Performance of four metaheuristics to solve a forestry production planning problem
3
Cad. Ciênc. Agrá., v. 12, p. 01–05, 2020. eISSN: 24476218 / ISSN: 19846738
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
8
, 10
6
and 10
4
;
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 GasparCunha 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.