Metaheuristics applied for storage yards allocation in an Amazonian sustainable forest management area

Highlights

• Optimized planning reduces the complexity of decision making.

• Optimized storage yard allocation reduces average drag distance.

• The amount of variables makes it impossible to solve by exact methods in a viable time.

• Simulated annealing metaheuristic was the most efficient in different instances.

Abstract

In the sustainable management of Amazonian forests, it is essential to carry out the optimal planning of logging infrastructures to reduce costs and environmental impacts. However, there is a high degree of complexity due to the number of variables involved. Among these infrastructures, wood storage yards are of utmost importance as they directly influence the opening of forest roads and trails. The objective of this research was to evaluate the allocation of wood storage yards through exact solution and metaheuristics in a forest management area. The study area was a native forest under sustainable forest management regime located in the Brazilian Amazon. Three instances were formulated involving 5947 trees and 3172 wood storage yards facilities. We used a binary integer programming model solved by CPLEX and the metaheuristics Greedy Randomized Adaptive Search Procedure (GRASP), Tabu Search (TS), Variable Neighborhood Search (VNS) and Simulated Annealing (SA). GAP values increased as a function of instances. Although all metaheuristics obtained significant solutions with shorter processing times, only SA obtained feasible solutions in all executions for all three instances. In general, the metaheuristics were efficient in obtaining feasible solutions faster than CPLEX, which represents the feasibility of the planning of allocation storage large areas, and without significant losses of best-known solution. The SA presented the best performance in the three evaluated instances. Contribution of this study can be highlighted: evaluation of alternative computational methods for planning the allocation of wooden storage yards; evidence was obtained of effectiveness and efficiency of assessed metaheuristics and, the applicability of approximate methods in this problem was evaluated.

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.