Research articleMetaheuristics applied for storage yards allocation in an Amazonian sustainable forest management area
Introduction
Sustainable forest management (SFM) is the main technique employed for tropical timber exploitation in Brazilian Amazon areas. SFM premises selective felling of commercial trees above a minimum felling diameter (MFD), in compliance with current Brazilian legislation. For execution of SFM activities, it is necessary to install logging infrastructures (forest roads, storage yards and skid trails). Forest roads are intended to connect all timber storage yards providing a more efficient transportation. After felled, and skidded, tree logs are kept in storage yards. Skid trail is the path usually taken by the Skidder during logging.
Thus, optimized planning is essential for these infrastructures as they generate costs and environmental impacts, and their allocation represents a complex decision making process due to involved variables (Contreras and Chung, 2007; E. F. Silva et al., 2018a, 2018b; Søvde et al., 2013). It is common an intuitive infrastructure planning (Philippart et al., 2012; E. F. Silva et al., 2018a, 2018b) with geographic information system (GIS) support (Baskent and Keles, 2005; Liu and Sessions, 1993; Newnham, 1995). This intuitive process is linked to decision makers experience, who spends more time allocating infrastructure than analyzing planning feasibility (E. F. Silva et al., 2018a, 2018b). Storage yards have fundamental importance in planning infrastructure because their location impacts on the forest roads and skid trails opening (Philippart et al., 2012). Therefore, optimized planning can reduce the amount of infrastructure required and, consequently, costs and environmental impacts.
Allocation of wood storage yards in forest management areas can be performed by mathematical programming. In this case, the mathematical model associated with the p-median problem, which is a Binary Integer Linear Programming (BILP) problem, can be adopted. However, defining storage yards allocation in large areas of SFM increases combinations exponentially. This factor makes it impossible to use exact methods to obtain solutions in acceptable computational time. (Philippart et al., 2012; E. F. Silva et al., 2018a, 2018b).
Thus, although recent studies have contributed to the definition of model, variables and constraints associated with the problem (Contreras and Chung, 2007; Philippart et al., 2012; Silva et al., 2018a, 2018b) it is necessary to investigate methods capable to be applied in areas of size consistent with the reality found in the planning of forestry companies.
Recent studies have investigated the solution of p-median problem using metaheuristics presenting good results with variations from Simulated Annealing (SA), Tabu Search (TS), Variable Neighborhood Search (VNS) and Greedy Randomized Adaptive Search Procedure [(GRASP)] (Bornstein and Azlan, 1998; Delmaire et al., 1999; Fernandes et al., 2014; Fleszar and Hindi, 2008; França et al., 1999; Guastaroba and Speranza, 2014; Ho, 2015; Montoya et al., 2016; Santosa and Kresna, 2015; Yaghini et al., 2013).
The p-median problem applied to the allocation of wooden storage yards has particularities (Philippart et al., 2012; Silva et al., 2018a, 2018b). Than above, the objective of this research was to evaluate wood storage yards allocation problem by metaheuristics and exact solution in an Amazonian forest management area located in Brazil.
This research contributes to evaluate alternative computational methods for planning the allocation of wooden storage yards. The analysis took into account two aspects: the effectiveness when applying the methods in large areas and the efficiency when considering the time need to obtain satisfactory results. In this sense, it was possible to evidence the effectiveness and efficiency of the metaheuristics and evaluate the applicability of these methods to solve the problem.
Section snippets
Methodology
The following methodological steps were adopted to perform the present research: formation of the processing database; optimization model and metaheuristics; parameters tuning and processing; and, analyzes and results. The methodological scheme (Fig. 1) represents the necessary steps for the development of this research.
Results
Considering that the yard allocation problem is an NP-hard problem, the area size is a key factor for the solving methods. In this research, three instances with different area sizes were used for comparison. The size of the resulting optimization model was summarized in Table 6 and for the three areas the number of variables ranged between 1 million and 19 million. The number of constraints ranged between 2 million and 38 million. These values exceed those of previous researches such as
Discussion
Studies related to storage yard allocation have generally been applied to small management areas (Contreras and Chung, 2007; Philippart et al., 2012; Silva et al., 2018a, 2018b). Clearly, there are limitations in obtaining exact solutions for mathematical models of integer linear programming, due to exponential growth in the number of variables. This can be observed in studies that show increasing complexity as the number of variables grows (Fernandes et al., 2014; Guastaroba and Speranza, 2014
Conclusion
In general, metaheuristics were efficient in obtaining feasible solutions faster than CPLEX, which represents feasibility of planning storage yards allocation over large areas, and without significant loss of accuracy of best-known solution. SA meta-heuristic had the best performance for the analyzed planning problem, followed by VNS, TS and GRASP. For the third and largest instance, the SA method was the only metaheuristic capable to obtain feasible solutions. The solutions obtained by SA were
CRediT authorship contribution statement
Marcelo Otone Aguiar: Conceptualization, Methodology, Software, Formal analysis, Writing - review & editing, Data curation. Gilson Fernandes da Silva: Supervision, Project administration. Geraldo Regis Mauri: Writing - review & editing, Supervision. Evandro Ferreira da Silva: Conceptualization, Methodology, Data curation. Adriano Ribeiro de Mendonça: Writing - review & editing. Jeferson Pereira Martins Silva: Writing - review & editing, Visualization, Data curation. Rodrigo Freitas Silva:
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research was partly supported by the National Council for Scientific and Technological Development – CNPq (Process 302261/2019–2), Foundation for the Support of Research and Innovation of Espírito Santo (FAPES) and Coordination for the Improvement of Higher Education Personnel (CAPES). This support is gratefully acknowledged. The authors thank the reviewers for their valuable suggestions.
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