Agrarian Sciences Journal
Performance of four meta-heuristics to solve a forestry production planning problem
Emanuelly Canabrava Magalhães
*, Carlos Alberto Araújo Júnior
, Francisco Conesa Roca
, Mylla Vyctória
Coutinho Sousa
The use of artificial intelligence as a tool to aid in the planning of forest production has gained more and more space.
Highlighting the metaheuristics, due to the ability to generate optimal solutions for a given optimization problem in a
short time, without great computational effort. The present study aims to evaluate the performance of the metaheuris-
tics Genetic Algorithm, Simulated Annealing, Variable Neighborhood Search and Clonal Selection Algorithm applied
in a model of regulation of forest production. It was considered a planning horizon of 16 years, in which the model
aims to maximize the Net Present Value (NPV), having as restrictions age of cut between 5 and 7 years and minimum
and maximum logging demand of 140,000 and 160,000 m
, respectively. Different combinations of configurations
were considered for each of the metaheuristics, 30-second processing time and 30 replicates for each configuration,
all processing being performed in MeP - Metaheuristics for forest Planning software. The Simulated Annealing me-
taheuristic obtained the best results when compared to the others, reaching the minimum and maximum demand
demanded in all tested configurations, in contrast, the Genetic Algorithm was the one with the worst performance.
Thus, the capacity to use metaheuristics as a tool for forest planning is observed.
Keywords: Artificial intelligence. Forestry. Forest management. Operational research.
Performance de quatro metaheurísticas para solução de um problema de planejamento da
produção florestal
O uso da inteligência artificial como ferramenta de auxílio ao planejamento da produção florestal tem ganhado cada
vez mais espaço. Destacando-se as metaheurísticas, em função da capacidade de gerar soluções ótimas para determi-
nado problema de otimização em um curto espaço de tempo, sem grande esforço computacional. Pensando nisso, o
presente estudo objetiva avaliar o desempenho das metaheurísticas Algoritmo Genético, Simulated Annealing, Variable
Neighbourhood Search e Clonal Selection Algorithm aplicadas em um modelo de regulação da produção florestal. Foi
considerado um horizonte de planejamento de 16 anos, no qual o modelo apresenta como objetivo a maximização
do Valor Presente Líquido (VPL), tendo como restrições idade de corte entre 5 e 7 anos e demanda mínima e máxima
madeireira de 140.000 e 160.000 m
, respectivamente. Considerou-se diferentes combinações de configurações para
cada uma das metaheurísticas, tempo de processamento de 30 segundos e 30 repetições para cada configuração, sendo
todo o processamento realizado no software MeP - Metaheuristics for Forest Planning. A metaheurística Simulated
Annealing obteve os melhores resultados quando comparada as demais, atingindo a demanda mínima e máxima exi-
gida em todas as configurações testadas, em contrapartida, o Algoritmo Genético foi o de pior desempenho. Assim,
observa-se a capacidade de uso da metaheurística como ferramenta de planejamento florestal.
Palavras-chave: Inteligência Artificial. Silvicultura. Manejo Florestal. Pesquisa Operacional.
Universidade Federal de Minas Gerais. Instituto de Ciências Agrárias. Montes Claros, MG. Brasil.
Universidade Federal de Minas Gerais. Instituto de Ciências Agrárias. Montes Claros, MG. Brasil.
Universidad de Huelva. Huelva. España.
Universidade Federal de Minas Gerais. Instituto de Ciências Agrárias. Montes Claros, MG. Brasil.
*Autor para correspondência:
Recebido para publicação em 28 de outubro de 2019. Aceito para publicação em 02 de fevereiro de 2020.
e-ISSN: 2447-6218 / ISSN: 2447-6218 / © 2009, Universidade Federal de Minas Gerais, Todos os direitos reservados.
Magalhães, E. C. et al.
Cad. Ciênc. Agrá., v. 12, p. 01–05, 2020. e-ISSN: 2447-6218 / ISSN: 1984-6738
One of the main challenges of the forest sector
is to attend to the growing demand for wood from legal
sources, which should be done to optimize the production
process and regulate the remaining stock over the years
(Araújo Júnior, 2012). A regulated forest is subject to
management regulations that allow the uniformity of
volumetric production. This avoids the lack of wood and
provides sustainability to the enterprise (Carvalho et al.,
These issues are related to the long-term planning
of forest production (Werneburg, 2015), whose planning
horizon is more than sixteen years due to the period of
growth and development of the raw material, which crea-
tes greater complexity for the process of creating strategic
plans. This task is commonly performed with the aid of
operational research tools, such as linear programming
(PL) and integer linear programming (PLI). However,
depending on the desired detail for the solution of the
problem, PL and PLI have limitations that result in the
impossibility to use or use with high computational effort
(Araújo Júnior et al., 2017).
This is due to the fact that there is a need to find
a solution composed by a considerable set of binary-type
decision variables that relate to each other both in time
and space. This makes the definition of forest production
plans fall into the category of combinatorial problems.
In this way, different search techniques from
artificial intelligence have been constantly applied to
determine a suitable solution for such problem. In this
aspect, the metaheuristics stand out, which have as ad-
vantage to obtain very good answers in a relatively short
time. Examples are the work of Gomide and Silva, 2009;
Binoti et al., 2017; Araújo Júnior et al., 2017, 2018;
Ferreira et al., 2018.
Among the aspects considered when indicating a
metaheuristic to solve a problem of forest planning, the
time spent to generate a very good solution is of extreme
importance. The aim of this study was to evaluate the
performance of the Metaheuristic Genetic Algorithm (GA),
Clonal Selection Algorithm (CSA), Simulated Annealing
(SA) and Variable Neighborhood Research (VNS) to obtain
potential solutions considering a short time interval.
Material and methods
The problem of forest production planning was
considered for a total area of 4,210 hectares comprising
120 plots, with ages ranging from 1 to 6 years and irre-
gular distribution of area by age class, under a planning
horizon of 16 years.
Silvicultural costs were R$ 4,059.05 ha
(year 1);
R$ 1,627.81 ha
(year 2); R$ 757.95 ha
(year 3); and
R$ 88.20 ha
for the remaining years from the fourth.
Revenues referring to the commercialization of wood
were: R$ 20.00 m
(less than 3 years old); R$ 30,00 m
(4 years old); R$ 40.00 m
(5 years old); and, R$ 80.00
(ages equal or superior to 6 years).
The mathematical model for integer linear pro-
gramming aims to maximize the Net Present Value (NPV),
including as restrictions the age of cut between 5 and 7
years and the minimum and maximum annual demand
for wood of 140,000 m
and 160,000 m
, respectively.
Max GNPV = (01)
Subject to
where: GNPV is the global net present value for all the forest, in reais;
Cij is NPV for stand i when assigned the prescription j, in reais; Xij is the
decision variable and represents the proportion area of stand i that will
be managed with prescription j; M is the total number of stands; N is
the total number of different prescriptions for each stand; Vij(k) is the
total volume of wood for the stand i, when assigned the prescription j,
in the period k of planning horizon; Dmink and Dmaxk are minimum
and maximum wood demand for the period k of the planning horizon.
Constraint (2) guarantee that all stand area re-
ceive one prescription. Constraints (3) and (4) limit
the annual harvested volume between a minimum and
a maximum values of demand. Finally, constraint (5)
impose that there is only one management prescription
for each stand.
Thus, the problem of forest planning described is
the definition of the sequence of harvest and planting of
each of the plots over the period of 16 years. With this,
each field can be managed under 81 different prescriptions
and in combination with the other 119 remaining fields
in order to meet the annual demand for wood. Thus,
120e81 solutions to the problem are possible, and it is
necessary to find the best of them or the best possible
For each metaheuristic, different combinations
of its parameters were tested, in order to find the one
that best solves the problem within the thirty second
processing interval.
For the Genetic Algorithm (GA), the following
parameters were considered: with and without elitism;
two types of crossing (1 cut-off point and uniform); two
types of parent selection for cross (roulette and tourna-
ment); and two types of mutation (random gene choice
and gene to gene). The initial population size was equal
Performance of four meta-heuristics to solve a forestry production planning problem
Cad. Ciênc. Agrá., v. 12, p. 01–05, 2020. e-ISSN: 2447-6218 / ISSN: 1984-6738
to 50 individuals, the mutation rate equal to 1% and
the crossing rate equal to 80%. For CSA, three different
values were considered for hypermutation (H), cloning
(C), selection (S) and substitution (Sub) rates, being
equal to 0.20, 0.50 and 0.80. Three values for initial
population (InP) size were evaluated, being 20, 50 and
80 individuals. In order to test the CSA parameters, it was
decided to follow the methodology proposed by Araújo
Júnior et al. (2018).
For the Simulated Annealing (SA) was evaluated:
three initial temperatures (IT), being 10
, 10
and 10
three temperature reduction rates (α), being 0.01, 0.05
and 0.10; and three numbers of neighbors evaluated in
each iteration (V), with quantities equal to 1, 10 and 30.
In the Variable Neighborhood Search (VNS), two
structures were analyzed: structure A with percentages
of changes of 1%, 2%, 3% and 4% and structure B with
percentages of 10%, 20%, 30% and 40%; each structu-
re was executed considering five different amounts of
neighbors evaluated (1, 10, 30, 50 and 100).
Data processing considering the different configu-
rations was carried out in the application Metaheuristics
for Forest Planning (MeP), developed in the Laboratory
of Operational Research and Forest Modeling (LPM) of
the Federal University of Minas Gerais.
With the results by the algorithms in each repeti-
tion, the amount of viable solutions obtained was counted.
After that, the fitness values related to the NPV and the
solutions that obeyed the demand for the required wood
demand were evaluated.
The entire linear programming model was exe-
cuted in the Lingo software considering a stop processing
time equal to fifteen minutes.
Results and discussion
The best solutions presented by each algo-
rithm and their respective configurations were: R$
31,954,028.00 for the VNS, with 100 neighbors and
structure 1; R$ 31,872,534.00 for CSA, with initial po-
pulation size equal to 20, substitution rate 0.2, selection
rate 0.2, cloning rate equal to 0.8, and hypermutation
rate equal to 0.2; R$ 30,782,473.00 for SA, with initial
temperature of 10e8, temperature decay rate of 0,01 and
evaluation of 30 neighbors. The GA did not present any
viable solution in all evaluations. The solution obtained
by the branch and bound algorithm presented value equal
to R$ 31,274,496.00.
The CSA presented feasible solutions in only
three parameter combinations. VNS presented feasible
solutions in four of the 10 combinations evaluated and
the SA presented feasible solutions in 26 of the 27 com-
binations tested. The mean of viable replicates for each
combination was 72.2% for SA, 10.8% for VNS and 4.4%
for CSA.
The viability of the solutions is related to the
fact that it is necessary to produce an annual quantity
of wood that does not exceed the established minimum
and maximum limits. This was observed for the best
solutions (Table 1). It is important to note that harves-
ting a larger total amount of wood (over 16 years) did
not reflect higher NPV. This is due to the fact that the
model seeks to optimize the financial return rather than
the maximization of production. Thus, the importance
of sequencing of the harvest is emphasized so that there
is a better yield in terms of NPV with lower volume of
harvested wood.
These results demonstrate the superiority of SA
metaheuristics in relation to the search for viable solu-
tions. Such performance had already been highlighted
in other studies, such as those of Ezquerro et al. (2016),
in which the authors mention that SA is one of the most
cited in the forest literature, and Rodrigues et al. (2004a),
where the authors state that SA is one of the metaheuris-
tics that are less affected by changes in their parameters.
The metaheuristics AG is widely applied to solve
forestry planning problems (Rodrigues et al., 2004b; Go
mide et al., 2009; Silva et al., 2009; Binoti et al., 2014 and
Matos, 2017). However, its use has been diminished as
new algorithms appear that are more efficient during the
search process of solutions. The algorithm was sensitive
to the parameter definition, as observed by Gomide et
al. (2009).
Another aspect is related to the number of ope-
rations that the algorithm needs to perform during the
same generation, especially when adopting a larger num-
ber of individuals for the initial population. Thus, too
much time is spent without evolution of populations to
generate better individuals, as discussed by Rodrigues
et al. (2004b). The fact that the algorithm found no fea-
sible solution in all cases reveals that it is necessary to
evaluate new ways of improving the GA search process
as suggested in Gaspar-Cunha et al. (2013).
The CSA and VNS metaheuristics presented bet-
ter solutions in terms of fitness value than the solutions
found by the SA. These algorithms were initially applied
to forest problems in the works of Araújo Júnior et al.
(2017, 2018) presenting efficacy above that found for
the traditional algorithms (SA and AG).
The values of the hypermutation and substitution
rates were the same ones found by Araújo et al. (2018).
However, the other parameters did not present the same
values. This shows the need to define a set of parameters
for each situation analyzed, which suggests the use of
adaptive mechanisms, so that these values are changed
during the execution of the algorithm.
Magalhães, E. C. et al.
Cad. Ciênc. Agrá., v. 12, p. 01–05, 2020. e-ISSN: 2447-6218 / ISSN: 1984-6738
Table 1 – Volume produced annually by the best solutions found
Volume of wood (m³)
1 - 142,698 146,998 142,698 140,484
2 - 140,065 142,086 142,581 141,675
3 - 146,319 147,853 141,840 156,355
4 - 140,834 159,368 151,911 152,074
5 - 149,847 149,718 144,807 155,084
6 - 144,031 146,717 142,817 158,132
7 - 145,744 152,802 140,022 140,001
8 - 140,562 140,041 142,686 141,386
9 - 141,206 144,331 142,760 140,070
10 - 140,775 142,422 140,324 144,200
11 - 144,692 149,017 140,029 142,836
12 - 144,966 156,897 140,644 144,871
13 - 140,441 141,289 142,833 142,846
14 - 143,707 141,128 140,250 141,286
15 - 140,053 141,115 140,356 140,040
16 - 146,823 141,788 140,636 140,168
Total - 2,292,763 2,343,570 2,277,194 2,321,508
The configuration determination of the metah-
euristics used is a process of great importance and com-
plexity, mainly because it is dependent on the problem
to be solved, so there is no standardization of the confi-
guration for each tool making scientific research in this
area necessary.
The Metaheuristic Genetic Algorithm was unable
to generate viable solutions in a short period of time and
was not indicated for the problem in question.
The simulated annealing metaheuristic was less
affected by the initial configuration of its parameters and
this is an important feature when choosing an algorithm
to optimize a forest production planning problem.
The metaheuristics Clonal Selection Algorithm and Va-
riable Neighborhood Search presented the highest values
of fitness, although they occur in few repetitions. It is
possible to conclude that there is great potential in such
algorithms to solve the problem in question.
It can be concluded that for all metaheuristics, it
is important to define an initial structure of parameters
that guarantee good solutions in a relatively short period
of time.
The authors express their thanks to The Minas
Gerais State Research Foundation (FAPEMIG) and Bra-
zilian National Council for Scientific and Technological
Development (CNPq) for their financial support and to
the Federal University of Minas Gerais for their scientific
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