Optimization of business processes by automatic reallocation of resources using the genetic algorithm

Abstract

Business process management is the process of modifying or adjusting an organization's business process in order to achieve higher productivity or lower costs. Each company or organization has a value creating process that usually involves people, machines and information. One of the main problems with such processes is that it is very difficult to predict how much of each resource is actually needed. In light of the above, the objective of this paper is to implement a methodology that is capable of optimizing the allocation of resources to tasks in a given business process. In this paper, the genetic algorithm was used for optimization. The idea is that once the units are properly presented, the optimal schedule of users should be determined using the genetic algorithm. The fitness function includes Key Performance Indicators of process: waiting time and cost of the resource. Since al the users are not qualified in performing all the tasks in the process, the algorithm has to consider minimal and the maximal available number of users for each activity. The usability of this approach is tested in the process of credit requirement. Finally, the results are compared to the current work process.

Full text

Optimization of business processes by automatic
reallocation of resources using the genetic algorithm

Info Studio Ltd, Sarajevo
Sarajevo, Bosnia and Herzegovina
almir.djedovic@infostudio.ba
emir.zunic@infostudio.ba
,
Faculty of Electrical Engineering, University of Sarajevo
Sarajevo, Bosnia and Herzegovina
zavdagic@etf.unsa.ba
akarabegovic@etf.unsa.ba
Abstract— Business process management is the process of
modifying or adjusting an organization’s business process in
order to achieve higher productivity or lower costs. Each
company or organization has a value creating process that
usually involves people, machines and information. One of the
main problems with such processes is that it is very difficult to
predict how much of each resource is actually needed. In light of
the above, the objective of this paper is to implement a
methodology that is capable of optimizing the allocation of
resources to tasks in a given business process. In this paper, the
genetic algorithm was used for optimization. The idea is that once
the units are properly presented, the optimal schedule of users
should be determined using the genetic algorithm. The fitness
function includes Key Performance Indicators of process: waiting
time and cost of the resource. Since al the users are not qualified
in performing all the tasks in the process, the algorithm has to
consider minimal and the maximal available number of users for
each activity. The usability of this approach is tested in the
process of credit requirement. Finally, the results are compared
to the current work process.
Keywords—Business process management, Process
optimization, Resource allocation, Business Process Modeling
Genetic algorithm, Simulation
I. INTRODUCTION
Business processes present set of logically connected
activities using the company resources, with the aim of
   needs for products or services of
appropriate quality in an adequate period of time, with
realizing some value at the same time [1]. During the global
competition in the market, companies can achieve competitive
advantage only by offering cheaper and better products and
services, and for realizing such objectives, effective and
innovative business processes are needed.
Business Process Management (BPM) is a process-oriented
management discipline [2]. Business Process Management is a
top-down methodology designed to organize, manage, analyze,
and reengineer the processes used in an organization. BPM is
      
techniques and software to design, enact, control and analyze
operational processes involving humans, organizations,

This means that BPM is linked with areas of Artificial
Intelligence (AI) as Knowledge Management (KM),
Knowledge Engineering (KE) and Business Intelligence (BI).
Nowadays, the optimization of business processes is an
important element of existing and functioning of any
organization. Continuous improvement of business processes
results in reducing the costs, time saving, improved quality and
competitive advantage as well as staying in the market.
Processes are of crucial importance to be effectively
implemented for the organization.
There are multiple approaches of optimizing a business
process. One approach is to redesign the process model so that
the tasks are done in different order. The purpose of such
optimization is to reduce the amount of tasks that get held up
by process bottlenecks. Relocating a bottleneck task to a
position which is reached by less process instances should
improve overall performance. Another situation where
relocating a task to a later stage might be useful is when one
has a very parallel business process and some tasks need all of
the branches to be finished before it can be executed. Leaving
such tasks until the end of the process might have a significant
impact on process throughput.
Another approach for optimizing business processes is to leave
the process model as it is but try out different amounts of
resources, consider training the employees so that the task
execution times are reduced or rearrange the resources which
are responsible for executing a given task. One can always
assume that increasing the amount of resources will improve
the average cycle time of the process until the minimum cycle
time is reached [4]. Meanwhile, there are a lot of cost
considerations that have to be taken into account when
  
their tasks more quickly. If the improvements in cycle time are
not large enough, they will not justify the training cost.
Rearranging tasks between resources is another optimization
technique. In this technique one task can be allocated from one
resource to another. This might be useful when the training
costs are low and the utilization of one resource is very low.
However, caution should be taken when reassigning tasks as it
is not easy to predict whether the new assignees will manage to
handle the additional workload or not. Another downside of

such rearrangement is that the quality might suffer if people
from one role have to start doing the job of other specialists.
This paper is about the optimatization of business processes by
reallocation of resources. It is very difficult to manually check
which the best schedule of the users in the process is. It is quite
evident in complex business      
with a large number of participants in the process. In this paper,
genetic algorithm is used for solving this problem. With the
help of genetic algorithm, it is necessary to find such a
schedule of the participants in the process in order to maximize
or minimize the corresponding fitness function.
The work is organized as following: First, the related work is
discussed in more details in Section II. In Section III, there is
the principle of genetic algorithm. Optimatization of business
processes by reallocation of resources realized by using genetic
algorithm is discussed in Section IV. A concrete
implementation is given in Section V in order to demonstrate
the applicability of the approach. Section VI provides the
conclusion of the paper.
II. RELATED WORK
The idea of using genetic algorithm in optimization of
business processes is not new. The genetic algorithm in the
optimization of business processes, used by other authors is
described in the following section.
The paper [5] examines the various metaheuristic searching
algorithms in problems of reallocation of resources and
arrangement. There are three algorithms being compared:
genetic algorithm, the algorithm of simulated annealing and
tabu search. The problems of reallocation of resources, with or
without constraints have been analyzed. In problems of
reallocation of resources without constraints, even the data
from the algorithm of ant colonies from the second paper have
been taken into consideration, and later, all four algorithms
have been compared. The genetic algorithm resulted in the best
performances, considering the least number of iterations with
its best optimal solution found in them. The same was in
problems of reallocation of resources with constraints. Genetic
algorithm found the best optimal solution in the shortest period
of time.
In paper [6], the authors deal with the problem of optimal
reallocation of human resources considering practical
constraints that may occur during the development of the
project. All constraints are being considered through the
coefficient in the fitness function. Those coefficients are: cost,
continual efficiency being reflected through multitasking,
coefficient of balance of allocated tasks and coefficient, which
shows how successful the distribution of tasks among
participants in the process is. After using genetic algorithm,
results show that it is necessary to gperform multitasking in a
shorter period of time as possible, to minimize performing of
tasks without defining priorities in the process, and it is
necessary to allocate a larger number of resources when it is
possible. These results were presented to programmers and
managers as well, who consider the attained results useful to
software managers.
Considering a long period of time necessary for calculations
the main disadvantage of genetic algorithm, the paper [7]
compares performances of genetic algorithm with a hybrid
genetic algorithm. Algorithms were compared in terms of
duration of the project and the time of algorithm operation.
Results show that integrated (hybrid) genetic algorithm has an
approximate optimal time of project execution and gives better
results than a standard genetic algorithm. Integrated genetic
algorithms are estimated to give more realistic and promising
solutions than genetic ones.
Optimization of business processes in cloud architecture can
be implemented in a way where the genetic algorithm could be
used for the optimal selection of web services that can realize
the required service. D. Agrawal in paper [8] uses a genetic
algorithm in order to select a set of services that meet agreed
quality of services. The fitness function is equal to the total
service quality. Chromosomes were composed out of
requirements and services that can realize the requirement.
The method of roulette selection was used for the selection.
This algorithm was suggested to be implemented in the load
balancing.
Unlike paper [6], the methodology of optimization of business
processes will be presented in this one. Simulation model
implemented in MATLAB will be used in order to ensure as
accurate results as possible. The usability of this approach will
be demonstrated in the process of credit requirement.
III. GENETIC ALGORITHM FOR BUSINESS PROCESS
OPTIMISATION
Genetic algorithm is guided random search algorithm based
on the principles of evolution and natural genetics. It
combines the exploitation of the previous results with the
exploration of new areas of the search space. In a genetic
algorithm, a population of strings (called chromosomes or the
genotype of the genome), which encodes candidate solutions
(called individuals, creatures, or phenotypes) to an
optimization problem, evolves toward better solutions.
Traditionally, solutions are represented in binary as strings of
0s and 1s, but other encodings are also possible [9]. The
evolution usually starts from a population of randomly
generated individuals and happens in generations. In each
generation, fitness is calculated for each individual, then, more
individuals are being selected out of a current population
(based on their fitness) and modified (by recombing or
mutation) into a new population. New population is used in
the new algorithm iteration. The algorithm usually ends when
the maximal number of generations is created or when
satisfactory fitness is reached. If algorithm ends by creating a
maximal number of generations, then fitness can or cannot be
satisfied [10].
Figure 1. Process of credit requirement management

Chromosomes, often referred to as a genome, represent the set
of parameters defining the solution of the problem genetic
algorithm is trying to solve. The chromosome is often
represented as a simple string, although a wide variety of other
data structures are also used [11]. The genetic representation
of individuals is called a genotype. The main criteria in
selecting the string representation of the search node are that
the new string generated from the application of genetic
operator must represent legal search node for the problem.
The reproduction process is typically based on the fitness
values of the strings. The principal is that string with higher
fitness value will have higher chance of surviving to the next
generation.
In genetic algorithms, crossover is a genetic operator used to
vary the programming of a chromosome or chromosomes
from one generation to the next. It is analogous to
reproduction and biological crossover, upon which genetic
algorithms are based. A crossover is a process of taking more
        
from them. There are methods for selection of the
chromosome.
In genetic algorithms of computing, mutation is a genetic
operator used to maintain genetic diversity from one
generation of a population of algorithm chromosomes to the
next. It is similar to biological mutation of the individuals.
Mutation changes one or more genes in the chromosomes. In
mutation, the solution may change entirely from the previous
solution. Hence GA can come to a better solution by using
mutation. Mutation occurs during evolution according to a
user-definable mutation probability. This probability should be
set low. If it is set too high, the search will turn into a
primitive random search [12]. One of the criteria of genetic
algorithm convergence is the change of the fitness function

change that is an indication that genetic algorithm has found
an optimal solution. In order to escape local optima mutation
operator can be used.
IV. AUTOMATIC REALLOCATION OF THE RESOURCES BY USING
GENETIC ALGORITHM
Human resource management usually called the personnel
management, in an inevitable and essential function of the
modern management. Human resource management is a
particular scientific discipline. Intellectual capital and large
internal reserves are in human resources and their activation
can achieve significant results regarding success and initiative.
Human resource management is a very demanding job in
business processes. It is very difficult to determine the optimal
number of resources in the process as well as their schedule.
Concerning less or unqualified resources, bottlenecks occur in
the very execution of the process. These bottlenecks prolong
the execution of the process, reduce the effectiveness of the
process and cause discontent among users. One of the possible
solutions of this problem is adding new users. Let us consider
the process of credit requirement in banks in Figure 1. For the
presentation of this process, the worldwide standard for
modeling business processes BPMN 2.0 was used [13].
Table 1. Simulation Scenarios for process of opening bank account to legal
entities
Generally, there are several ways for acquiring process model.
A process model can be attained by analyzing log files
containing information about the execution of the process, by
using the documentation containing detailed process
description, or by interview with the owner of the process. An
interview with the owner of the process was conducted in this
paper and the model of the process was presented in the Figure
1. Oracle Business Process Management [14] was used as
software for implementation. The process begins with
receiving the credit requirement (Acceptance of the requests).
After filling the given form, the necessary documents are
collected (Collection of documents) and verified if they are
complete (Completeness check). When all the documents are
competed, the next step is verification of the creditworthiness
of the applicant of the requirement (Creditworthiness check)
and collateral check (Collateral check). If everything is
successfully done, the credit committee (Credit committee)
decides on the credit requirement and verifies requests that
could be accepted or rejected. The final activity is
Requirements review. The process is modelled according to
the work principle of processing of credit requirement in one
of the banks in Bosnia and Herzegovina. Interviewing the
owner of the process, it was found out that 3 participants
performed the step Acceptance of the request, 2 participants
performed Collection of documents etc. A detailed schedule of
users is shown in the first column of the Table 1. There is also
other information for the process of credit requirement
obtained from the interview with the owner in order to create a
valid simulation model. This is information about the duration
of certain tasks in the process, the number of submitted
requests etc. After setting the parameters of the business
process model, the simulation has been initiated [14]. The last
row in the table shows the total cost of process execution
obtained by simulation. The total cost of the process depends
on the number and cost of resources, process execution time,
bottlenecks in the process etc. For the schedule of the users
presented in Scenario 1, the total process execution cost is
67679 BAM, which can be seen in Table 1. Increasing the
number of users on the activities Collection of documents
from 2 to 3, the cost of the process almost remained
unchanged: 60618 BAM (Scenario 2). On the other hand, if
the number of users is increased on the activities Completness
check from 2 to 3 and Creditworthiness check from 1 to 2, the
total cost of the process is reduced to about 2000 BAM.
Scenario
#1
#2
#3
Acceptance of the
requests
3
3
3
Collection of
documents
2
3
2
Completeness check
2
2
3
Creditworthiness
check
1
1
2
Collateral check
2
2
2
Credit committee
3
3
3
Requirements review
1
1
1
Total cost
67679
60618
47277

This shows that the process of human resource management in
business process is demanding and complex. It is difficult to
determine the optimal schedule of the users in the process of
minimizing the total execution cost or some other criterion.
Increasing the number of users in the process can make the
very process better or worse. Improvements are seen in
Scenario 2 and 3. It is unacceptable to manually change the

it is particularly expressed in complex processes with
numerous numbers of activities and users. Therefore, a genetic
algorithm for searching the optimal solution is suggested in
this paper. The idea is that genetic algorithm, through iterative
searching of the space of possible solutions determines the
schedule of users which will minimize or maximize a defined
fitness function. It is important to pay attention that all the
users being available in the process are not qualified to
perform all the tasks in the process. There is a constraint of the
total number of users that could be involved in the process, as
well as a constraint of qualified users for each activity in the
process. It is important to notice that this constraint exists in
terms of the maximum and minimum number of users in every
activity. There are some activities that can occur in the process
where the number of users cannot be less than a specific value,
Generate population P0
Initialize population P0 and generation counter g=1;
while (g < the maximum number of generation) {
Run the simulation based on chromosome;
Evaluate fitness of each chromosome;
Select c1 and c2 from population using
tournament selection;
Mutate c1 and c2;
Generate c3 from c1 and c2;
Replace the weakest candidate of Pg with c3
g= g+1;
end;
Algorithm 1: Pseudocode of Genetic Algorithm
i.e. deciding committee and it has 3 users. It would not be
correct to take that kind of schedule of users, where the
number of users would be less than 3 on the committee.
Therefore, the resource pool is defined in the process. A
resource pool is a collection of resources that can perform a
given role or that have a certain capability required to perform
certain tasks. The mathematical model of the problem being
solved is shown in Figure 2. and pseudocode in Algorithm 1.
A. Representation
Every schedule of users in the process presents one
chromosome. Length of chromosomes matches the number of
activities in the process. If it is supposed there are 5 activities
done by 3, 2, 2, 1 and 3 users, respectively. The chromosome
that is equivalent to that model of the process is of the form [3
2 2 1 3], as shown in Figure 3.
B. Fitness Function
After, the way of representing is defined the process model
via chromosomes, it is necessary to define the fitness function.
In the beginning of the optimization of business processes, it is
preferable to choose the fitness function with KPI (Key
Performance Indicators). These indicators can be an average
time of the process, the total process cost, resource cost, an
average waiting time in the entire process or specific (critical)
activities. In addition, all the constraints that may occur in the
process can be taken as penalties in the fitness function. For
example, an unauthorized schedule of users can provide a
great value of fitness function in the process of its
minimization. In this way, solutions will be rejected during the
selection due to a high value of the fitness function.
C. Selection
Tournament selection is probably the most popular selection
method in genetic algorithm due to its efficiency and simple
implementation [15]. In tournament selection, n individuals
are randomly selected from the wider population, and then, all
the individuals are compared (compete) with each other. The
individual with the highest fitness wins and will be included as
one of the next generation population. The number of
individuals competing in each tournament is referred to as
tournament size, commonly set to 2 (also called binary
tournament). Tournament selection also gives a chance for all
individuals to be selected and thus it preserves diversity,
Figure 2. Model for Business Process Optimization using Genetic
Algorithm
Figure 3. Model for Business Process Optimization using Genetic Algorithm

although keeping diversity may degrade the convergence
speed.
D. Crossover
A single point crossover will be used for crossover. Such
crossover operator is selected as the most efficient in task
allocation in the process in [16]. Out of all compared
crossover operations, single point crossover managed to find
the most satisfactory solution in the shortest period of time.
Single point chooses a random integer n between 1 and the
size of the chromosome, and selects the vector entries
numbered less than or equal to n from the first parent, selects
genes numbered greater than n from the second parent, and
concatenates these entries to form the child. For example if
parents are: ,  and n=3 then
the child is  ].
E. Mutation
In Mutation, the Adaptive Mean Mutation Operator
(AMMO) will be used. AMMO generates directions that are
adaptive with respect to the last successful or unsuccessful
generation. AMMO uses a combination of the Gaussian
normal and Cauchy distributions, but rather than creating a
different offspring with each the density. Functions are
convolved into one distribution and only one offspring is
created. For AMMO, offspring was created [17]:


 

 
Where the    is the vector of the population.  is a
Gaussian normally distributed random variable with mean 
and  newly generated for every  of every population
member. Also,  is also a Gaussian normally distributed
random variable with mean  and variance  but is only
generated only once for each population member. The values 
and  allow for the evolution of the strategy parameters of the
EA and are typically s]:


The AMMO method was selected, because it converges faster
in most of the time together with FMO (Fast Evolutionary
Programming) and MMO (Mean Mutation Operator) methods.
More about AMMO method and the reason for its selection
can be found in [17]. The newly created individual is added to
the generation and the weakest one is removed from it.
V. CASE STUDY
The presented method of the optimization of business
processes using genetic algorithm, was tested in the process of
credit requirement (Figure 1.). MATLAB was used for the
implementation. SimEvents library [19] was used for the
in MATLAB by using SimEvents library. The equivalent
presentation of the process. The first step was to present the
process from BPMN 2.0 notation with the appropriate model
model of the process is shown in Figure 4. As previously
mentioned, for adjusting the process model parameters as the
execution time of some tasks in the process, generating time of
new process instances, minimal number of users necessary for
performing the task etc., information were provided by the
owner of the process. Also, the limits of certain resources have
been defined for each activity in the process, i.e. the capacity
of the resource pool. They are presented in the form of vector
constraints:


Which means there cannot be less than 1 or more than 3 users
on the first activity, there cannot be less than 1 or more than 4
users on the second activity, there cannot be less than 1 or
more than 3 users on the third activity etc. It is necessary to
point that Credit committee always has to have exactly 3
members involved. In the processes where the clients are
being served, such as this one, it is necessary to ensure less
waiting time for the clients. Therefore, the fitness function has
to take into consideration the sum of all waitings times in the
process. The schedule of the users in the process of such a
model is obvious to be equal to vector , because when the
maximal number of users is scheduled, then the clients will
wait for the service as short as possible. The cost of the
process has to be considered, too. The fitness function

vector of the resource cost was defined per one hour of work
for each activity in the process:

All delays in the process have to be punished by penalties in
the fitness function. The minute of waiting of client in the
process is taken to be equal to the cost of working hour of the
cheapest activity. In accordance with all these facts
mentioned, the fitness function has the following form:
Figure 4. Equivalent process model in Matlab

  
where the  is the total waiting time of the
instances (clients) in the process and equals to the sum of the
waiting time in all activities, while  is the
number of scheduled resources in the process. After
application of genetic algorithm, results are obtained and
shown in Figure 5. Process has been tested for the period of
one month. The upper part of the Figure 5. shows that the
algorithm has managed to converge to the best solution after
about 15 generations. Genetic algorithm converged because
there is no significant improvement in the values of fitness
function of the population from one generation to the next.
The change in fitness function was below the threshold value,
which was 1e-6. Also, the case study was relatively small and
it was proved by brute-force approach that the solution
obtained by genetic algorithm was optimal. More complex
processes and processes with more participants are expected to
have a higher number of generations. The lower part of Figure
5. presents the algorithm that gave the optimal resource
schedule:
 
The total delay in the process for the optimal model is 3719.6
minutes. The total resource cost is 282, while the value of the
fitness function is 37478. It is interesting to compare the
results with the current condition used in the bank. It is
important to mention that the current number of users in the
process has been determined on the basis of experience and
many years of work as shown in Table 1. in the third column
(Scenario 3). Total delay obtained for this model is 4227
hggggh
Table 2. Comparison of current and optimized process
minutes. Total resource cost is 204 and value of the fitness
function 42474. It is obvious the resource cost has been
increased, but the total waiting in the process has drastically
been reduced. This result is logical because every additional
resource in the process results in increasing the total cost of
the resource as well as speeding up the process. Comparison
of current and optimizes process are shown in Table 2. It is
necessary to mention that the real total cost of the optimal
process is higher than it is shown in the table, because here
only resource costs are taken into account. Actually, in
realistic processes, for each new job, it is necessary to provide
the space, equipment etc., which represents additional
expenses. However, additional costs are expected to be during
a longer period of time, compensated with retaining the
clients, preserving their confidentiality and acquiring new
clients. It should be noted that the algorithm was able to find
the optimal solution considering practical constraints that can
occur in the process, such as, on one hand, the minimal
number of users that can perform a certain activity, and on the
other hand, the maximal number of the users which cannot be
exceeded because of the insufficient number of available
positions or some other reasons. The algorithm has found the
solution taking into account the number of users on Credit
committee that has to be 3. There are always 3 members of
hhh
the committee who decide if the credit requirement will be
accepted or rejected. The algorithm was run several times on
the same process. Suggested mutation was used in order not to
fall into a local minimum. Also, the proposed algorithm was
performed on larger problems. Business processes with 9, 14
and 20 activities were tested and the algorithm has found the
solution. Due to complexity of business process algorithm
needed more time and more generation were needed to
generate to find the optimal resource reallocation. For
example, in business process with 20 activities algorithm has
found the solution in 93 generation.
VI. CONCLUSION
In this paper, method for optimization of business processes
using the genetic algorithm is presented. First, it is necessary
to define the model of business process and corresponding
parameters in the process such as: time of the activity
duration, maximal and minimal number of resources and
number of generated instances of the process. This
information is provided by the owner of the process.
Furthermore, genetic algorithm was used for obtaining the
optimal schedule of the users in the process. The fitness
function takes into consideration KPI processes such as
waiting time of process instances and the total cost of the
resources. It is proved the algorithm is able to find the optimal
schedule of users from the aspect of defined fitness function.
Also, the algorithm takes into consideration the practical
constraints such as the limited number of qualified resources
or fixed number of resources as it was in activity Credit
Committee. The algorithm has already found an optimal
solution for a small number of generations, which is better in
KPI
Current process
Optimized process
Waiting time (min)
543.2
5.5
Total resource cost
3000
3350
Figure 5. Results after the application of genetic algorithm

state of fitness function compared to the current schedule of
users in the process.
REFERENCES
[1] Smith, Howard; Fingar, Peter: Business Process Management. The Third
Wave.bMeghan-Kiffer,bUS,b2003.
[2]           
ACM Crossroads, vol. 15(4), Summer
2009,epp.e1118.
[3] W. M. P. van der Aalst, A. H. M. ter Hofstede, and M. Weske,
ss process management: A survey  Proc. Business Process
Management: International Conference, BPM 2003, Eindhoven, the
Netherlands, ser. LNCS. Springer, June 26-27, 2003, pp. 112.
[4] J. Xu, C. Liu, X. Zhao, Resource Allocation vs. Business Process
Improvement: How They Impact on Each Other in BPM, vol. 5240,
2008, pp. 228-243.
[5] A. M. Connor, A. Shah Resource Allocation Using Metaheuristic
Search  Proceedings of the 4th International Conference on
Computer Science and Information Technology, 2014, pp. 353-364.
[6] J. Park, D. Seo, G. Hong, D. Shin, J. Hwa, D. H. Bae, Human Resource
Allocation in Software Project with Practical Considerations, in
International Journal of Software Engineering and Knowledge
Engineering, vol. 25(1), 2015, pp. 5-26.
[7]       and its Applications for
       
Winter Simulation Conference, 2010, pp. 3212-3219.
[8] D. Agrawal,        
       Computer
Engineering and Intelligent Systems, vol. 3(4), 2012, pp. 47-54.
[9] D. Beasley, D. R. Bull, R. R. Martin, "An Overview of Genetic
Algorithms,Part 1, Fundamentals", in University Computing, vol. 15 (2),
pp. 58-69
[10] W. Banzhaf, P. Nordin, R. E. Keller, F. D. Francone, "Genetic
Programming  An Introduction", Morgan Kaufmann Publishers,US,
1998.
[11] J. Yang, C. Wu, H. P. Lee, Y. Liang, "Solving traveling salesman
problems using generalized chromosme genetic algorithm", in Progress
in Natural Science, vol. 18, 2008, pp. 887-892.
[12] M. Obitko (2016, June, 13). Crossover and Mutation. [Online].
Available:hhttp://www.obitko.com/tutorials/geneticalgorithms/crossover
-mutation.php
[13] Object Management Group, (2016, June, 14). Business Process
Management and Notation. [Online]. Available: http://www.bpmn.org/
[14]        
Oracle Business Process Management. U.S., 2013.
[15] D. E. Goldberg, K. Deb, "A Comparative Analysis of Selection Shemes
Used in Genetic Algorithms", in G. J. E. Rawlins (Ed.), Foundations of
Genetic algorithms, 1991, pp. 69-93.
[16] J. Magalhães-Mendes, "A Comparative Study of Crossover Operators
for Genetic Algorithms to Solve the Job Shop Scheduling Problem", in
WSEAS Transactions on Computers, vol. 12(4), 2013, pp. 164-173.
[17] A. C. Koenig, "A Study of Mutation Methods for Evolutionary
Algorithms", in Advanced Topics in Artifical Intelligence, 2002, pp. 1-8.
[18] T. Bäck, H-P. Schwefel, "An Overview of Evolutionary Algorithms for
Parameter Optimization", in Evolutionary Computation, vol. 1(1), 1993,
pp. 1-23.
[19] MathWorks, (2016, June, 18). SimEvents  Model and simulate discrete-
event systems. [Online]. Available: http://www.mathworks.com/
products/simevent.