CADERNO DE CIÊNCIAS AGRÁRIAS

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

Abstract

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

Resumo

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.

https://orcid.org/0000-0002-1240-2766

Universidade Federal de Minas Gerais. Instituto de Ciências Agrárias. Montes Claros, MG. Brasil.

https://orcid.org/0000-0003-0909-8633

Universidad de Huelva. Huelva. España.

https://orcid.org/0000-0002-8722-4263

Universidade Federal de Minas Gerais. Instituto de Ciências Agrárias. Montes Claros, MG. Brasil.

https://orcid.org/0000-0001-6139-1250

*Autor para correspondência: emanuellymagalhaes1@gmail.com

Recebido para publicação em 28 de outubro de 2019. Aceito para publicação em 02 de fevereiro de 2020.

Magalhães, E. C. et al.

Cad. Ciênc. Agrá., v. 12, p. 01–05, 2020. e-ISSN: 2447-6218 / ISSN: 1984-6738

Introduction

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.,

2015).

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

-1

(year 1);

R$ 1,627.81 ha

-1

(year 2); R$ 757.95 ha

-1

(year 3); and

R$ 88.20 ha

-1

for the remaining years from the fourth.

Revenues referring to the commercialization of wood

were: R$ 20.00 m

-3

(less than 3 years old); R$ 30,00 m

-3

(4 years old); R$ 40.00 m

-3

(5 years old); and, R$ 80.00

-3

(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

(02)

(03)

(04)

(05)

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

ones.

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

Period

Volume of wood (m³)

AG* CSA SA VNS PLI

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.

Conclusion

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.

Acknowledgment

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

support.

References

Araújo Júnior, C. A.; Leite, H. G.; Soares, C. P. B.; Binoti, D. H. B.;

Souza, A. P.; Santana, A. F; Torre, C. M. M. E. 2017. A multi-agent

system for forest transport activity planning. Cerne, 23: 329–337. Doi:

http://dx.doi.org/10.1590/01047760201723032335.

Araújo Júnior, C. A.; Mendes, J. B.; Cabacinha, C. D.; Assis, A. L. de;

Matos, L. M. A.; Leite, H. G. 2018. Meta-heuristic clonal selection

algorithm for optimization of forest planning. Revista Árvore, 41: 1–10.

Doi: http://dx.doi.org/10.1590/1806-90882017000600007.

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

Araújo Júnior, C. A. 2012. Simulação multiagentes aplicada ao

planejamento da produção ﬂorestal sustentável. Viçosa: Universidade

Federal de Viçosa. Dissertação.

Binoti, D. H. B.; Binoti, M. L. M. S.; Leite, H. G.; Gleriani, J. M.; Ribeiro,

C. A. A. 2014. Inclusão e inﬂuência de características espaciais em

modelos de regulação ﬂorestal. Cerne, 20: 157–164. Doi: http://dx.doi.

org/10.1590/S0104-77602014000100019.

Carvalho, K. H. A.; Silva, M. L.; Binoti, D. H. B.; Binoti, M. L. M. S.

2015. Inﬂuência da taxa de juros e do preço da madeira em modelos

de regulação ﬂorestal. Pesquisa Florestal Brasileira, 35: 143–151. Doi:

https://doi.org/10.4336/2015.pfb.35.82.554.

Ezquerro, M.; Pardos, M.; Diaz-Balteiro, L. 2016. Operational research

techniques used for addressing biodivertity objetives into forest

management: an overview. Forests, 7: 229–247. Doi: https://doi.

org/10.3390/f7100229.

Ferreira, P. H. B.; Matos, L. M. A.; Assis, A. L.; Cabacinha, C. D.;

Araújo Júnior, C. A. 2018. Inﬂuência dos parâmetros da metaheurística

simulated annealing em um problema de planejamento da produção

ﬂorestal. Caderno de Ciências Agrárias, 10: 59–67.

Gomide, L. R.; Arce, J. E.; Silva, A. C. L. 2009. Uso do algoritmo genético

no planejamento ﬂorestal considerando seus operadores de seleção.

Cerne, 15: 460–467.

Matos, L. M. A. 2017. Utilização da metaheurística algoritmo genético

em um modelo de regulação da produção ﬂorestal. Montes Claros:

Universidade Federal de Minas Gerais. Dissertação.

Rodrigues, F. L.; Leite, H. G.; Santos, H. N.; Souza, A. L.; Ribeiro, C.

A. A.S. 2004a. Metaheurística simulated annealing para solução de

problemas de planejamento ﬂorestal com restrições de integridade.

Revista Árvore, 28: 247–256. Doi: http://dx.doi.org/10.1590/S0100-

67622004000200011.

Rodrigues, F. L.; Leite, H. G.; Santos, H. N.; Souza, A. L.; Silva, G. F.

2004b. Metaheurística algoritmo genético para solução de problemas de

planejamento ﬂorestal com restrições de integridade. Revista Árvore, 28:

233–245. Doi: http://dx.doi.org/10.1590/S0100-67622004000200010.

Silva, G. F.; Piassi, L.C.; Mora, R.; Martins, L.; Teixeira, A. F.; Júnior, A.

A. B. 2009. Metaheurística algoritmo genético na solução de modelos

de planejamento ﬂorestal. Revista Brasileira de Ciências Agrárias, 4:

160–166. Doi: http://dx.doi.org/10.5039/agraria.v4i2a7.

Werneburg, M. A. P. 2015. Planejamento em grandes empresas ﬂorestais

no Brasil. Diamantina: Universidade Federal do Vale do Jequitinhonha

e Mucuri. Dissertação.