REDUCED-IMPACT LOGGING BY ALLOCATING LOG-DECKS USING MULTIOBJECTIVE EVOLUTIONARY ALGORITHM IN WESTERN AMAZON

– To reduce the damage caused by logging in the Amazon rainforest, new metaheuristics have been implemented and tested to ensure the sustainability of this economic segment. Therefore, this study aimed to compare alternatives for road sizing and log deck allocation. In a forest management unit, the skidding to log decks was evaluated in two diﬀ erent areas. To determine the skidding/log deck relation, georeferenced points were generated equally spaced every 50 m. In area 1, the Integer Linear Programming (ILP) model and the Multi-Objective Evolutionary Algorithm (MOEA) were compared. In area 2, only the MOEA was considered. In both areas, these models were also compared to the current planning used in the forest management unit. Solutions were then generated to identify the best management alternative. In both areas, the MOEA showed greater eﬃ ciency regarding the processing time, as well as the reduction of log decks number and the road sizing. The multi-objective evolutionary approach assists the decision-making process, due to the presentation of alternatives based on Pareto-optimal solutions, making the choice more ﬂ exible and well supported.


INTRODUCTION
The activities planning involving the extraction of wood in the Amazon region are ruled by Normative Instruction No. 5/2006(Brasil, 2006, of the Ministry of the Environment, andby Resolution No. 406/2009 (Brasil, 2009), of the National Environment Council. In general, these legal instruments seek to standardize criteria to ensure the sustainable management of these forests.
In this context, logging Brazilian Amazon consists of three phases: pre-exploratory, exploratory, and postexploratory. These phases allow the manager, in terms of forest planning, to reduce the impacts caused by logging. The damage caused by the lack of planning is: tree felling near the tree to be exploited due to lack of silvicultural treatments, construction of roads and patios more than necessary, lack of maintenance of forest exploitation area after harvest, among other factors. One problem in the Amazon, which involves decision making, is to determine the location of log decks allocation in the Annual Operational Plan. Martinhago (2012) used Integer Linear Programming (ILP) method, based on the P-median technique, in Acre and Pará states in order to reduce the impacts of log deck allocation. However, this author identifi ed that log deck allocation is a diffi cult task to be solved due to the large number of variables, which prevents the use of classical techniques such as ILP. Due to confl icting interests in the planning of the activity, natural resource managers can approach the problem of forest management as a multi-objective optimization problem, since such objectives are conservation and production.
The metaheuristics, or approximate methods, are part of a class of algorithms considered at a higher level than the heuristics, and can be applied in a range of problems and can be customized through logical rules of programming and components (Boussaïd et al., 2013). These algorithms are usually based on laws or behaviors found in nature and are successfully applied in several problems in forestry by researchers such as Steiguer et al. (2003), Ducheyne et al. (2006), Fotakis et al. (2012), Gomide et al. (2013), Hernandez et al. (2014), Maier et al. (2014), Fotakis (2015), Liu andLin (2015), andÁ lvarez-Miranda et al. (2018).
This study aimed to compare alternatives for road sizing and for log deck allocation, in order to reduce the impacts of logging on the Amazon rainforest, by comparing the planning used in a forest management unit with ILP and Multi-Objective Evolutionary Algorithm (MOEA) methods. The main contribution is to provide a number of fl exible responses to the same problem, a fact not usually observed in exact resolution methods, allowing the selection of options at each favorable time of forest planning.

Problem description
In order to carry out the sustainable forest management plan activities, it is necessary to follow certain criteria established by Normative Instruction n. 5, December 11, 2006(Brasil, 2006. These criteria demand from the technical manager -a forest engineer -that the fi eld team accomplishes the forest exploitation planning respecting current laws, in other words, causing minimal damage to the forest. Thus, in order to reduce forest operations impacts, it is fundamental to defi ne an ideal number of log decks in the forest management area.
The log decks number is directly related to whether it is capacitated facility location problem or not. The capacitated log desks consider the maximum amount of wood that can be stored in it, and only after the log decks have their full capacity fi lled, the stocked wood will be removed. The non-capacitated log deck has no storage limit because wood transport is carried out continuously. Thus, it is necessary to defi ne the ideal number of log decks to be built in the managed area, since it implies the entire planning of forest exploitation area.

Sustainable forest management plan
The study was developed in a forest management unit named "Cipoal Farm". This unit was divided into area 1 (189.19 ha) and area 2 (2,609.22 ha). Both present vegetation consisting of open tropical rainforest, with the presence of trees, bamboos, and palm trees (Acre, 2010). Besides, "Cipoal Farm" is predominantly characterized by a fl at terrain composed of argisol (Acre, 2010). Timber transportation took place through forest roads; furthermore, the farm has easy access to BR-364 near the Rio Branco timber processing center. The forest inventory was started with the marking and the numbering of trees in aluminum tags. Subsequently, the botanical identifi cation of the individuals, the measurement of diameter at breast height (DBH) and commercial height, and the quality of the stem were determined. Finally, the individuals were georeferenced.
To simulate the location of log decks, points were generated every 50 m along the forest road, considering only its layout, that is, the forest road established in forest planning, in a Geographic Information System (GIS). These geo-referenced points were considered as the center of the log decks.
In order to solve the problem, in the capacitated and non-capacitated forms, two approaches were used, one exact and the other approximate, using the integer linear programming (ILP) and the multiobjective evolutionary algorithms (MOEA).

Integer linear programming
The proposed model for ILP solution was based on a mathematical model formulated to solve the problem of p-medians. In this approach, the proposed objective-function was to reduce the skidding to log decks. Thus, the objective-function (1) seeks to reduce the sum of the displacement of the N logs i to the P decks j, where the displacement was represented by the Euclidean distance, defi ned as a linear metric measure. The restrictions used were: (2) selection of logs i to be directed to a single deck j, (3) exclusive log skidding to a single deck, (4) restriction defi ning the number of decks to be installed for log storage (ND), (5) restriction defi ning the maximum capacity of log storage (capacitated form), defi ned as V J = 1.000 m³ according to Martinhago (2012), (6)  Where: Z = vector resulting from the sum of log displacement i to the decks j; x ij = binary decision variable {0, 1} used to displace the log i to the decks j; y j = binary decision variable {0, 1} used to activate the deck j; v ij = individual merchantable volume with bark (m 3 ) of the log i allocated to the deck j; ND = number of decks to be capacitated; c ij = skidding cost in meters (Euclidean distance) between log i and deck j, where i = {1,2, ..., 900}; J = {1,2, ..., 30}. The ILP mathematical model was formulated and processed in the Language for Interactive General Optimizer (LINGO) software (Lindo, 2015), version 16.0, on a computer with Intel® Core™ i3 3.10 GHz processor and 8 Gb of RAM.

Multi-objective evolutionary algorithm
In MOEA approach, a vector optimization problem was elaborated formed by two confl icting objectives: i. to reduce log skidding to the respective deck; ii. to reduce the number of capacitated decks (ND). This problem was written according to Equations 7 and 8, subjected to the same restrictions presented in ILP approach, excepted for Equation 4, which in this proposal became one of the objectives to be reduced. In this situation, from the moment that a deck becomes capacitated, the trees less distance from the deck are assigned to this deck, provided that it does not exceed the allowed volume (capacitated form). Eq.7 Eq.8 Where: Z = vector resulting from the sum of log displacement i to the decks j; x ij = binary decision variable {0, 1} used to displace the log i to the decks j; y j = binary decision variable {0, 1} used to activate the deck (j); ND = number of decks to be capacitated; c ij = displacement in meters cost (Euclidean distance) between log i and deck j, where i = {1,2, ..., 900}; J = {1,2, ..., 30}.
For bi-objective problem solving, it was used the Improved Nondominated Sorting Genetic Algorithm (NSGA-II), proposed by Deb et al. (2002) (Figure  1). Although other evolutionary multiobjective optimization algorithms have been proposed for many-objective problems (3 or more objectives), the use of the NSGA-II is still recommended for two objectives optimization problems (Deb and Jain, 2014;Zhou et al, 2019).
In the fi rst step of this algorithm, a population sized Nd with bit-string type individuals (binary coding) was created. Each individual has D binary values corresponding to the activation or not of the log deck j. To make the algorithm more effi cient, the initial population was created from the k-means clustering algorithm, using Euclidean distance as a metric. Thus, if the individual to be created has ND = 15 (capacitated decks), the k-means is executed to defi ne 15 centroids according to the trees' location. Therefore, log decks whose coordinates are closest to the centroids are enabled.
After evaluating each individual through biobjective functions it was used the fast non dominated sort function, a procedure to classify the population in diff erent non-dominance layers. First, the Pareto set is determined in the population (F1). Shortly after, individuals belonging to F1 are excluded from the process and the next Pareto set is obtained (F2). This procedure is repeated until all individuals are sorted into one layer.
Since then, the crowding distance (CD) assignment function estimates the population solutions density around a particular solution taking the mean value of the distance between this solution and the two solutions on either side of it along each of the objectives (Deb et al., 2002). As well as the fast non dominated sort function, this function is fundamental for the selection procedure because it maintains a certain degree of diversity in the population.
The selection procedure is implemented by stochastic tournament, where two individuals are randomly chosen and the best one is selected, considering their non-dominance (F) layer and the density of solutions around them. After this step, crossing operators (two cut-off points) and mutation (uniform) common to evolutionary algorithms (EA) are implemented and the algorithm is executed by Ng generations. NSGA-II was performed on a population of 300 individuals, 200 generations, crossover probability equal to 0.9, and mutation probability equal to 0.1.
The minimum number of log decks for capacitated form was defi ned considering the total volume of trees to be harvested and the total volume capacity of each deck. Thus, for area 1 and area 2, the minimum numbers of decks to be activated in 6 units and 52 units, respectively, were defi ned. Their maximum values were equal to 30 units and 150 units, in this order. These values were attributed following the recommendation of Braz and Oliveira (2001) who reported that a viable distance for log dragging should be established between 150 m to 200 m, and it can be extended up to a maximum of 400 m in order to not compromise the log dragging operation performed by the Skidder (forestry tractor), which could cause an increase in the operation cost.

ILP and MOEA comparison
In area 1, the ILP and MOEA methods were compared to the current planning used in the forest management unit, where 1 to 30 log decks were considered, for the not capacitated problem. used in the forest management unit. In this case, only the capacitated problem was undertaken. The decks' location total number was 871 and trees number was 8,319, which makes this combinatorial optimization problem quite complex. In order to carry out the comparison, the minimum value of 52 and the maximum of 150 decks were considered. For this example, the size of the population was 2,000 individuals and 1,000 generations, and the remaining confi guration was equal to the previous problem of area 1.
The NSGA-II algorithm was implemented using Matlab software (Matlab, 2011), version R2011b. The exploration maps were performed in ArcMap software (Esri, 2015), version 10.3. The results fi gures were created in the free software Gimp, version 2.8.20 (Gimp, 2020).

RESULTS
In area 1, it was found that MOEA obtained results close to the ILP (mean percentage error of 0.29%), as can be seen by the solutions of both presented in (Figure 2). When comparing the number of log decks to 6 and 13 decks, the results of the objective function were 180,631.80 m and 178,857.70 m, capacitated and non-capacitated, respectively, for ILP. Meanwhile, the results of the MOEA were 182,904.31 m and 179,525.27 m, capacitated and non-capacitated, respectively, concerning the results of ILP objective functions. The average processing time of ILP was 4min09s and 1min01s, capacitated and non-capacitated, respectively, while MOEA was 46s for capacitated and 30s for non-capacitated form.
Subsequently, MOEA was performed for the entire area 2. The MOEA obtained solutions in an average time of 38.174s. The Pareto-optimal solutions obtained are presented in (Figure 3).
Comparing MOEA to the current planning used in the forest management unit (Table 1), a scenario with 119 active decks, a reduction of 5.80% in road sizing by MOEA were observed.
( Figure 4) shows the log decks allocation determined by MOEA, compared to the current planning performed in the fi eld.
It should be noted that the proposed multiobjective evolutionary approach helps to reduce computational processing time (which made it feasible obtaining solutions in the total area), and assists the team responsible for the project to choose the most suitable alternative among several other management alternatives (through Pareto-optimal solutions), with more fl exibility and technical-scientifi c support.

DISCUSSION
Unlike the ILP that considers optimal solution, the MOEA presents the results according to the Pareto solution, in which the best results are shown, allowing the selection of those that aid in the decision-making in planning.
Comparing the MOEA to ILP, it can be observed (Figure 2) they are close to the optimal solution for  capacitated and non-capacitated problems. The mean percentage error was 0.29% of MOEA concerning the ILP. Nascimento et al. (2012) obtained the best solution with Particle Swarm Optimization (PSO) algorithm with the gbest topology concerning the ibest topology. The result considering the gbest topology was 99.07% of optimal forest planning but did not present satisfactory results concerning the mean and the minimum value. Liu and Lin (2015) proposed the use of Cultural algorithm to maximize the total volume in logging and they got better results of 0.44% and 1.13% concerning the Simulated Annealing (SA) algorithm.
MOEA processing time was better than the ILP. However, it should be noted that the MOEA present several results simultaneously, which does not occur with ILP. Gomide et al. (2013) observed that, by improving the confi guration of AS metaheuristic, it was possible to improve processing time and to obtain results close to the optimal solution.
Observing area 2, MOEA presented better results regarding the reduction of log decks and, consequently, a reduction in road construction in the forest management area. However, the solution found by MOEA will no longer allocate log decks at strategic points in the forest management area, where the log could not be moved to the deck through protect areas, such as Permanent Preservation Areas (PPA).
It should be noted that the solution obtained by MOEA will only consider the road outlined in the forest management plan. Consequently, some restrictions on log deck allocation were not considered, such as bridges, PPA, sharp relief, swampy or rocky areas. However, MOEA presents high fl exibility, allowing further inclusion of some conditions imposed by the forest, such as streams, fallen trees, and land slope in the optimization process, useful information for choosing the best number of log decks to be enabled.
The 119-log deck scenario generated by MOEA, unlike the current planning performed in the fi eld, reduced their oversize, since it was possible to fi nd a smaller number of capacitated decks. This scenario contributed to forest road reduction as well as the damages caused in remnants of native vegetation. As can be seen in (Figure 3), when considering 52, 60, 70, and 119 log decks, there is a decrease in road sizing. Thus, the specialist can carry out a better planning for the forest management area, reducing the impacts generated by logging.
However, the presented results show that the NSGA-II algorithm obtained good solutions for the log/deck allocation problem. Proper planning, that is, proper log deck allocation, reduces the damage caused to the forest and allows the logging of remaining trees for the next forestry (Braz and Oliveira 2001).
The proposed evolutionary multi-objective approach enabled the reduction of computational processing time (which allowed the achievement of solutions in the whole area) as well as the presentation of several management alternatives (Pareto-optimal solutions) to the project manager, rendering the decision-making more fl exible and well-supported. Medjibe and Putz (2012) affi rm that lack of proper planning in logging (such as maps for log deck allocation, forest roads, and skidding tracks) results in damage to the forest. Ducheyne et al. (2006) found that spatial analysis has a set of objective functions but, in some situations, the objectives may be confl icting. Therefore, these researchers realized that the multi-objective genetic algorithm implementation in spatial analysis with operational research is advantageous, as it allowed working with confl icting objectives between objective functions. Fotakis et al. (2012) and Fotakis (2015) used a special approach with a multi-objective genetic algorithm in forest planning and they found better results regarding wood volume maximization, and sediment levels minimization.

CONCLUSIONS
MOEA presented satisfactory results when compared to ILP in a management problem for area 1. MOEA was also implemented for log deck allocation in a larger management area, where it was not possible to implement ILP due to a large number of decision variables. Thus, for both area 1 and area 2 the proposed approach was compared to the current planning performed in the fi eld, which proved the effi ciency of the algorithm since, for the same number of capacitated log decks, a smaller skidding was found. In addition, MOEA provides several other solutions, with a smaller number of capacitated log decks, promoting fl exibility in decision-making. This fl exibility allows conditions imposed by the forest not considered during the optimization process that can be used to choose the best number of log decks to be enabled.

6.ACKNOWLEDGMENTS
This work was supported by Coordination for the Improvement of Higher Education Personnel (CAPES). The authors thank the University of Lavras for scientifi c support, especially the Forest Sciences Department and the Laboratory of Signal Processing from Engineering Department and Lindo Systems Inc.. This research did not receive any specifi c grant from funding agencies in the public, commercial, or not-for-profi t sectors.

AUTHOR CONTRIBUTIONS
Marcos Antonio Isaac Júnior -organization, data processing with integer linear programming, analysis of results, and writing.Bruno Henrique Groenner Barbosa -data processing using the genetic algorithm, and review.Lucas Rezende Gomide -methodological design, analysis of results, and review.Natalino Calegario -methodological design, analysis of results, and review.Evandro Orfanó Figueiredo -availability of the database, analysis of results, and review. Luiz Otávio Moras Filho -bibliographic research, discussion of results, revision, and translation.Elliezer de Almeida Melo -bibliographic research, discussion of results, and review.Daniel Dantas -bibliographic research, discussion of results, and review.