https://orcid.org/0000-0003-3374-6565
Figures & data
Table 1. Previous review papers on meta-heuristics in logistics and SCM.
Figure 1. Publishing trend in the area of meta-heuristic-based solution approaches in forward SSCM.
Line chart illustrating the publishing trend since 2007. The number of papers published before 2014 is scant. Since then, the number of papers begins to increase and follows a considerable growth in recent years such that almost 50% of all papers have been published in 2019 and 2020.
Figure 2. Distribution of publications by journals.
Bar chart showing the number of publications by each contributing journal in the extant literature. Among these journals, the “Journal of Cleaner Production”, the “Computers and Industrial Engineering” and the “International Journal of Production Research” place at the top of the list with 27, 14 and 11 contributions, respectively.
Figure 3. Selected categories to classify and analyze the literature of interest.
Diagram categorizing the extant literature into three classes of metaheuristics, sustainable supply chain problems and aspects of sustainability.
Figure 4. Distribution of the top-ten meta-heuristics used in the reviewed literature.
Column chart illustrating the frequency of the use of top-ten metaheuristics including GA, NSGA-II, PSO, SA, TS, MOEA, MOPSO, VNS, LNSA, and EA/DE in both pure and hybrid format.
Figure 5. Combination of algorithms used in the literature to craft hybrid single-objective meta-heuristics. Figure (5-a). Hybridisation between common and more used meta-heuristics. Figure (5-b). Combination between common meta-heuristics and other algorithms.
Two graphs presenting how different algorithms are combined to develop hybrid singleobjective metaheuristics. Nodes show the algorithms and edges show the hybridization between them.
Figure 6. Combination of algorithms used in the literature to build hybrid multi-objective metaheuristics.
Graph presenting how different algorithms are combined to develop hybrid multi-objective metaheuristics. Nodes show the algorithms and edges show the hybridization between them.
Figure 7. Matheuristic algorithms used in the reviewed literature.
Graph presenting the link between metaheuristics and mathematical programming techniques to construct matheuristic algorithms.
Table 2. Classification of meta-heuristics for forward SSCM and related number of algorithms used in each class.
Table 3. Type and number of algorithms used for each category of problems.
Table 4. Full list of sustainability indicators considered in the reviewed literature.
Figure 8. Distribution of papers over sustainability categories (based on Carter and Rogers (Citation2008)).
Venn diagram showing the number of papers in each category of sustainability.
Figure 9. Evolution of two most-noticed categories of sustainability in the reviewed literature.
Line chart showing the ascending trend of publications since 2013 considering economicenvironmental and economic-environmental-social categories of sustainability.
Table 5. Type and number of meta-heuristics used for each category of problems and aspects of sustainability.
Figure 10. Trend of the meta-heuristics used in the reviewed literature over the last five years. Figure (10-a). Trend of five leading single-objective meta-heuristics over the last five years. Figure (10-b). Trend of two major multi-objective meta-heuristics over the last five years.
Two line charts showing the trend of the most-used meta-heuristics in the literature over the last five years where GA and NSGA-I are the dominant single-objective and multi-objective algorithms, respectively.
Figure 11. Trend of pure and hybrid meta-heuristics used in the reviewed literature over years.
Line chart showing the comparative trend of pure and hybrid meta-heuristics used in the literature over years where hybrid algorithms are overtaking the pure ones since 2019.
Figure 12. Trend of the six most-addressed problems in the reviewed literature over years.
Line chart showing the comparative trend of the six most-addressed problems in the literature over years where the line for VRP is mostly above the others.
Figure 13. Number of papers using single-objective and multi-objective meta-heuristics to solve models considering economic-environmental and economic-environmental-social issues.
Comparative column chart including four columns showing the number of papers using single-objective and multi-objective meta-heuristics to solve models considering economic-environmental and economic-environmental-social issues. The highest belongs to single-objective metaheuristics used in economicenvironmental category.
Data availability statement
The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.