Evolutionary Multi-objective Optimization of Business Process Designs with Pre-processing

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1 Evolutionary Multi-objective Optimization of Business Process Designs with Pre-processing Kostas Georgoulakos Department of Applied Informatics University of Macedonia Thessaloniki, Greece George Tsakalidis Department of Applied Informatics University of Macedonia Thessaloniki, Greece Kostas Vergidis Department of Applied Informatics University of Macedonia Thessaloniki, Greece Nikolaos Samaras Department of Applied Informatics University of Macedonia Thessaloniki, Greece Abstract This paper discusses the problem of business process optimization within a multi-objective evolutionary framework. Business process optimization (BPO) is considered as the problem of constructing feasible business process designs with optimum attribute values such as duration and cost. The proposed approach involves a pre-processing stage and the application of a series of Evolutionary Multi-Objective Optimization Algorithms (EMOAs) in an attempt to generate a series of diverse optimized business process designs for the same process requirements. The proposed optimization framework introduces a quantitative representation of business processes involving two matrices one for capturing the process design and one for calculating and evaluating the process attributes. It also introduces an algorithm that checks the feasibility of each candidate solution (i.e. process design). The work presented in this paper is aimed to investigate the benefits that come from the utilization of a pre-processing stage in the execution process of the EMOAs. The experimental results demonstrate that the proposed optimization framework is capable of producing a satisfactory number of optimized design alternatives considering the problem complexity and high rate of infeasibility. The addition of the pre-processing stage appears to have a positive effect on the framework by producing more nondominated solutions in reduced time frames. Keywords business process; optimization; pre-processing; evolutionary algorithms I. INTRODUCTION The overall understanding of the concepts and technologies that are relevant in business process management involve the comprehension of a business process lifecycle [1]. The lifecycle features are distinctive and serve different purposes, all of which are essential towards business process enactment. A rounded approach should decisively capture the business process (business process modelling), provide all necessary means for bottleneck identification and performance analysis and finally generate alternative improved business processes based on specified objectives. But often the last part (business process optimization) is overlooked if not completely neglected [2]. According to Völkner and Werners [3], business process modelling is essential for the analysis, evaluation and improvement of business processes as it is used to structure the process, such that the existing and alternative task sequences can be analyzed systematically and comprehensively. This paper presents an extension of the business process optimization framework [14] that is based on EMOAs and also includes a pre-processing stage. BPO is one of the key research areas that provide a formal perspective towards the concept of business processes. There are only a few approaches towards multi-objective optimization of business processes that either use complex mathematical models or assume a fixed design for the process and optimize only the participating tasks. The approach presented in this paper is a significant extension of the initial evolutionary framework also presented in [13]. The proposed representation and composition algorithm support a series of business process patterns and the framework supports pre-processing of the problem for four different EMOAs: NSGA2, SPEA2, PESA2 and PAES. The utilization of evolutionary techniques in business processes provides the advantage of working with a population of designs thus providing the capability of generating a series of diverse business process designs based on specific process requirements. II. RELATED WORK BPO as a formal approach for improving business processes has not received the necessary attention in literature due to its requirement for formal techniques. On the contrary, soft /17/$31.00 c 2017 IEEE 897

2 approaches for restructuring and redesigning business processes are more frequent as they are more straight-forward. An example is Business Process Re-engineering that had an influential effect on business process related literature. However, Valiris and Glykas [4] claim that most of Business Process Re engineering methodologies lack the formal underpinning to ensure the logical consistency of the generation of improved business process models. With Business Process Re-design projects, the task of developing optimal designs of business processes is left to the designer's intuition [2]. BPO lies on the other end of the spectrum and can provide a formal approach towards improving a business process based on predefined criteria. Evolutionary techniques use the principles of evolution to guide the optimization process and have been effectively applied to several combinatorial problems. Genetic algorithms (GAs), have already been used to find solutions to scheduling problems and their variants [2]. According to Moon and Seo [5] the most attractive feature of evolutionary algorithms is the flexibility of handling various kinds of objective functions with few requirements on mathematical properties. Evolutionary optimization could benefit business processes by discovering process designs that may be overlooked by a human designer. In addition, these techniques can evaluate a significant number of alternative designs based on the same configuration and determine the fittest, based on specific objectives. However, Wang et al. [6] note that process optimization is a difficult task due to the non linear, non convex and often discontinuous nature of the mathematical models involved. Regarding business processes, the evolutionary approaches reported are limited. Hofacker and Vetschera [2] have attempted to transform and optimize a business process model using GAs but they report non satisfactory results. Tiwari et al. [7] and Vergidis et al. [8] extended this mathematical model and applied multi objective optimization algorithms, such as the Non-Dominated Sorting Genetic Algorithm 2 (NSGA2) and the Strength Pareto Evolutionary Algorithm 2 (SPEA2) and report satisfactory results that provide encouraging opportunities for further investigation. Towards the same direction, Ahmadikatouli and Aboutalebi [9] proposed a novel algorithmic approach to optimize business processes, modelled with petri net, through involving a variety of issues to determine the optimum model such as cost, time, quality of products, etc. Another similar approach introduced by Wibig [10], involved Petri Nets, business processes scalability and dynamic programming concept, to produce measurable results regarding the reduction of necessary computations. The application of such algorithms has further been used in determining the preferable process paths for selected criterions, in the course of workflow map evaluation [11]. The evolving procedure incited Vergidis et al. [12] to introduce and research the concept of composite business processes. This approach also involved evolutionary multi-objective optimization and focuses on the tasks that compose a business process rather than the business process design itself. This paper presents the extension of the optimization framework presented in [13] that generates optimized business processes with diverse designs that are constructed based on predefined process requirements that have been further refined with the addition of the pre-processing stage. III. REPRESENTATION AND OPTIMIZATION OF A BUSINESS PROCESS DESIGN A business process is perceived as a collective set of tasks that when properly connected perform a business operation. The aim of a business process is to perform a business operation, i.e. any service-based operation that is producing value to the organization. The main elements involved are the tasks and resources of the business process. The attributes of the tasks and the process are also taken into consideration to provide the capability of evaluating a business process design. Finally, the patterns that interconnect the tasks are also included, as they are identified as one of the key characteristics that distinguish business processes. As task attributes we consider measurable (quantitative) characteristics of the tasks. Examples involve task cost and task duration. The task attributes can be mapped to the corresponding process attributes (e.g. process cost) using a suitable aggregate function. We consider the input and output products of a task as task resources. The nature and the type of the resources are not taken into account by the proposed framework. The task resources connect the various tasks based on common inputs and outputs. Also, the resources can shape the requirements for a process design in the form of required process input and expected process output. Table I shows the main process elements. Parameter n n d n min r t in t out r in r out p N N d R I i O i R in R out TA i PA TABLE I. MAIN PARAMETERS Description No. of tasks in the library No. of tasks in the process design Minimum no. of tasks in the process design No. of available resources No. of task input resources No. of task output resources No. of process input resources No. of process output resources No. of task/process attributes Set of the n tasks Set of the n d tasks Set of the r resources Set of the t in resources for a task i Set of the t out resources for a task i Set of the r in resources Set of the r out resources Set of the task attribute values for a task i Set of the p process attribute values The set of n d tasks that belong to a particular process design is N d = {t 1, t 2, t 3,, t nd}. The set of r d resources in the design R d = {r 1, r 2, r 3,, r rd} accommodates the subsets R in and R out that store the process input resources and process output resources respectively. The business process design utilizes all the resources in R in and produces all the resources in R out. Also, each task i in the design has t in input resources stored in I i R d and t out output resources stored in O i R d. Finally, each task i 898

3 has p attribute values stored in the TA i set and the corresponding p process attributes are stored in the PA set. The participating tasks in the process design are captured using two matrices, one for capturing the task sequencing (process design) and another for capturing the task attributes. The first matrix to capture the process design itself, is a two-dimensional matrix called Task-Resources Matrix (TRM) and maps the input and output resources for each task. The second matrix, Task- Attributes Matrix (TAM), is similar to TRM and aims at capturing the attribute values of the tasks that participate in the business process design. For an example of TRM and TAM see Vergidis and Tiwari [13]. Having a business process represented with TRM and TAM, two things need to be checked: (a) whether the tasks in TRM can be assembled as a feasible business process design based on the process requirements and (b) the calculation of the process attributes based on the tasks in TAM. The calculation of the process attributes is based on straightforward aggregate functions, whereas the composition of a business process design is a much more complicated task. The tasks in TRM can be assembled in a design based on their common input and output resources. A feasible business process design is one that starts with the resources in R IN and by properly sequencing the tasks in TRM produces the requested R OUT resources. In order to address this challenge, the Process Composition Algorithm (PCA) as described in [13] attempts to construct a feasible process design given the R IN, R OUT and TRM. In the case that not all the tasks in TRM are used to produce the R OUT, PCA updates the TRM with the tasks that have been utilized in the feasible process design and removes those that have not been used. The problem formulation is based on the parameters shown in table 1 assumes that there are more than one process attributes used as optimization objectives and thus is considered as a multi-objective optimization problem. The multi-objective problem formulation for business process optimization is as follows: For a business process design with a set of n d tasks and p process attributes: Minimize / maximize (PA 1, PA 2,, PA p) T Subject to: 1. DoI = 0 2. n n d > 0 3. r r in, r out, t in, t out > 0 4. p 2 Where the Degree of Infeasibility (DoI) is a result of the PCA execution and measures to which degree a set of n d tasks forms a feasible business process design. We assume that the process attributes are used as the optimization objectives. A process attribute (PA j) can be calculated as an aggregate of the corresponding task attributes stored in TAM for all the n d tasks in the process design according to the following equation: = and j=1,...,p (1) Each process attribute can either be subjected to maximization or minimization depending on its nature. The problem formulation involves four constraints. The problem formulation described gives rise to some challenging issues in terms of generating optimized business process designs. The main challenges for business process optimization are: A. Nature of the problem Based on the problem formulation, business process optimization is a discrete problem as the main variable is a set of tasks (N d) that form the business process design. B. Multi-objective formulation of the problem In addition to the discrete nature of the problem, we have assumed a multi-objective nature for the business process optimization problem. Assuming that the participating objectives are conflicting and that each solution represents a different trade-off between the objectives, discovering the Pareto-optimal front across all of the objectives is another major challenge for the proposed optimization framework. C. Solution representation The problem formulation requires different aspects of the business process design for different stages. For example, evaluation of the objectives would require TAM, while to check the infeasibility constraint (1) would require TRM and the execution of PCA. In addition to these, the application of EMOAs to the framework requires appropriate solution representation for each of the genetic operators (selection, crossover, mutation). The framework needs to devise a strategy in order for a solution to address the different requirements that emerge during the optimization process. D. Degree of Infeasibility (DoI) The first constraint of the problem requires the execution of the PCA algorithm to measure the Degree of Infeasibility (DoI) of a solution. However, PCA also updates the solution (either removing or replacing tasks in the N d set) to ensure its feasibility. This is a major challenge for the optimization framework, to handle a solution that is modified by an algorithm during the optimization process. The framework should ensure that the different phases that a solution undergoes are consistent during all of the optimization stages. Additionally, the DoI constraint is an equality constraint. E. Solution size BPO requires solutions of variable size. Having a fixed solution size and thus fixed number of tasks in the business process design would be a major barrier towards lean design composition. The framework must be capable of handling solutions of variable size for the same design requirements. 899

4 IV. DESCRIPTION OF THE PRE-PROCESSING STAGE Due to the complexity of the problem, the authors extend the BPO [14] with an additional stage: the pre-processing of the library of available tasks according to the solution requirements in an effort to reduce the problem complexity and enhance the performance of the EMOAs. The main goal of this stage is to remove the redundant tasks from the task library, reduce the available resources and scale down the input problem to the proposed optimization framework. The business process multi-objective optimization problems belong to the NP-hard problems, which indicates that both the efficiency of optimization algorithms and quality of produced results relies upon the size of the examined problem. In general, business processes have many available alternatives for the participating tasks and these, in turn, can involve many different resources as either requirements or products of their utilization. The process, though, of algorithmically seeking the set of alternative non-dominated optimal business process designs can be particularly complex due to the numerous combinations that have to be produced and evaluated. These challenges induced the authors to introduce a series of preprocesses combined together in a module that aims to filter business process datasets out of redundant data, and thus increase the computational behavior of the evolutionary algorithms. The proposed pre-processes are: A. Removal of tasks that require an input resource that belongs to the set of global outputs Every business process has a set of global output resources that is produced at the end of the process design composition. This set of resources indicates the end of the execution and is one of the requirements for a feasible business process design. Therefore, if a task s input resource belongs to the global output set, it cannot be part of a feasible business process design of the examined problem and thus it is removed from the task library. B. Removal of tasks that produce an output resource that belongs to the set of global inputs Every business process has also a set of global input resources that has to be entirely utilized at the beginning of the execution. This is another requirement for a feasible business process design. If a task has an output resource that belongs to the global input set, it cannot be part of a feasible business process design of the examined problem and as such it is removed from the task library. C. Removal of tasks that require an input resource not produced by any other task Another compulsory rule for a feasible business process design is that the participating tasks have to be provided with all available input resources before their execution. These resources can derive either from the execution of preceding tasks in the business process design or directly from the set of the global input resources. As a result, if an input resource of a particular task does not belong to the set of global inputs, or cannot be obtained from another task in the library as output resource, the referred task has to be removed from the library. Also the particular resource is removed from the corresponding set of resources. D. Removal of tasks with a single output resource not required as input by any other task Another rule related to the business process problem is that a participant task in a feasible process design has to provide at least one of its output resources as input resource to one of the consecutive tasks. In any other case it is considered redundant. Based on this pre-processing rule, any tasks of the library that have a single output resource not required by any other task as input resource are eliminated from the library. In this case too, the particular resource is removed from the corresponding set of resources. After this stage, the remaining tasks in the library provide at least one of their output resources to another task as input. E. Removal of tasks with identical input and output resources dominated by others based on their attribute values The final pre-processing step is directly linked to finding the optimal business process design based on the attribute values of the participating tasks. Tasks in the library can be classified into separate groups based on their input/output resources similarity. Two tasks are considered alternatives in the case of identical input and output resources differentiating only in their attribute values. The participation in potential solutions of a task that has worse attribute values than its alternatives leads to feasible sub-optimal business process designs. Therefore, the final step of the pre-processing module is to locate tasks in the library that can be classified into groups of alternatives and eliminate the tasks that are dominated in each group thus reducing the overall task library. V. OPTIMIZATION FRAMEWORK WITH PRE-PROCESSING The proposed business process optimization framework with pre-processing (bpo F wp) applies a series of existing EMOAs to a business process design captured using the proposed representation. The aim of the framework is to fully utilize the proposed representation technique and the capabilities of the EMOAs in order to generate a series of alternative optimized designs. Based on the aim, the main operation of the framework is the generation and optimization of business process designs. The outcome of the framework is the population of optimized business process designs. For each design the framework produces: The tasks in the design, stored in the N d set. The process graph, which is the diagrammatic representation of the design. The Degree of Infeasibility (DoI), which for the optimized process designs should be equal to zero. The process attribute values, which are calculated based on the input functions. These are the objective values which quantitatively show how well the design performs based on the criteria it has been assessed with. Given the problem formulation, BPO is not a typical optimization problem in the sense of optimizing a series of objective functions given the constraints. The outcome of the 900

5 framework involves the generation of business process diagrams an outcome which is not explicitly included in the original problem formulation. The only outcomes that the problem formulation requests are the process attribute values (optimization objectives) and DoI (constraint feasibility check). Based on the problem formulation, PCA is triggered to check the first constraint zero degree of infeasibility. Therefore the proposed approach involves an anomaly in the optimization process: Most of the outcomes are the result of an algorithmic procedure (PCA) within a constraint of the problem. Only the process attribute values are the products of the objective functions. Essentially, the framework employs a generic optimization structure which is handled each time by a specific EMOA. Each of these optimization steps however, is adjusted to reflect the business process problem and ensure that the framework utilizes the inputs and produces the required outputs. The optimization framework in [13] consists of five steps: A. Generate random population The first step of the optimization process is the generation of random population. This step occurs only once in the optimization process as then the population is evolved for a defined number of generations. The generation of random population creates a fixed number of sets of n d tasks. The number of the sets generated equals the specified population size that the algorithm is working with. Each of the population sets contains n d randomly allocated tasks from N the task library. However, for each of the sets there is a constraint in the random allocation of tasks. The constraint is that a task must appear only once in the same set. This constraint avoids having duplicate tasks in one set and in a potential business process design. After the random population is generated, steps B-E are repeated for a predefined number of generations. B. Check constraints For each solution of the population, the problem constraints are checked. Contrary to most optimization procedures where the solution is first evaluated, bpo F wp checks the constraints prior to solution evaluation due to a specific reason: the constraints modify the solution. The first constraint measures the Degree of Infeasibility (DoI) of the solution. For this to happen, two actions are triggered on the basis of the proposed business process representation: (i) TRM is formed and (ii) PCA is executed. TRM reflects the relationships of the tasks in the N d set with the resources of the problem and PCA uses this information to compose a business process design based on the process requirements. The outcome of the PCA is the diagrammatic version of the business process design, its DoI and the updated N d the updated set of tasks in the design which is necessary for two reasons: A design might be composed with less than n d tasks; as a result, the remaining tasks are removed from the N d set and A design might have been repaired during composition; as a consequence, some tasks in N d might have been replaced. PCA ensures that there is one-to-one relationship between the input and the output solution to ensure consistency in the optimization process. That means that for an N d set the same updated N d will be produced each time that PCA is executed. At this stage of the optimization process, the process design has been created, its DoI is measured and the N d set is updated to reflect the actual tasks in the solution. These are three of the bpo F wp outcomes. The last part of this step is to check the (updated) solution on whether it violates any of the problem s optional constraints if any is included in the problem. Each of the selected EMOAs employs a different strategy in terms of constraint violation and how to handle a solution. These different strategies are discussed in more detail in the following sub-section. C. Evaluate solution The solution evaluation involves two stages based on the proposed representation: (i) TAM is created and (ii) the various process attributes are calculated based on their functions. TAM is created based on updated version of the solution involving the tasks in the design and their attribute values. Based on this matrix the solution is evaluated in terms of the process attribute values. The reason for solution evaluation after the constraint checking is that only the tasks that participate in the process design are actually taken into account in the evaluation process. Each of the EMOAs employs a different strategy to evaluate, compare and select the solutions of the population that will pass through the genetic operators. D. Perform crossover After evaluation, the solutions undergo crossover a genetic operator that exchanges information between two solutions. For the business process optimization problem, crossover occurs directly in the N d set of each solution. Initially, the solutions are selected for crossover based on a given crossover probability defined separately by each of the EMOAs. The solutions that are chosen for crossover are split into pairs. For each pair a unique crossover-point is defined based on a random number (between 1 and nd-1). Based on this crossover-point, the parent solutions exchange their tasks after this point to form the child solutions. At the end of the process, each of the child solutions contains tasks from both parents. The process crossover operator does not check whether the solution is feasible; this is the concern of step B. E. Perform mutation The last operator of the optimization process is mutation a genetic operator that randomly alters information in a chosen solution. Similar to process crossover, the process mutation operator is applied on the N d set of tasks of a particular solution. The probability of mutation occurring is again defined by the EMOA. When mutation occurs for a chosen task, the task is replaced with an arbitrary task from the task library. The framework is programmed using the Java programming language. Java was selected because of its object-oriented approach and the large availability of Java libraries 901

6 collections of programs that implement various algorithms. The framework was programmed as a combination of three Java libraries. Two of the libraries (jmetal and jgrapht) were opensource and available on-line and the third was developed for the purpose of the framework. VI. EXPERIMENTAL RESULTS In order to generate satisfactory results, the EMOAs need to achieve two goals: (i) convergence to the Pareto-optimal front (for obtaining optimal business process designs) and (ii) maintenance of the population diversity across the front (for obtaining a variety of different sizes of business process designs). Based on these performance measures, the features of the problem that require further investigation are three: The number of feasible non-dominated solutions in a given business process, The different acceptable process sizes of a feasible business process design, and The execution time of the EMOAs. Each of these problem features is equally important as it is related with the performance goals of the framework and the EMOAs. The work presented in this paper is aimed to investigate the benefits that come from the utilization of a preprocessing stage in the execution process of the EMOAs. After pre-processing the library of tasks, the optimization framework is expected to increase the quality of generated solutions in shorter time periods. The proposed business process scenarios will examine the effects of the pre-processing stage of the bpo F wp in relation to task library size. The second feature of the problem is important in order to assess the framework s capability of locating optimal solutions across all the process sizes of a given business process scenario using pre-processing. This feature puts to test both the convergence and diversity capabilities of the EMOAs. The optimization algorithms need not only to discover feasible solutions across the feasible region, but also to converge to the optimal. The third feature of the problem is important because the optimization algorithms have to discover the optimal solutions in reasonable time frames. The series of the experiments presented seek to investigate the effect of a preprocessing module before the execution of the EMOAs for different library sizes. TABLE II. PROBLEM PARAMETERS FOR THE SCENARIOS A, B AND C. Parameter scenario A scenario B scenario C n n d n min r t in / t out 2 / 2 2 / 2 2 / 2 r in / r out 2 / 2 2 / 2 2 / 2 p (min) Attribute (max) Attribute Table II shows three different scenarios that constitute the experiments, each with different library size. The reason is that we need to capture the maximum process size so in each scenario we test for a significant range of process sizes to get a more accurate picture of the framework s boundaries. Also the problem is set up to minimize the Attribute A (x-axis) and to maximize the Attribute B (y-axis). Table III shows the parameters for each of the EMOAs employed by the proposed optimization framework. All the EMOAs perform 25,000 evaluations; it might seem excessively high but initial experiments showed that it produced better quality results in comparison with lower numbers and in a timely fashion. The remaining parameters were the ones typically employed in such problems. For each experiment, each algorithm is executed for 10 independent runs. TABLE III. PARAMETER SPECIFICATION FOR THE EMOAS EMPLOYED IN BPO F WP Parameter NSGA2 PAES PESA2 SPEA2 Population Archive Bisections Evaluations Crossover prob Mutation prob Scenario A NSGA2 PAES PESA2 SPEA2 Scenario B NSGA2 PAES PESA2 SPEA2 TABLE IV. OPTIMIZATION DATA FOR SCENARIO A Pre-processing Average time (sec) Generated non-dominated solutions NO YES NO YES NO YES NO YES TABLE V. OPTIMIZATION DATA FOR SCENARIO B Pre-processing Average time (sec) Generated non-dominated solutions NO YES NO YES NO YES NO YES Figures 1, 2 and 3 show the combined optimization results for all scenarios accordingly. The time required for the preprocessing stage is not taken into account. It is evident that the EMOAs following a pre-processing stage lead to more 902

7 satisfactory results, especially for process sizes of 14 and 15 tasks. Tables IV, V and VI show the combined optimization results for scenarios A, B and C respectively. For all scenarios we have a significant decrease in execution time of EMOAs with pre-processing (table VII). On the other hand, the number of the non-dominated solutions produced from EMOAs with pre-processing is greater in most cases than this without preprocessing. Fig. 1. Combined optimization results for scenario A (b) Results for scenario B with pre-processing TABLE VI. OPTIMIZATION DATA FOR SCENARIO C Scenario C Pre-processing Average time (sec) Generated non-dominated solutions NSGA2 NO YES (a) Results for scenario A without pre-processing PAES NO YES PESA2 NO YES SPEA2 NO YES TABLE VII. EMOAS OPTIMIZATION PERFORMANCE SCENARIO A B C (b) Results for scenario A with pre-processing NSGA2 TIME DECREASE ND SOLUTIONS 42.38% 49.72% 53.58% 20.51% 33.33% % Fig. 2. Combined optimization results for scenario B PAES TIME DECREASE ND SOLUTIONS 51.64% 42.65% 49.62% % 2.85% 31.06% PESA2 TIME DECREASE ND SOLUTIONS 60.37% 60.27% 48.38% 7.57% % % TIME DECREASE 46.74% 48.32% 52.44% SPEA2 ND SOLUTIONS 178.1% 74.29% 6.33% (a) Results for scenario B without pre-processing 903

8 VII. DISCUSSION The outcomes of the experiments are summarized in the table VII which presents the decrease rate of execution time of all EMOAs and the increase rate of the non-dominated solutions generated from EMOAs derived from the usage of a preprocessing stage. These two rates, represent the benefits of preprocessing on business process data sets exploited by EMOAs. Fig. 3. Combined optimization results for scenario C (a) (b) Results for scenario C without pre-processing Results for scenario C with pre-processing In more detail: Pre-processing has a very good impact on the execution time of EMOAs for all scenarios. Resulted in execution time decrease rate from 42.38% for NSGA2 to 60.37% for PESA2. Pre-processing also seems, in most cases, to assist EMOAs in generating more non-dominated solutions. The increase rate of the generated non-dominated solutions comes up to 178.1% for SPEA2. The capabilities of the EMOAs to converge towards optimal solutions and maintain the population diversity across the front, are a little bit better for all EMOAs using preprocessing for process sizes as Figure 3 shows. For process sizes is clearly seen in Figure 3 that EMOAs have much more and better solutions with the aid of preprocessing. However, there are two cases that the number of the generated solutions has decreased using pre-processing, NSGA2 for scenario C and PESA2 for scenario B. However, as it is evident in Figure 3, NSGA2 has increased its convergence capability and maintained its diversity of solutions in scenario C. For PESA2 in scenario B both convergence and diversity are kept consistent. In summary, the pre-processing stage on business process data has proved to enhance the performance of the EMOAs in an effort to optimize any given business process scenario by decreasing their execution times and leading to more nondominated solutions. VIII. CONCLUSIONS This paper presented an extended framework for BPO. The framework involved a quantitative representation for business processes, an algorithm that composes feasible process designs, a series of optimization algorithms that generates diverse optimized designs and a pre-processing stage for business process optimization problems. The results have demonstrated that the framework with the aid of the pre-processing stage, has increased its capability of generating diverse designs and selecting those with optimal objective values for business processes in less time. REFERENCES [1] M. Weske, Business process management architectures, in Business Process Management, Springer, 2012, pp [2] I. Hofacker and R. Vetschera, Algorithmical approaches to business process design, Computers & Operations Research, vol. 28, no. 13, pp , [3] P. Völkner and B. Werners, A decision support system for business process planning, European Journal of Operational Research, vol. 125, no. 3, pp , [4] G. 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Aboutalebi, New Evolutionary Approach to Business Process Model Optimization, in Proceedings of the International MultiConference of Engineers and Computer Scientists, 2011, vol. 2. [10] M. Wibig, Dynamic Programming and Genetic Algorithm for Business Processes Optimization, International Journal of Intelligent Systems and Applications, vol. 5, no. 1, p. 44, [11] L. Osuszek, Workflow map optimization by using multiobjective algorithms, in Proceedings of the International Conference on Software Engineering Research and Practice (SERP), 2012, p. 1. [12] K. Vergidis, A. Tiwari, and B. Majeed, Composite business processes: An evolutionary multi-objective optimization approach, in 2007 IEEE Congress on Evolutionary Computation, 2007, pp [13] K. Vergidis and A. Tiwari, Business process design and attribute optimization within an evolutionary framework, in 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), 2008, pp [14] K. Vergidis, C. 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