studies related to the proposed theme. As exclusion criteria, it was established that the results would be excluded if: (i) they were not related to the proposed theme; (ii) did not have full text available; (7) Remove duplicate articles.
From the protocol presented, we obtained 1,744 research results that, after the protocol filter, resulted in 76 articles for the research sample, from 38 journals. From this selection of articles, this study conducted a critical analysis of the research scope and sought to answer three questions: 1)What are the main discussions regarding MOOGVRP in recent surveys?
2)What are the most relevant studies regarding MOOGVRP?
3)What are the trends regarding MOOGVRP that may guide future research?

Theoretical framework
In this section, we briefly present the problems of MOO, the VRP and its variations, as well as the VRP with Environmental Considerations, which will be subdivided into the GVRP, Pollution Routing Problem (PRP) and Vehicle Routing Problem in Reverse Logistics (VRPRL).

Multi-objective optimization
MOO addresses the process of simultaneously optimizing two or more conflicting objectives subject to restrictions (Kumar et al., 2016;Steiner Neto et al., 2017). Its mathematical representation is presented using the objective function in Eq. (1) and restrictions in (2)(3)(4)(5).
where, x: vector of decision variables of dimension n; Z and f(x): correspond to the vector of the objective functions of dimension k; g(x): It is the set of inequality constraints of size m; h(x), the set of equality constraints of dimension p. In (1), the space Z = f(x) deals with the image of X, called feasible region in the space of objective functions. The restrictions presented in (2) and (3) define the space of the decision variables in R n feasible region X and any point x ∊ X as a feasible solution.
MOO methods can be classified into generative methods and preference-based methods. The generative methods seek to generate one or more Pareto optimal points and can take into account the "non-use" for preferences, a scale approach or a multi-objective approach. The preference-based methods use information provided by the decision maker a priori or iteratively, as part of their solution process.
The classic methods commonly used for solving MOO problems can be organized into four categories. The first addresses the methods that do not articulate the given information of preference, such as the Method of Global Criterion. In the second one, we have a priori preferences, such as the Methods for Cardinal Information Given (Utility Function and Bounded Objective) and the Methods for Mixed Ordinal and Cardinal Information Given (Lexicographic Method and Goal Programing). In the third category, we have the methods for progressive articulation, most notably the Methods for Explicit Trade-Off Information Given (iterative methods) and implicit methods. Finally, we have a posteriori methods, among which we find the Parametric Method, є-constraint, Multi-objective Linear Programming and Adaptative Search (Demir et al., 2014a;Kumar et al., 2016).
According to Heilig et al. (2017), the most frequently used Multi-objective techniques are: weighted sum scalarization, the є-constraint method, goal programming, lexicographic ordering and Pareto optimization. In relation to weighted sum scalarization, we must assign weights and treat the problem as a linear combination of established objectives. In the case of the є-constraint method, only one objective must be optimized, and the others must be considered as problem restrictions. In goal programming, the purpose is to meet all objectives, taking account of the goals established for each criterion. Lexicographic ordering considers an order of importance from the sequence in which the proposed objectives were listed. Finally, in Pareto optimization, an a posteriori approach provides the Pareto frontier with the intention of performing the trade-off of the solutions of the different objectives. According to Marler and Arora (2004), the drawbacks of MOO are related to the complexity in developing the algorithms and usually require more computational effort than mono-objective techniques.

Vehicle routing problem
VRPs have many variations in the literature, and some of them are presented in Table 1 (in alphabetical order), as proposed by Lin et al. (2014) and Braekers et al. (2016), followed by a brief description. It is worth mentioning that two or more of these variations can be combined, generating new variations for the VRP.

VRP with environmental considerations
When addressing the VRP with Environmental Considerations, the classification proposed by Lin et al. (2014) was used here, which sticks to the PRP, GVRP and VRPRL. The PRP search vehicle routing plan produces a lesser amount of pollution, in particular with a reduction in GHG and may include broader objectives that reflect the environmental cost. The GVRP considers the optimization of energy consumption in transport and reduction of fuel consumption. The objective of the VRPRL focuses on aspects of reverse logistics distribution. The latter category, VRPRL, can be divided into sub-categories: Selective Pickups with Pricing, Waste Collection, End-of-life Goods Collection and Simultaneous Distribution and Collection.
Selective Pickups with Pricing selects only profitable collection points to visit. Waste Collection (waste management) includes waste reuse, prevention and recycling. End-of-life Goods Collection is useful for remanufacturing. Finally, the Simultaneous Distribution and Collection addresses applied modeling in the context of reverse logistics (Demir et al., 2014b;Lin et al., 2014;Soleimani et al., 2018).
Additionally, Demir et al. (2014a), in their review article, present, systematize and compare techniques for measuring GHG emission and fuel consumption applied to the road transportation of green loads.
Environmental Considerations can be addressed in one or more Objective Functions (OF) subject to restraints through mathematical modeling, be it a linear, non-linear, integer, mixed or dynamic programming model or other approach. In this study, emphasis will be placed on the OFs focusing on the environmental, social and economic contexts, reverse logistics, fuel consumption and CO 2 emissions.
Thus, it can be said that many authors are concerned with minimizing costs, be they operational, general, financial or for transport (Abad et al., 2018;Govindan et al., 2017;S. Wang et al., 2018b) or maximizing revenues or profit (Niknamfar & Niaki, 2016;Zohal & Soleimani, 2016)  Multi-depot VRP Has more than one deposit. Each script starts and ends in the same deposit.
Multi-echelon VRP Easily applied to true needs, aims to minimize the total cost of transportation of the vehicles involved at all levels, i.e., freight delivery covers the entire chain and is required to be carried out through an intermediary deposit; therefore, several stages are performed.
Open VRP Each route is a Hamiltonian path instead of a Hamiltonian cycle. The vehicles are not required to return to the depot after finalizing their activities.
Periodic VRP Seeks feasible routing so that the cost associated with the time horizon is minimized.
Pickup and Delivery Problem Considers the collection and/or delivery of goods. Large variations are available in the literature.
Site-dependent VRP There is compatible independence between clients (sites) and types of vehicles. Each customer can be visited by only a predefined group of vehicle types.
Split-delivery VRP Each customer can be served by one or more vehicle.
Stochastic VRP Occurs in non-randomness of elements such as travel times, customer demand or customer groups. aspect, a point in question is maximizing work opportunities (Ouhader & El Kyal, 2017), in addition to working hours (Ramos et al., 2014) and social responsibility (Govindan et al., 2016;Zhu & Hu, 2017). When it comes to reverse logistics, this is more difficult to measure, as not all problems found are clearly attributed to an OF, but rather to the consequent stratifications of its results

Results and discussion
In this section, we present the bibliometric data. This study identified information such as the quantity of publications per year, type of works published in the sample and percentage of journals that focus on sustainability (environmental, economic and social aspects). The study also shows the most frequently journals, countries and institutions that published the most works on the proposed theme, a frequency analysis of protocol terms in the title, abstracts and keywords and the relation between the taxonomies employed. Other information includes the relationship regarding the Triple Bottom Line, the fleets that are used and the most commonly used MOO procedures, VRP procedures, solution procedures, number of objectives and most frequently used metaheuristic methods. The software and programming languages for computational implementation and the frequency of the most used objectives were also identified.
The study also includes the works related to the theme in question and a table summarizing the most frequently cited articles in the sample.
As presented in Section 2 (Methodology), this research sample was composed of 76 articles. Figure 3 shows that the number of articles on the proposed theme has increased over the years. It should be highlighted that the sample of 76 articles was collected from 2012 to 2018. Table 2 shows the number of authors, article types and the journals on sustainability in the sample. Regarding the number of authors, the articles with two, three and four authors correspond to 65 papers in the sample, demonstrating the existence of research groups or works developed in academic environments. As the article types, the articles were classified as General (27 articles), Case studies (43 articles) and Reviews (6 articles). The journals on sustainability, as also shown was verified that only 10 of the 38 journals in the sample focus on issues related to sustainability (more specifically, they show interest in environmental aspects, sustainability, ecology, green manufacturing, the environment and related contexts). Where namely: Applied Energy, Computers & Operations Research, Decision Science Letters, Ecological Indicators, International Energy & Environment, Journal of Cleaner Production, Journal of Manufacturing Systems, Journal of Manufacturing Technology Management, Sustainability and Transportation Research Part D. Table 3 shows the journals, institutions and countries that contributed to the MOOGVRP sample. They are organized by name and quantity. For the journals, it is worth noting that marked with (*) consider sustainability aspects, of which the Journal of Cleaner Production is the most used. For the institutions (institutions, research centers and companies with which the authors are associated), note that several articles cover more than one affiliation. We can particularly highlight three universities in Iran, Iran   (2); Belgium, Chile, Indonesia, Italy, Japan, Morocco, New Zealand, Portugal, Singapore, Turkey and the United Arab Emirates (1).
This relationship is made clearer in Figure 5(a). This analysis is extremely important to the study because it is through these terms that the researchers achieved the sample for their works. It can be seen that the greater frequency of terms is concentrated in the abstract of articles and that there are few works that contain the search terms in the three fields.
Figure 5(a) shows the relationship between the taxonomies of the VRP with Environmental Considerations presented here. We can observe (yellow circle on the left) that 12 articles in the sample address the MOO-GVRP (Abad et al., 2018;Androutsopoulos & Zografos, 2017;Coelho et al., 2017;Demir et al., 2014b;Hassanzadeh & Rasti-Barzoki, 2017;Norouzi et al., 2017;Poonthalir & Nadarajan, 2018;Psychas et al., 2016;Rani & Reddy, 2017;Rao et al., 2016;Rau et al., 2018;S. Wang et al., 2018b). Ten articles address the MOO-GVRP in conjunction with MOO-PRP (Khoo & Teoh, 2014;Amer et al., 2016;Baykasoğlu & Subulan, 2016;Niknamfar & Niaki, 2016;Kumar et al., 2017;Toro et al., 2017aToro et al., , 2017bDas & Jharkharia, 2018;Shui & Szeto, 2018;Rad & Nahavandi, 2018). Five articles address the MOO-GVRP in conjunction with the MOO-PRP and with the MOO-VRPRL (Farrokhi-Asl et al., 2018;Gupta et al., 2017;Lin et al., 2014;Malladi & Sowlati, 2018;Soleimani et al., 2018). Finally, one article addresses the MOO-GVRP together with the MOO-VRPRL (Gong et al., 2018). Thus, a total of 28 articles are related to the MOO-GVRP. Likewise, we can interpret the other circles (left and right). It should be highlighted that the goal of the GVRP is different from that of the PRP, since the objective of the former is to reduce fuel or energy consumption (or the battery, alternatively) and the latter seeks to minimize GHG emissions, mainly CO 2 . It was observed that in some articles the authors implicitly used their own taxonomy, as in Heilig et al. (2017), Tricoire and Parragh (2017)  In Figure 5(b), for the stratification of the pillars of the Triple Bottom Line, according to Dias (2011), it was considered that for the economic dimensions, companies have to be economically feasible, in the sense of providing a return on investment. For the environmental dimension, companies should adapt to achieve ecoefficiency. In the social dimensions, companies should make changes such as providing better working conditions for their employees. In this context, articles will be categorized as economic when the OFs of their mathematical models are related to minimizing costs (general and/or operational, for instance), environmental when they seek to minimize GHG emissions and fuel, and social when they seek to improve working conditions for employees, for example, by increasing the number of jobs.
In this way, with Figure 5(b), we can verify that most of the works are related to economic (costs) and environmental (GHG emission and fuel consumption) aspects. However, the lack of articles that address the social aspects indicates a good opportunity for advances in the literature. The same is true when trying to unite the three pillars in this context. For example, the article published by Y. Wang et al. (2018a) was considered only economic in nature because the goals of its mathematical model sought to minimize costs and the number of vehicles. The work by Shui and Szeto (2018) was considered only environmental in nature because the bi-objective problem involved GHG emissions and fuel consumption in the second OF, while the first OF was not related to the Triple Bottom Line. The article by Ouhader and El Kyal (2017) was considered Triple Bottom Line (the link between social, economic and environmental) because the tri-objective problem sought to minimize costs, minimize GHG emissions and maximize social impacts through the creation of work opportunities in accordance with the capacities of the facilities.
Figures 6 to 11 are related to articles classified as General and Case Studies (70 articles). The review articles (six articles) will not be considered in these figures because of their wide coverage. Figure 6 shows the fleet classification (homogeneous or heterogeneous) through the sample articles.
Regarding the MOO procedures presented in Figure 7, we can verify the predominance of the Pareto to analyze the dominance or non-dominance of the obtained solutions. We then have the classification of the use of heuristic, є-constraint and weighted procedures. It is worth noting that several articles include more than one procedure.
Pareto Optimal is a complementary technique for multi-objective procedures, showing the better feasible solutions (options) in a graph for the decision maker. In this paper, it is used as part of the heuristic algorithm procedure or evaluate a population formed by the є-constraint method.
As for the VRP procedures shown in Figure 8, it must be taken into account that the same problem may contain more than one variant, in accordance with the works conducted by Ramos et al. (2014), Ghezavati and Beigi (2016) Figure 9(b) shows that 45 (64%) of the articles analyzed presented an approach with only two objectives and 22 (31%) are tri-objective. Figure 9(c) shows the use proportion of heuristic procedures in the MOO context. We can observe that the techniques derived from population algorithms are predominant, where GA and PSO correspond to 54%.   language, and that some software accepts different languages. Some authors reported only the software, others only the programming language, and there were some works lacking this information.
Legend: AMPL (A Mathematical Programming Language), CPLEX (Simplex method as implemented in the C programming language), GAMS (General Algebraic Modeling System), LINGO (Language for Interactive General Optimizer) and MATLAB (MATrix LABoratory). Figure 11 presents the main objective used in the 70 analyzed works. They were grouped into GVRP (Figure 11(a)), PRP (Figure 11(b)) and VRPRL (Figure 113(c)), with all of them being multiobjective. We can observe that all prioritize the minimization of costs among the main objectives. In the case of the GVRP, the minimization of fuel consumption is also among the main objectives. The same occurs with the PRP with CO 2 minimization.
The most cited works in the sample are presented in Table 4. This table is structured by references, journals, article type and number of citations obtained through SCOPUS. A description of these works, listed according to their number of citations, is given below. In Appendix A we present brief reports of the sample of 76 articles in this study.
The three most frequently cited works were literature reviews, conducted by Dekker et al.

Figure 9. Solution approaches (a), approach (b) and metaheuristics used (c).
a proposed taxonomy for the VRP with environmental considerations (GVRP, PRP and VRPRL). A study on green road freight transportation was presented by Demir et al. (2014a), making use of different ways to measure CO 2 emissions and fuel consumption. They identified the criticality of factors to explain consumption, type of vehicle, freight, speed and road gradient, among others.
A case study addressing perishable food distribution was conducted by Govindan et al. (2014). For this purpose, the authors used MOPSO, adapted multi-objective variable neighborhood search and the multi-objective hybrid approach, comparatively. Seeking to optimize fuel consumption and journey time, Demir et al. (2014b) used the є-constraint together with the weighting method for the adaptive large neighborhood search algorithm, in addition to a hybrid method. With a view to obtaining a sustainable distribution by minimizing costs and CO 2 emission for milk transportation in Ireland, Validi et al. (2014) presented a mixed integer linear programming model and solved the problem through procedures derived from the GA: multi-objective GA of kind II (MOGA-II), NSGA-II (non-dominated sorting GA II) and a Hybrid combining GA and sequential quadratic programming. Ramos et al. (2014) resolved a case study on a recyclable waste collection system in Portugal, more specifically, in 19 rural municipalities. This reverse logistics problem was modeled as a multi-  2012) presented a case study on the routing of bicycles in New Zealand, seeking to minimize journey time and maximize the adequacy of the routes that were used. Finally, Kumar et al. (2016) presented production and PRP with Time Windows, in which they implemented the hybrid Self-Learning PSO. The authors sought to minimize costs and fuel consumption.

Final considerations and suggestions for future works
This study presented bibliometric data involving MOOGVRP from 2012 to 2018. This study adopted a protocol that resulted in 1,744 articles that, after a filtering definition, provided a sample of 76 articles from 38 journals. Its main contribution that it highlights the synergy between the VRP, MOO and the approach with Environmental Considerations, which is a relatively new trend that has grown in recent years. The bibliometric analysis was essential to understanding the profiles of published works.
The most relevant studies during the period in question were presented in Table 4, in which the three most frequently cited articles were reviews. Dekker et al. (2012) and Demir et al. (2014a) addressed aspects related to logistics, while Lin et al. (2014) sought to demonstrate the evolution and relationship of the VRP with environmental considerations. The other most frequently cited articles sought to improve techniques and apply them to real contexts. Appendix A summarized the proposal of the 76 articles focused on reviews, general application and case studies. The sample authors are associated with 96 institutions, research centers and companies, and the largest contributions, so far, have come from Iran, China, the US and the UK. Figure 5(a) proved to be very interesting, as it shows the amount of work developed considering GVRP, PRP and VRPRL, as well as their interactions in the analyzed sample. In Figure 5(b), this study conducted a similar analysis, taking into account the triple bottom line.
It was possible to verify the dominance of bi-objective models, which have been solved through heuristic, є-constraint and weighted procedures, with "a posteriori" Pareto optimization, based on GA and PSO. The most used VRP procedures in the analyzed sample were the LRP and CVRP. As shown in Figure 11, the main objectives addressed in the problems were to minimize costs, fuel consumption and CO 2 emissions. There was great concern over improving the studies related to the reduction of GHG emission and the considerations of reverse logistics.
Many opportunities to explore applications and techniques related to MOOGVRP remain. We hope that the information presented here can aid those interested in their future research. Thus, by "going against the grain" of the most frequently researched themes, there is a great opportunity to make unprecedented contributions, of which the following may be mentioned: (c) Exploring applications that involve four or more objectives due to the serious lack of such applications in the literature; (d) Developing studies with large instances given the computational difficulty; (e) Presenting works that address the relationships between the MOO-GVRP, MOO-PRP and MOO-VRPRL or all of them simultaneously; (f) Researching better the social aspect of the Triple Bottom Line, addressing themes such as working hours, customer and/or employee satisfaction and risks in routes to be traveled.

Appendix A
A summary of the 76 articles related to MMGVRP is presented in Table A1. This Table is organized by references, presented in alphabetical and chronological order. The type of research of the articles was classified as a case study (c), general application (g) when the focus is on technique and literature review (r). The fleet of vehicle was classified as homogeneous (ho), heterogeneous (he) or not informed (ni). The VRP with EC was classified by the taxonomy used in this study: GVRP, PRP and VRPRL. It was determined whether the articles sought to meet the Triple Bottom Line requirements and whether the procedures used were exact, heuristic or, alternatively, both approaches. The number of objectives was organized as bi-objective (bi), tri-objective (tri) or multi-objective (multi). The desired outcomes of the study, the proposed application of the work, the solution techniques and number of citations were then specified (May 2018 through SCOPUS).    Legend: ABC (artificial bee colony); ALNS (adaptive large neighborhood search algorithm); AMOSA (achieved multi-objective simulated annealing); AMOVNS (adapted multi-objective variable neighborhood search); AUGMENCON (augment constraint algorithm); BEG-NSGA-II (bee evolutionary algorithm guiding nondominated sorting genetic algorithm II); BIOBAB (bi-objective branch-andbound); CA (Cultural algorithm); CW_NSGA-II (Clarke and Wright savings method and the non-dominated sorting genetic algorithm-II); EABC (enhanced artificial bee colony); ESMPO (evolution-strategybased memetic pareto optimization); HQIA (hybrid quantum immune algorithm); MIP (mixed integer programming); MILP (mixed integer linear programming); MNIP (mixed non-linear integer programming); MOACO (multi-objective ant colony optimization); MODE (multi-objective differential evolution); MOGA (multi-objective genetic algorithm); MOLS (multi-objective Local Search);