=Paper=
{{Paper
|id=Vol-2748/Paper8
|storemode=property
|title=Application of Multiple Population Genetic Algorithm in Optimizing Business Process
|pdfUrl=https://ceur-ws.org/Vol-2748/IAM2020_paper_8.pdf
|volume=Vol-2748
|authors=Nadir Mahammed,Mahmoud Fahsi,Souad Bennabi
|dblpUrl=https://dblp.org/rec/conf/iam/MahammedFB20
}}
==Application of Multiple Population Genetic Algorithm in Optimizing Business Process==
https://ceur-ws.org/Vol-2748/IAM2020_paper_8.pdf
Application of multiple population genetic algorithm
in optimizing business process
Nadir Mahammeda , Mahmoud Fahsib and Souad Bennabid
a
LabRI-SBA Laboratory, Ecole Supérieure en Informatique Sidi Bel Abbès, P.O 73, post office El Wiam Sidi Bel Abbés
22016, Algeria
b
Djillali Liabes University, P.O 89 Sidi Bel Abbès 22000, Algeria
d
Hassiba BenBouali University, Ouled Fares Chlef 02180, Algeria
Abstract
In a highly competitive environment, enterprises success depends on the effectiveness of their business
processes, which leads to the search of a continuous improvement in the time. This kind of improvement
is called business process optimization. Yet, two major challenges often prevent processes optimization.
First, the skills of the analysts to choose the right process among a number of propositions. Second, the
techniques applied to generate and evaluate solutions during optimization process are poor and do not
include all relevant data. Our Evolutionary Business Process Optimization approach addresses these
challenges through a well-defined mathematical representation and a novel evolutionary algorithm as
optimization facilities. In this paper, we focus to use of a formalized process optimization approach for
generating and improving business process designs
Keywords
Multi-criteria optimization, genetic algorithm, business process, multiple population,
1. Introduction
A business process (BP) can be defined as a set of tasks that when properly connected perform
a business operation, e.g. a service or a product with benefit for the enterprise [1]. The main
elements of a BP are the resources, the tasks and their attributes. Each BP design is evaluated
with their tasks’ attributes (discrete values that describe a task, such as cost and duration). The
present definition does not include the notion of sub-process.
Coello Coello in [2] defines a multi-criteria optimization as finding a set of best possible
solutions where not one but several in conflict objectives are involved. Such problem can be
solved using either mathematical programming techniques or metaheuristics [3] Coello Coello
in general; in particular, evolutionary computing is used. By their simplicity of implementation,
genetic algorithms (GA) have been used in several studies on multi-criteria optimization of BPs
[4].
This article explores a way to build satisfactory BP designs in an evolutionary multi-criteria
optimization problem. What authors mean by a BP design (as defined by Adamo in [5]) gener-
IAM’20: Third conference on informatics and applied mathematics, 21–22 October 2020,Guelma, ALGERIA
" n.mahammed@esi-sba.dz (N. Mahammed); mfahci@univ-sba.dz (M. Fahsi); s.bennabi@univ-chlef.dz (S.
Bennabi)
0000-0001-7865-5937 (N. Mahammed)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
Figure 1: Business Process Design Representation
ated from a BP model is a BP where each composing task is described by one or more existing
functional entity as web service and not a general description as a use case. A satisfactory,
feasible or functional BP design is a BP which consumes all the input resources and produces
all output resources as defined by the original BP model.
The result is an approach dealing with an evolutionary multi-criteria business process opti-
mization (BPO) issue by minimizing cost and duration. The approach utilizes a multiple pop-
ulation GA adapted for the stated problem. The rest of the paper is organized as follows. Sec-
tion 2 presents a state of the art on BPO with evolutionary algorithms (EA). Section 3 presents
the optimization approach with the mathematical representation of BP designs and introduces
properly the proposed multi-population GA. Experimental results are presented in section 4.
Finally, section 5 summarizes the paper with conclusion and directions for future work.
2. Related work
The work of Hofacker [6] is the first to quote. The authors worked on how to compose each
BP design in a correct way to guarantee their high performance by focusing on the resources’
allocation to activities. Vergidis in [7] and [8] presented major work in BPO using EAs. They
proposed an effective approach for automated multi-objective optimization of BP designs with
multiples EAs leading to promising results. Vergidis in [9] came back proposing an interest-
ing improvement of their optimization approach. The work is summed by considering each
activity composing a potential BP design as a Web service with its features. Cited work have
approached the problem of multi-objective optimization of BPs regarding to up to two criteria
to optimize. But, Mahammed in [10] worked on a multi-objective combinatorial optimization
problem up to three criteria. The authors proposed an approach that combines a novel geo-
metric Fitness function with an improved NSGA-II. [12] improved the results of [9] work.
Georgoulakos in [11] resumed [9] proposal and added a pre-processing stage to categorize
Web services for the working optimization framework. Thereafter, the work of Tsakalidis [12]
summarizes Vergidis’ work on BPO with evolutionary computing. In Si [13], the BPO is dis-
cussed in regards to resources allocation. A GA is used with color Petri nets to reach desired
results. The authors of [4] worked on the improvement on BPO by using a proposed selec-
tion operator independent from Fitness function calculation, leading to improve [11]] results
in time execution and number of appropriate solutions. The authors in Comuzzi work [14]
looked to the BPO by proposing a technique to implement process navigation of BP models as
a restricted class of directed hypergraphs using an EA, the ant-colony optimization algorithm.
Kurniasih in [15] proposed to study the query processing on data storage to maintain the per-
formance of BP of a system. They used a modified memetic algorithm based on GA combined
with local search technique and a tabu search technique on the crossover operation. In [16],
Shajahan searched to optimize a specific BP, the product development process using a design
structure matrix and a particle swarm optimization technique for the design and sequence of
activities composing the BP. Rekik in [17] proposed to optimize BP in outsourcing by focusing
on the selection of BP activities and the most suitable infrastructure as a service in the cloud
life cycle. They proposed a system that used NSGA-II. Neira-Tovar [18] presented a study en-
abling to identify the pertinent elements of a methodology that allows the development of a
model to optimize BPs. Deshmukh [19] explored how to generate several competing BP mod-
els from event logs using EAs in multi-objective optimization for process mining. Another
interesting work, Li [20] aimed to optimize BP by proposing an approach based on a GA to
improve the efficient of selection and composition of resource-service chain in a distributed
cloud manufacturing problem.
This article describes authors’ investigation and experimentation on the benefit from using
a multiple population GA in BPO. The idea to propose the use of a multiple population within a
GA comes from authors previous successful work which implied using a modified GA but still
with a unique population. The authors are working to demonstrate that applying a multiple
population approach in such issue can lead to explore more search space and in a shorter
execution duration, at the same time.
3. Optimization approach
3.1. Mathematical Representation
The development of a functional and efficient optimization approach needs to overcome a num-
ber of variant challenges:
1. A simple representation technique able to capture the main features of a solution and
easily used by optimization methods (e.g. GA).
2. An algorithmic approach for the composition of new solutions and evaluating them in a
good manner.
During the optimization process, the authors work on the appended value by using a multiple
Table 1
Business Process Design Example
StarT T01 T02 T03 T04 T05 T06 EnD
StarT r01
T01 r07 r02
T02
T03 r03
T04 r08
T05 r06 r09
T06 r10
EnD
population GA with the aim of reducing execution constraints such as calculation duration, and
improve execution results.
A solution is defined by authors as a BP design has a mathematical representation (Table
1) which results to a graphical representation: a Task Task Matrix (TTM) (see figure 1) and
its calculated attributes values. In order to represent a BP design, two nodes are added StarT
and EnD, which represent the beginning and the end of a design, respectively. Each design has
tasks (𝑇𝑖 ) that consumes and produces one or more resources (𝑟𝑠𝑖 ).
• If 𝑇 𝑇 𝑀𝑖𝑗 = 𝑟𝑠𝑘 then 𝑇𝑖 ∩T𝑗 = 𝑟𝑠𝑘
• If 𝑇 𝑇 𝑀𝑖𝑗 = {} then 𝑇𝑖 ∩T𝑗 = {}
3.2. Multiple Population Genetic Algorithm
Non-dominated sorting genetic algorithm II or NSGA-II is an EA that helps to solve this cate-
gory of problems. It conducts the non-dominated sorting of the initial population, then applies
genetic operators to obtain a brand-new population, merges the parent population with the re-
sulting population, and conducts a non-dominated sorting to obtain a nondominated solutions
front.
In former version of NSGA-II, a single population is maintained during the algorithm exe-
cution. A consequence of such choice is that population diversity may be poor as many local
optima in some multi-objective optimization issues. Using a multiple population method with
an EA helps to accelerate the convergence and because it uses multiple sub-populations, it ac-
celerates individuals’ migration too, compared to a simple and unique population, which leads,
to improve the results quantity.
Tanese [21] and Pettey [22] were the first to add a multiple population aspect with a GA based
on the parallel computing paradigm. Chen in [23] describes two manners in which individuals
are selected to migrate:
• Uniform selection chooses individuals and replaces them in a sub-population with indi-
viduals randomly.
• Selection based on Fitness picks individuals with high Fitness level and replaces them in
a sub-population uniformly at random.
Chen in [23] proposed three migration manners between sub-populations of those being
selected individuals.
• Adjacent migration: When individuals are allowed to transfer between adjacent sub-
populations unidirectional.
• Neighborhood migration: When individuals are allowed to transfer between nearest sub-
populations in either direction.
• Free migration: When individuals are allowed to transfer from any sub-population to
another.
The authors have developed a novel multiple population GA based on NSGA-II which called
MP-NSGA-II. The core functioning in figure 2:
1. An initial population of 𝑛 individuals is randomly generated.
2. The population is sorted in 𝑚 sub-population based on the crowding distant of NSGA-II.
3. The population is decomposed in 𝑚 sub-population based on the sorting result.
4. NSGA-II is applied separately on each population.
5. After a defined number of iterations all sub-populations share their information (Figure
2):
• Best individuals of each sub-population are chosen to migrate.
• A new main population is formed by the combination of best individuals (Fitness-
based) of each sub-population using a migration rate.
6. The 𝑛 best individuals are kept to form the new parent population.
7. Steps 2 to 6 are repeated for a number of iterations.
3.3. Approach Description
The proposed approach generates a set of optimized BP designs from an initial BP model. Its
inputs and its outputs resources primarily define the model. Figure 3 outlines the steps making
up the approach.
1. Perform MP-NSGA-II. The approach begins with the production of a set of populations
of BP designs randomly. Which happens once during the approach execution. The pop-
ulation is not assessed until the evaluation stage (step 4). During the future iterations,
MP-NSGA-II is applied rigorously.
2. Create mathematical representation. After the generation of a population of 𝑛 BP de-
signs, each individual is represented by its 𝑇 𝑇 𝑀 (Table 1). Each matrix represents the
relationship between the tasks composing a design using resources.
Figure 2: MP-NSGA-II Flowchart
3. Apply and verify a set of restraints. During the approach course, a set of requirements
needs to be examined regarding to the input and output resources, used and produced by
each solution, respectively. Then, checks a set of constraints regarding the design itself.
4. The evaluation consists of calculating the attributes of each individual created and on
which different constraints have been applied. The attributes of a BP design are calcu-
lated based on the tasks’ attributes composing it. Subsequently, these attributes are the
objective values used to calculate the Fitness function of each solution which used later
by MP-NSGA-II.
5. Apply Steps 1 to 4 are repeated for a number of iterations defines by the experimenters.
It would be advisable to specify that the execution of the first step differs after the first
iteration.
• MP-NSGA-II generates the first population randomly from scratch during the first
iteration.
• MP-NSGA-II generates the new population (always) randomly but from the off-
spring of the first iteration results, during all of the following iterations.
Figure 3: Optimization Approach Steps
4. Experimentation
The proposed optimization approach aim is to generate a set of optimized feasible BP designs.
A feasible solution is a BP design which:
1. Consumes all input resources of the original BP model,
2. Produces all output resources of the original BP model.
3. With limited length.
4. It leads to define the features and summarizes what is expected from the approach as:
• The amount of feasible non-dominated solutions.
• The solutions with different sizes and different solutions with same size i.e. solu-
tions variety
4.1. Design and Measures
The present work focuses on a combinatorial multi-criteria BPO and seeks to minimize two
criteria. These two criteria’ units of measure are not specified. As example, criteria can be
assumed as cost and duration, and the aim is to minimize them on a design as studied in [24].
The authors assumed that tasks composing a solution are in sequential order. So, the calcu-
lation of a BP design attributes (objective values) for the tasks is shown in equation (1):
𝑛𝑑
𝑏𝑝𝑑𝑖 (𝑎𝑗 ) = ∑ 𝑎𝑗𝑘 (1)
𝑘=1
• 𝑏𝑝𝑑𝑖 : BP design.
Table 2
Optimization Approach Parameters
Parameters Values
Initial population size 1000
Binary tournament selection -
One-point crossover 0.9
Bitwiser mutation 1/𝑘
Number sub-populations 5
Number individuals per sub-population 200
Migration period 30 generations
Migration rate 0.2
Insertion rate 0.8
• 𝑛𝑑 : Tasks’ number composing 𝑏𝑝𝑑𝑖 .
• 𝑎𝑗 : Objective value.
• 𝑎𝑗𝑘 : Value of 𝑎𝑗 for a task 𝑘.
The Fitness function used by MP-NSGA-II where k the number of criteria to optimize is in
equation (2):
𝑘
𝑓 (𝑏𝑝𝑑𝑖 ) = ∑ 𝑏𝑝𝑑𝑖 (𝑎𝑗 ) (2)
𝑗=1
To explore the influence of the multiple sub-population feature on the performance of MP-
NSGAII, it seems necessary to know how to measure it. Therefore, as described in [25], an
average optimal value (𝐴𝑂𝑉 ) and a success rate (𝑆𝑅) are used in this study to measure the per-
formance of MP-NSGA-II. For a given population size, the algorithm runs several times. Table
2 summarizes the optimization approach parameters. It itemizes also the genetic operators
features used within MP-NSGA-II.
4.2. Materials
First, the impact of the sub-population size, and the sub-population number, affect the per-
formance of MP-NSGA-II is studied. The results are shown in figure 4 for the sub-population
number experiments and figure 5 for the sub-population size experiments.
The experiment results of the optimization approach are presented then analyzed using five
(05) different scenarios borrowed from [9] and [11]. The scenarios gather a different tasks
library size (set of tasks used to generate solutions).
Tables ?? and ?? show computational results where all tests were performed using the set-
tings summarized in Table 2. For the purpose of comparison, the authors conducted experi-
ments on two axes, with one hundred (100) iterations each:
• Diversifying used GAs: Simple genetic algorithm (SGA), NSGA-II, MP-SGA and MP-
NSGA-II.
Table 3
Test Scenarios Parameters
Scenarios Resources number Tasks library size
A 20 9
B 30 11
C 50 30
D 500 30
E 1000 30
Figure 4: Effect of Sub-population Size on MP-NSGA-II
Figure 5: Effect of Sub-population Number on MP-NSGA-II
• Diversifying migration process: Adjacent migration, neighborhood migration and free
migration.
4.3. Results and Discussion
The influence of the sub-populations size on the performance of MP-NSGA-II is studied (like-
wise for the sub-population number). The size is changed from 0 to 450 with a step size of 50.
Figure 4 presents the experiments results. The algorithm runs 50 times, and the average of the
values of these runs are used to measure the performance of MP-NSGAII.
In figure 4, the X-axis, Y-axis (left), and Y-axis (right) represent sub-population size (𝑆), 𝐴𝑂𝑉 ,
Figure 6: Solutions increase rate (%): a) Adjacent migration process. b) Neighborhood migration pro-
cess. c) Free migration process
and 𝑆𝑅, respectively. For 𝑆<50, the performance of the algorithm is extremely poor (𝐴𝑂𝑉 <10
and 𝑆𝑅=20). For increasing 𝑆, the performance of MP-NSGA-II improved rapidly. For 𝑆 = 200,
MP-NSGA-II shows an improved performance with an 𝐴𝑂𝑉 of 73, and 𝑆𝑅 is 90%. At this
level, MP-NSGA-II performs best. However, as 𝑆 continues to increase, the performance of
MP-NSGA-II slowly decreases. Therefore, it can be concluded that, the performance of pro-
posed algorithm improves rapidly with increasing 𝑆, and then decreases slowly. To obtain an
improved approach, the value of the size of sub-populations cannot be too small, specifically,
a value around 200 is a good choice.
Second, the influence of the sub-population number on the performance of MP-NSGA-II
is studied. The number is changed from 0 to 25 with a step size of 5. Figure 5 presents the
obtained results. In figure 5, the X-axis, Y-axis (left), and Y-axis (right) represent number of sub-
populations, 𝐴𝑂𝑉 , and 𝑆𝑅, respectively. For 𝑁 <20, the performance of MP-NSGA-II is poor
and 𝐴𝑂𝑉 is less than 20, and 𝑆𝑅 is 20%. The performance of MP-NSGA-II increases slowly with
increasing of the number of sub-populations (𝑁 ). For 𝑁 = 5, MP-NSGA-II performs the best,
𝐴𝑂𝑉 =75, and 𝑆𝑅=79%. As 𝑁 continues to increase, the performance of MP-NSGA-II rapidly
decreases. Therefore, it can be concluded that, the performance of MP-NSGA-II first improves
slowly and then decreases rapidly with increasing 𝑁 . To obtain an improved optimization
approach, the value of sub-populations should be a value around 5, for the present issue. These
values (𝑆=200, 𝑁 =5) is used later on the forthcoming experiments as shown in the approach
parameters (Table 2).
The number of non-dominated solutions by scenario with the optimization approach using
Figure 7: Solutions increase rate (%): a) Scenario A. b) Scenario B. c) Scenario C. d) Scenario D. e)
Scenario E
multiple population GAs with different migration processes is summarized in figure 6. The
amount of solutions obtained differs between the different GAs can be observed evidently.
Among the four tested GAs, MP-NSGA-II outperforms on each scenario and with every mi-
gration process applied. Even if the values are close (by migration process) for each scenario,
which can be explained by the discrete nature of values used in different scenarios (tasks li-
brary and available resources). But, if the comparison in done by focusing on the GA instead
of different migration process, the obtained results differ significantly.
Figure 6 presents the increase rate (%) of number of solutions generated compared to a sim-
ple GA. Figure 7 depicts the efficiency of the proposed multiple population GA for different
scenarios. It summarizes the average results classified by scenario. It clearly highlight and
confirms that the different versions of the approach with multiple population GAs obtain the
best overall results compared with a simple GA or NSGA-II. It is clear that for scenarios sample
in the experiments, the performance of MP-NSGA-II is significantly better than the single-
population GA not only in the number of results, the execution time but also in the convergent
speed of searching. In addition, since the multi-population GA let the sub-populations evolve
separately, it might be able to explore more extreme solutions.
5. Conclusion
A GA based on multi-population (MP-NSGA-II) is presented in this study for solving a multi-
objective BP designs problem. The algorithm can be summarized as follow: First, sub-populations
are created from a unique initial population, using a crowding distance sorting. Then, in or-
der to prevent the premature convergence of all individuals into a local optimal, NSGA-II is
applied separately on each sub-population. Finally, sub-populations are regrouped (by migra-
tion) as a single population. To do so, each individual in the final population is chosen based on
a non-dominated sorting randomly which may help to explore for more solution spaces next
iterations.
So, this paper explores the idea of using MP-NSGA-II in a multiple objective problem of
BPO. This work concretely aims at giving a tool capable to enhance the generated BP designs
in quantity and diversity. Further investigations and experimentation would be welcomed to
improve the proposed approach and its EA. In the future, tests with MP-NSGA-II can be further
extended to a larger number of tasks to work with. Working with more optimization criteria
is the next step to follow. It would be interesting to manipulate the number of sub-populations
and population size within the chosen GA.
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