Biotechnology and Bioprocess Engineering 15: 254-260 (2010)
Optimization of Lipase Production using Differential Evolution
Vijay Kumar Garlapati and Rintu Banerjee
Received: 2 July 2009 / Revised: 31 July 2009 / Accepted: 3 August 2009
© The Korean Society for Biotechnology and Bioengineering and Springer 2010
Response Surface Methodology (RSM) has been used for
the optimization of extracellular lipolytic enzyme pro-
duction by Rhizopus oryzae NRRL 3562 through sold state
fermentation. The input space of the experimentally vali-
dated RSM-model was optimized using a novel Differ-
ential Evolution approach (DE), which works based on the
natural selection and survival of the fittest concepts of the
biological world. The maximum lipase activity of 96.52 U/
gds was observed with the DE stated optimum values of
35.59oC, 1.50, 5.28, and 4.83 days for temperature, liquid
to solid ratio, pH, and incubation time respectively. The
optimal levels of control parameters namely number of
population, generations, crossover operator, and mutation
constant were equal to 20, 50, 0.6, and 0.20, respectively.
The developed model and its optimization are generic in
nature and thus appear to be useful for the design and
scale-up of the extracellular lipase production by R. oryzae
NRRL 3562 through solid state fermentation.
Differential Evolution (DE) coupled with
Keywords: Optimization, lipase, solid state fermentation,
Rhizopus oryzae NRRL 3562, Differential Evolution (DE)
Microbial lipase (triacylglycerol acylhydrolases, EC 18.104.22.168)
being an industrial enzyme has got many applications in
the synthesis of industrially important products such as
fatty acid methyl esters, flavor esters, and enantiopure
compounds . The exquisite chemoselectivity, regioselec-
tivity, stereoselectivity, non-requirement of cofactors, stabi-
lity in organic solvents, and mild conditions associated
with lipase mediated transformations make microbial lipases
versatile biocatalysts in the pharmaceutical, food, biofuel,
oleaginous, cosmetic, detergent, leather, textile, and paper
industries [2-4]. The production of microbial lipases
through solid state fermentation (SSF) by filamentous
fungi utilizes low-cost agricultural residues as substrates,
economic space, and gives high yields [5-7]. Many re-
searchers have been reported the production of intra and
extracellular lipases by different Rhizopus sp. mainly
through submerged fermentation (SmF) with main focus
on production, purification, characterization, cloning, and
sequencing [8-13], but there is less information available
on the modeling and optimization of extracellular lipase
production from R. oryzae through SSF by using stasti-
stical and evolutionary approaches.
Modeling and optimization are two of the most vital
steps in a fermentation process for maximizing the efficacy
of the process. Most of the studies carried out till date was
using one variable at a time approach that is invariably
time consuming, requires more number of experimental
runs, and fails to give information regarding the inter-
actions between the variables. These limitations can be
overcome by developing a non-linear multivariate process
model for optimization. It was felt that model the experi-
ment for obtaining the second order polynomial equation,
so as to simulate the experimental data by using mathe-
matical modeling and computational tools. For doing so
RSM coupled Differential Evolution has been chosen for
the present study. RSM is a statistical technique which
defines the effect of the independent variables (alone or in
combination), on the processes and generates a mathe-
matical model in addition to analyzing the effects of the
independent variables of the process . DE is a stocha-
stic, vector population based optimization technique with a
conceptual base of simulating the evolution of a population
Vijay Kumar Garlapati, Rintu Banerjee*
Microbial Biotechnology and Downstream Processing Laboratory, Agri-
cultural and Food Engineering Department, Indian Institute of Technology,
Kharagpur, West Bengal 721-302, India
Tel: +91-3222-283104; Fax: +91-3222-282244
Optimization of Lipase Production using Differential Evolution255
of individuals using a predefined set of operators namely
selection and search . It is based on a particular way of
constructing so-called mutant vectors by using differences
between randomly selected elements from the current
DE is one of the globally accepted less expensive and
fast convergent evolutionary optimization approach com-
pared to other optimization approaches (RSM and GA) due
to its requirement of small population size and less number
of generations for converge to the optimal zone. Hence, in
the present investigation the RSM coupled DE optimi-
zation approach has been attempted to maximize the
lipolytic activity by R. oryzae NRRL 3562 through solid
2. Materials and Methods
p-nitrophenyl palmitate was procured from Sigma Chemi-
cal Co., USA. The media components were procured from
Hi Media Laboratories (Mumbai, India). All other solvents
and reagents were either of HPLC grade or AR grade and
were obtained from Merck (Germany).
2.1. Microorganism and inoculum preparation
A lipase producing fungal strain was isolated on the PDA
plates using serial dilution technique from the local soil of
IIT Kharagpur. The isolated fungal strain was identified as
R. oryzae and deposited in Northern Regional Research
Laboratory (NRRL), USA with the strain number “NRRL
3562”. The spore suspension (3 days old inoculum) having
6 × 105 spores/mL of R. oryzae NRRL 3562 was used as
2.2. Substrate preparation and solid state fermentation
Four grams of sieved medium sized dried wheat bran
(Kharagpur, India) was taken in a 100 mL Erlenmeyer
flask and moistened with 6 mL of Czapek-dox medium
(pH 6.0) supplemented with glucose (5%) and coconut oil
(10%). The contents of the flask were autoclaved at 121oC
for 20 min. The sterilized wheat bran with the media was
inoculated with 6 × 105 spores/mL. The flasks were incu-
bated for 5 days at 35oC at 90% relative humidity.
2.3. Enzyme extraction
After five days of incubation, 16 mL of water and dimethyl
sulfoxide (1:1) was added to the fermented biomass and
the moistened fermented biomass was placed for 2 h at
room temperature for enzyme extraction. It was sub-
sequently squeezed through a double layered cheese cloth
and was centrifuged at 6,987 g for 20 min at 4oC . The
clear supernatant obtained was used as the extracellular
2.4. Lipase assay and biomass yield
Lipase activity was determined spectrophotometrically using
p-nitrophenyl palmitate (p-NPP) as the substrate . One
unit (U) of enzyme is defined as the amount of enzyme that
liberates one micromole of p-nitrophenol per minute under
the assay conditions. Enzyme activity is expressed in U/gds
(gram dry substance). Dry weight of the samples was
determined by drying them in a hot air oven at 80oC for 24 h.
2.5.1. Selection of process parameters
The process of solid state fermentation for determining the
lipase activity of R. oryzae NRRL 3562 mainly depends
upon the process variables namely temperature (oC), liquid
to solid ratio, pH, and incubation time (day) and its second
order response surface was generated using central compo-
site design (CCD) after considering its parameters at five
levels (Table 1).
2.6. Modeling and optimization by RSM
Non-linear regression analysis was carried out based on the
data collected as per CCD (Table 2) planning for response,
namely lipase activity using MINITAB 14 software which
resulted in a second-order polynomial equation. The coeffi-
cients of the non-linear regression model (Equation 1) can
be determined using the method of least squares. The effect
of the parameters and their interaction terms on the
response has been studied by conducting the significance
tests and Analysis of variance (ANOVA) has been carried
out on each response to check the adequacy of the model.
The detailed analysis of the effect of parameters and their
interactions on the response was also done through the
Table 1. Solid state fermentation variables and their levels
Coded Uncoded Lowest (−2) Low (−1) Center (0) High (+1) Highest (+2)
Liquid to solid ratio
Incubation time (day)
256Biotechnology and Bioprocess Engineering 15: 254-260 (2010)
surface plots using MINITAB 14 software. The optimized
variables for the higher lipase activity (U/gds) have been
chosen through the response optimizer function of the
MINITAB 14 software.
2.7. Optimization by differential evolution
DE is a simple population-based search algorithm for
global optimization of real valued functions. Its robustness
and effectiveness was demonstrated in a variety of appli-
cations. Unlike genetic algorithms, where perturbation
occurs in accordance with a random quantity, DE employs
weight difference between solution vectors to perturb the
population. It can be noted that DE does not require any
derivative information and is controlled by means of three
parameters, namely scaling factor (mutation constant, F),
crossover operator (CR), and number of population (NP).
To start DE, initially NP design vectors have to be gene-
rated at random to form the initial population, namely [X10,
X20 … XNP0]. The size of the population NP is kept
constant throughout the optimization process. It is to be
noted that the value of NP should not be less than four. The
dimensions of each vector depend on the problem to be
optimized . The initial population is generated random-
ly and it covers the entire parameter space uniformly.
DE extracts distance and direction information from the
current vectors and adds random deviation for diversity to
generate new parameter vectors. Considering Xik as the
target vector in kth iteration, a corresponding donor vector
Vik+1 is obtained. In the present paper, “DE/rand/1” muta-
tion scheme was employed to generate the donor vector
. The formulation of generation of donor vector for the
said mutation scheme was written as:
Vk+1i = Xkr1 + F (Xkr2 – Xkr3) (1)
where F is mutation constant or scaling factor (0~2) which
controls the amplification of the difference between two
individuals and i, r1, r2, and r3 are the index of individual
selected randomly and are distinct. The crossover operator
was introduced to increase the diversity among the mutant
vectors. The trail vector Uk+1j,i is developed from the ele-
ments of target vector, Xki, and the elements of the donor
vector, Vk+1i as follows:
( j = 1, 2, ... n) (2)
To determine the member for the next generation, the trail
vector produced by the crossover operator was compared
with the target vector. If the trail vector produces a smaller
objective function value, it is passed to the next generation
otherwise target vector is copied in the next generation.
(i = 1, 2, ... NP) (3)
Mutation, recombination, and selection processes continue
until some stopping criterion is met. The simplified flow
chart of DE is shown in Fig. 1.
In the present paper, maximization of the lipase activity
of R. oryzae NRRL 3562 using DE has been attempted. In
this case the maximization problem is converted to
minimization problem utilizing the principle of duality. The
dimensionality (D) of the problem is equal to four, as there
are four process variables i.e., temperature, liquid to solid
ratio, pH, and incubation time.
k 1+ =
Vj i ,
k 1+, if randj i ,
Xj i ,
k 1+ =
k 1+, if f Ui
k 1 +
Table 2. Central composite design with the experimental, pre-
dicted responses, and its R-studentized residuals
Input parameters Response
L : S
Optimization of Lipase Production using Differential Evolution257
3. Results and Discussion
3.1. Model development, statistical analysis, and valida-
Temperature, liquid to solid ratio, pH, and incubation time
are the critical factors in SSF and their importance in
enzyme production has been well established. The lipase
activity (La) of R. oryzae NRRL 3562 was expressed as a
non-linear function of the input process parameters in
coded form as follows:
La = 95.9533 + 4.0771X1+ 0.4779X2– 2.8038X3
– 1.1221X4– 0.9531X1X2+ 2.7719X1X3
– 0.7806X1X4+ 0.1719X2X3+ 1.4669X2X4
+ 2.3094X3X4– 12.7141X12– 8.9853X22
– 3.2678X32– 6.6603X42
Significance test results (Table 3) suggesting that consi-
dering 95% (a = 0.05) as a level of confidence, the P-
values (Table 3) of X1, X3, X12, X22, X32, X42, X1X3, and
X3X4 are found to be less than 0.05 and are considered to
have significant impact on the lipase activity. The P-value
of the factors X2 and X4 is found to be more than the
confidence level (0.05) but their square terms P value is
found to be less than the confidence level which indicates
its non-linear relationship with the response. Based on the
ANOVA results (Table 4), the P values were less than the
value of significance level α 0.05 for all the terms, which
indicates the significant contribution of the linear, square
and interaction terms towards the response. The surface
plots shown in Figs. 2A~2F were found to be curved in
nature, which indicates the non-linear relationship between
the interaction terms X1X2, X1X3, X1X4, X2X3, X2X4, and
X3X4 and response, lipase activity.
The response equation can be written in the uncoded
form as follows:
Fig. 1. Flow chart representing a Differential Evolution.
Table 3. Results of significance test on the non-linear model-
coefficients, standard errors, T statistics, and P values for the lipase
activity (coded form)
Sl. no Terms Coeffecient
SS = 3.568 R-sq = 97.4% R-sq (adj) = 95.0%
Table 4. Results of ANOVA-lipase activity
Source DF Sequential
Residual error 15
7207.29 7207.29 514.81 40.45 0.000
623.31 623.31 155.83 12.24 0.000
6316.53 6316.53 1579.13 124.06 0.000
Total 29 7398.22
258Biotechnology and Bioprocess Engineering 15: 254-260 (2010)
La = −842.551 + 31.6692o+ 103.673B + 75.2450C
+ 41.1417D − 0.381250AB + 1.10875AC
− 0.156125AD + 0.687500BC+ 2.93375BD
+ 4.61875CD − 0.508562A2− 35.9412B2
− 13.0713C2− 6.66031D2 (5)
where A, B, C, and D represents the input process para-
The predicted values are in close agreement with the
experimental values (Table 2) which indicates the good
prediction accuracy and generalization ability of the pre-
dicted model. The coefficient of multiple regression, R2,
and the adjusted R2 values was found to be 97.4 and 95.0%
respectively, which indicate the fitness and adequacy of the
model . The range of externally studentized residuals
(−3 ~ +3) indicates the model adequacy (Table 2). Thus,
the developed model appears to be useful for the design,
scale-up, control, and optimization of the extracellular
lipase production by R. oryzae NRRL 3562 through solid
state fermentation. The optimized lipase activity of 95.32
U/gds with the variables of 34.99oC, 1.48, 5.60, and 4.94
days for temperature, liquid to solid ratio, pH, and incu-
bation time respectively was predicted by the response
surface optimizer. The predicted variables were chosen for
the triplicate experimental sets for lipase production, which
resulted in the lipase activity of 94.87 U/gds with a close
agreement with the predicted lipase activity (95.32 U/gds)
with a % deviation of −0.47.
3.2. Optimization by differential evolution
The limitations associated with the traditional statistical
optimization approaches i.e., search for a single point,
requirement of derivative information or other auxiliary
knowledge, not straightforward due to restrictions for the
definition of the objective function exist, can be overc-
ome by using Differential Evolution based optimization
In the present study, lipase activity (La) model of R.
Fig. 2. Surface plots of lipase activity with: (A) temperature and liquid to solid ratio, (B) temperature and pH, (C) temperature and
incubation time, (D) liquid to solid ratio and pH, (E) liquid to solid ratio and incubation time, and (F) pH and incubation time.
Optimization of Lipase Production using Differential Evolution259
oryzae3562 was posed as an optimization problem for
maximizing the lipase activity. The maximization problem
was converted to minimization problem as given below.
Minimize = (6)
subject to 30 ≤ A ≤ 40, 1 ≤ B ≤ 2, 5 ≤ C ≤ 6,
4 ≤ D ≤ 6.
where La indicates lipase activity (Equation 6), and A, B,
C, and D represent the uncoded values of the variables
temperature, liquid to solid ratio, pH, and incubation time,
respectively. A systematic study was conducted to select
the three important controlling parameters of DE, namely
number of population (NP), crossover operator (CR), and
scaling factor. Mutation constant (F) is an important aspect
in solving the problems using DE. In this study, the
population size was kept equal to 20 (5 × D), where D is
the dimension of the problem. Both the crossover rate and
mutation factor were varied in the range of [0~1]. A careful
study was conducted to identify the values of CR and F,
after varying one parameter at a time, and keeping the
other parameters at a fixed level. Initially, the study is
performed to determine the appropriate value of CR, keep-
ing the other parameters fixed at one level (NP = 20, Gen
= 50, and F = 0.5). It is to be noted that the maximum
value of lipase activity (that is, minimum value of objective
function value) is found to be equal to 96.9012, 96.9013,
96.9014, and 96.9013 U/gds for different values of CR, 0.0,
0.3, 0.6, and 0.7, respectively. The variation of objective
function value (1/La) with the number of generations at
CR = 0.6 is shown in Fig. 3A. Similarly, the value of F
which will produce maximum value of lipase activity was
also determined with the help of a similar procedure. In
this case, the values CR, NP, and Gen were taken as 0.6
(which results in maximum value of lipase activity/mini-
mum value of objective function), 20, and 50, respectively.
The maximum values of lipase activity obtained are
found to be equal to 96.8452, 96.9014, 96.9013, and
96.9013 U/gds, when the value of mutation constant F is
fixed at 0.05, 0.2, 0.35, and 0.5, respectively. The objective
function value (1/La) variation with the number of gene-
rations at F = 0.20 is shown in Fig. 3B. The optimum
values of process variables obtained are found to be equal
to 35.59oC, 1.501, 5.28, and 4.83 days for temperature,
liquid to solid ratio, pH, and incubation time, respectively.
Moreover, the optimal levels of control parameters NP,
Gen, CR, and F were seen to be equal to 20, 50, 0.6, and
0.20, respectively. It is to be noted that the maximum value
of lipase activity was found to be equal to 96.901 U/gds.
The DE optimized parameters obtained are validated experi-
mentally by conducting the experiment in triplicates. The
extracellualr lipase production under the DE stated condi-
tions resulted in the lipase activity of 96.52 U/gds, which
was found to be in close agreement with the DE maximi-
zed value 96.901 U/gds with a % deviation of −0.395.
Moreover the optimization through the DE resulted in
slightly higher lipase activity (96.52 U/gds) than the RSM
optimized lipase activity (95.32 U/gds) with reduced pH
and incubation time conditions. The requirement of small
population size and less number of generations for con-
verge to the optimal zone, makes DE a computationally
less expensive compared to other optimization approaches.
Lipase activity of 48.0 U/g substrate was reported from
Rhizopus oligosporous using almond meal as substrate
. In another case Cordova et al. (1998)  obtained
lipase activities of 79.6 and 20.24 U/gds by cultivating
Rhizopus rhizopodiformis and Rhizomucor pusillus in mix-
ture of olive oil cake and sugar cane bagasse. Whereas
lipase activity of 40 U/gds  and 30.3 U/gds  was
reported from Penicillium verrucosum and Penicillium
restrictumusins respectively. Sun and Xu (2008) 
Fig. 3. Variation of objective function value with the number of
generations at (A) CR = 0.6 and (B) F = 0.20.
260 Biotechnology and Bioprocess Engineering 15: 254-260 (2010) Download full-text
reported the lipase activity of 24.447 U/gds from Rhizopus
chinensis under solid state fermentation by utilizing wheat
flour with wheat bran as a substrate. The lipase produced
through solid state fermentation by Penicillium restrictum
proved to be efficient process than the submerged fermen-
tation with a lipase activity of 17 U/mL . Hence, the
obtained DE optimized lipase activity (96.52) through
solid-state fermentation in the present work is higher than
(1.21 fold) the previous reports of lipase activities from
other fungi through solid state fermentation.
To summarize, this paper presents optimization strategy for
extracellular lipase production by R. oryzae NRRL 3562
through solid state fermentation by using DE based on
experimentally validated RSM model. The obtained results
of optimization of the extracellular lipase production by R.
oryzae NRRL 3562, were experimentally validated which
showed that the maximum lipase activity of 96.52 U/gds
was observed with the DE stated optimum values of, and
35.59oC temperature, 1.50 liquid to solid ratio, 5.28 pH,
and 4.83 days with the optimal levels of control parameters
NP, Gen, CR, and F were seen to be equal to 20, 50, 0.6,
and 0.20, respectively. The developed model and the
optimization both being generic in nature, appear to be
useful for the design, scale-up, and control the extracellular
lipase production by R. oryzae NRRL 3562 through solid
stry of Human Resource Development, Government of
India is acknowledged gratefully.
The financial support from the Mini-
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