Using Ant Colony Optimization in Software Development ... - IEEE Xplore

Using Ant Colony Optimization in Software Development Project Scheduling Bharti Suri

Pooja Jajoria

Guru Gobind Singh Indraprastha University Delhi, India E mail: [email protected]

Guru Gobind Singh Indraprastha University Delhi, India E mail: [email protected]

Abstract— Resource allocation and tasks assignment to software development teams are very crucial and arduous activities that can affect a project’s cost and completion time. Solution for such problem is NP-Hard and requires software managers to be supported with efficient tools that can perform such allocation and can resolve the software development project scheduling problem (SDPSP) more efficiently. Ant colony optimization (ACO) is a rapidly evolving meta-heuristic technique based on the real life behavior of ants and can be used to solve NP-Hard (SDPSP) problem. Different versions of ACO meta-heuristic have already been applied to the software project scheduling problem in the past that took various resources into account. We have applied elitist strategy of ACO (elitist ant system) for solving SDPSP in a parameter-constrained environment taking project’s cost and duration into consideration. The objective of the ACO-SDPSP methodology allows software project managers and schedulers to assign most effective set of employees that can contribute in minimizing cost and duration of the software project. Experimental results show that the proposed ACO-SDPSP methodology is promising in achieving the desired results.

Software Development Project Scheduling Problem (SDPSP) is to find an optimal solution that can help software project managers to accomplish one or more activity with minimum salary and minimum project duration [5]. The resource-constrained Project Scheduling Problem (PSP) is considered to be a general scheduling problem that contains open-shop, job-shop, and flow-shop problems as special cases [35-37]. We have applied elitist ant colony optimization [38] methodology to solve software development project scheduling problem that uses elitist behavior of ants in a parameter-constrained environment. The elitist behavior of ant (elitist ant system) ensures to deposit pheromone on iteration along with all the other ants. The proposed methodology assists software project managers to assign valuable employee(s) that can contribute in minimizing the cost (salary of employees) and time (overall duration) of the project. The intuition behind the approach is to give a simplistic approach for solving the scheduling problem using ACO, since ACO have many variants (as described in section 5); we wanted this type of ACO to be applied on our problem to check the effect of ACO on parameter-constrained SDPSP. This had shown that the methodology is promising and provides optimal results to the scheduling problem.

Index Terms – Ant colony optimization, Software project management, Software development project scheduling.

I. INTRODUCTION

T

he scheduling of a given software project is the initial task manually developed by software project managers in managing and developing a project. This task requires substantial amount of time, effort, and experience in managing projects. Various tools and techniques have been created to help software project managers in the difficult task of planning the development process of a software project [1, 2]. In software project management, the main objectives of a project manager are to minimize the duration of a project, minimize the cost of computing and to maximize the product quality tradeoffs. For achieving these objectives, project manager has to use the available resources (these resources can include employee(s), skills, salaries, and time) to accomplish the tasks or activities in a way such that the overall performance of the developed software is maximized. Software project management comprises of five groups of process in managing a project, namely, 1) initiating, 2) planning, 3) executing, 4) controlling, and 5) closing. The

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II. SOFTWARE PROJECT MANAGEMENT Software Project Management (SPM) is the process of planning, organizing, staffing, monitoring, controlling and leading a software project [20]. Complex management involving scheduling, planning, and monitoring activities or tasks are the current demand of large and complex software projects, therefore, SPM [21] can be seen as the application of skills, knowledge, tools and techniques to meet the project’s requirements [3, 4] in various activities of software project. Some of the existing project management [21] techniques and research prototypes deficit in computational capabilities and provide only passive project tracking. Hence, many researchers are experimenting to provide these computational capabilities by using metaheuristic algorithms and hybridization of these algorithms. The SPM tells that a schedule comprises of activities and deliverables that often calculated in terms of budget, time duration and available resources. Figure 1 shows activities covered by Software Project Management.

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Figure 1. Activities covered by Software Project Management

III. ANT COLONY OPTIMIZATION An ant as a single individual has a very limited effectiveness and as a part of a well-organized colony, it becomes one powerful agent that works for the development of whole colony. Ant colony optimization (ACO) is a probabilistic algorithm that has evolved from the social behavior of ants. ACO was introduced and developed by Dorigo et al. [24-27]. ACO is based on the fact that ants have the capabilities of searching the shortest path from their nest to the source of food that is regarded as the best path [28, 32-34]. The searching of shortest path is being done via chemical substance called pheromone that provides stigmergy communication between ants. These pheromone trails are laid on the path on which they travel and are used by the ants to communicate with other ants of the colony. The ants choose the path where pheromone concentration is high and is regarded as the best and shortest path.

Figure 2. ACO: Ants searching for shortest path to food source. Solid arrows represent optimal path [28]

Initially ants deposit equal amount of pheromone on every direction. When ants in the shorter direction find a source of food, they carry food and start returning back to the nest following their already laid pheromones as depicted in figure 2. It shows the optimal path taken by an ant when returning back to the nest with food, as this path will have the most deposited pheromone. Over the time, this positive feedback (autocatalytic) process prompts all ants to choose the shorter path [27, 28]. Implementing the ACO for a certain problem requires a representation of variables for each ant, with each variable has a set of some options with their values, and their associated pheromone concentrations. IV. SOFTWARE DEVELOPMENT PROJECT SCHEDULING PROBLEM A project can be viewed as a collaborative enterprise, frequently involving research and design that is planned very carefully to achieve a particular aim. A project consists of a temporary endeavor that ensures completion of a unique product or service, within a certain period of time. The Software Development Project Scheduling Problem (SDPSP)

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is a variant of Project Scheduling Problem (PSP) [5]. SDPSP can be defined as to find an optimized way of arranging software engineers (or employees) with minimum salary and minimum time in a set that can cover all the activities to develop a project. This can contribute in minimizing the overall project’s cost and total duration of software project. SDPSP is NP-hard [23, 38] problem with enormously complex combinatorial optimization issues. It is timeconsuming to optimize the problem manually and this is the reason why automating the scheduling process is needed to schedule a software project with high project qualities that can prove beneficial to software project managers in real time. The automation of scheduling by proposing ACOSDPSP methodology has solved the problem of SDPSP in this paper and end results shows the minimization of overall project’s cost and duration. The parameters considered in our Software Development Project Scheduling Problem (SDPSP) are Resources that include number of employees, skills of employees, salary per working day, monthly salary of employees, and Activities, containing number of activities, resource requirements, activity processing time, and time parameters for a project. V. RELATED WORK Several algorithms based on swarm intelligence [6, 7] have been proposed for the optimization of software development project scheduling. Various multi-criteria resource constrained scheduling problems have been solved by Particle Swarm Optimization (PSO) [8] that considered PSO algorithm for minimizing the cost of project scheduling problem. The multi objective problem of project selection problem of selecting the most appropriate projects out of a given set of proposals so as to maximize the total benefits while minimizing total risk and total cost simultaneously have been studied in the past [9]. In [4], authors proposed ant colony optimization approach which is called ACS-SPSP algorithm and have divided the tasks and distributed the dedications of employees to different tasks nodes and a construction graph for ACO to solve a software project scheduling problem had been generated. The authors of [4] have compared ACS-SPSP algorithm with another search heuristic called genetic algorithm to solve the SPSP and have considered many resources and parameters to solve the scheduling problem. Since every application does not require the same number of resources, therefore we have considered limited number of resources and applied elitist strategy of ACO for solving Software Development Project Scheduling Problem (SDPSP) in this paper. Many researchers [10-12] contributed comprehensive surveys to the resource constrained project scheduling problem. Genetic algorithms were used as the meta-heuristic approaches to solve software project scheduling problem. In [5], software project management has been solved with genetic algorithm. In [5], genetic algorithm proved to be accurate for software project scheduling but the algorithm did not investigated how the number of employees, skills and tasks would influence the solutions to the problems. Generating software project schedules has attracted increased interest in recent years [14, 15], that include time-

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line based models for SPSP with many computer algorithms. In [16], a hybrid algorithm for resource constrained project scheduling problem, named ANGEL have been proposed that combined ACO with GA, while in [17], a hybrid algorithm named ACOSS that combined ACO, local search strategy and a scatter search have been proposed for RCPSP in real time. Many scheduling problems like backward production scheduling [18] were solved by ACO. Another paper [19] had implemented ACO on the project resource scheduling problem. The algorithm [19] was proposed to find the best schedule with minimum fluctuation. ACO has been applied to resource constrained project scheduling in [22] that considered combination of direct and summation pheromone evaluation methods and bidirectional planning to construct new solutions. The resource constrained project scheduling problem has attracted many researchers earlier [12, 14]. Since project scheduling problem is NP-Hard problem, different types of heuristics have been proposed [30]. Variants of ACO including Ant Colony System (ACS) [4], Bidirectional planning of ACO [27], and Max-Min ant system [31] have already been applied to project scheduling problem that took various resources into consideration. In this paper, we have proposed ant colony optimization methodology [28] for the limited number of parameters in SDPSP. Since ACO has many variants as discussed above, thereby, to see the effect of elitist strategy, also known as elitist ant system [38] of ACO on SDPSP, we have used this ACO to our software development project scheduling problem. ACO-SDPSP methodology is proposed in the paper that is promising and can be utilized by software project managers for reducing the project’s cost by selecting minimum number of employee(s), and reducing their salary, additionally, minimizing overall duration by reducing time taken by employee(s) to complete all the required activities.

weight of ith edge). It represents pheromone trail associated with the edge. Initially it is set to zero for all the edges and increases as per iterations and adds +1 to the best edge and reduces 10% [28, 33] as the pheromone evaporation rate from other edges. The edge is selected by the ant with every iteration of the algorithm as it moves from employee (vertex) ‘i’ to employee ‘j’, achieving better solutions with every iteration, therefore every ant ‘k’ computes a set ‘ak (x)’ of feasible solutions with every iteration and moves to one of these solutions probabilistically [27]. SDPSP is NP-Hard problem [23, 38] and solved by maintaining an array list ‘P’ that stores the pheromone information of each ant. SDPSP problem can be represented in the form of an undirected graph G (V, E) as the final outcome after each iteration of examples, where V is the set of vertices representing employee(s) ‘E’ is the set of edges in the graph representing flow of activities from activity ‘i’ to activity ‘j’. VII. PROBLEM REPRESENTATION A. Flowchart of the proposed methodology:

VI. PROBLEM DESCRIPTION In the software companies, there is adequate number of eligible workforce to develop their projects. This workforce requires number of employees, number of activities and time taken to complete all the allocated activities. In this paper, we think through the problem of developing software to schedule in a way that the solution can minimize project’s overall cost and duration. Specifically, each activity requires one or a number of skills [29] to develop a project, and a given number of employees that are able to do particular activity. On taking into consideration a given project, the activity set ‘A’ has ‘n’ activities to develop a software project with employee set, ‘E’. The number of activities A and employee E are known for each project. It has been taken into account that an employee cannot be assigned to more than one activity concurrently. However employee(s) can be assigned to various activities at different times. The ACO approach is applied to the given SDPSP to take the best path as chosen by ants (employees) with different iterations, until sufficient amount of food has been gathered or reached to the stopping criterion. The pheromone evaporates with time and with some amount of percentage thereby giving best and shortest path to food source. The evaporation rate for the methodology is assumed to be 10% [28, 33] of wi (current

Figure 3. Flowchart of the ACO-SDPSP Approach


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The above Figure 3 represents proposed ACOSDPSP approach in a flowchart mentioning the basic workflow of the solution to the software development project scheduling problem. B. Assumptions: The Assumptions taken for the proposed ACO-SDPSP algorithm are as follows: 1. Software Development Project Scheduling Problem has some Activity Set, A= {A1, A2… An} 2. There are available employee(s) to complete a particular activity under the Employee Set, E= {E1, E2… En} 3. Each employee have possible work context, that is, some prior skills to complete an activity. 4. Each employee, ‘E’ from the original employee set covers some or all the activities from activity set ‘A’. 5. ‘Xk’ is the time elapsed for each ant (k= 1 to n) as it moves from one activity node to another activity node in the graph. 6. ‘TC’ is the Total Time Constraint (Maximum Execution Time) placed on the software development project scheduling problem. It is the total time constraint for evaluating complete path of an ant. It is set to constant MAX for ACO-SDPSP. 7. The artificial ants ‘k’, {a1…an}, represents employee(s) that searches for the best path and covers all the activities by minimum number of employees to minimize the overall cost and duration of a software project. 8. For each next ant ‘j’, a list that contains already completed activities by employee(s) is represented in array list by Pj= {P1…Pn} 9. ‘wi’ is the weight of each edges ‘i’, and assumed to be the amount of pheromone deposited on the edge. 10. Assume pheromone deposition rate to be +1[28, 33] for each ant (employee) that has crossed the edge on a best path. 11. Evaporation rate of pheromone trails is assumed to be 10% [28, 33] of the current weight of the ith edge that has to be reduced after iteration from each edge and one is added to the best edge after iteration as the pheromone deposition rate. 12. The ACO-SDPSP algorithm run until some stopping criterion is met. For the proposed algorithm, the stopping criterion is to cover all the activities. VIII. PROPOSED ALGORITHM 1.

2.

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Initialization Initialize wi = 0 Initialize TC = MAX Initialize Xk = 0 Produce ‘n’ number of artificial ants {a1…an} that is equal to ‘n’ number of employees P1… Pn = Ø Do For k = 1 to n Pk = Pk + {AK} //The initial activity Ak for ant ak is the starting node for ant ak on the graph. TempT = Ak Do A = call select_activity (ak, tempT) Update Pk = Pk + {A} Xk = Xk + execution time for A

TempT = A While (all activities are covered); EndFor MinTime = min {Xk} where k = 1 to n MaxTime = max {Xk} where k = 1 to n CurrTime = CurrTime + MaxTime Xk = 0, ‫׊‬k = 1 to n Update pheromone at all the edges for the best path corresponding to minTime Evaporate 10% of pheromone from each edge where wi 0 Pk = Ø, ‫ ׊‬k = 1 to n While (TC CurrTime); Select_activity (ak, tempT) { If there is no pheromone deposited on the edge starting from activity node tempT and ending at node ‫ ב‬Pk and is starting from tempT, then choose random edge Elseif (number of edges starting from node tempT and ending at node ‫ ב‬Pk having maximum pheromone is one) Then return that edge Else Return an edge randomly among edges that is selected from start of tempT and ending at node ‫ ב‬Pk having maximum pheromone } IX. ILLUSTRATIVE EXAMPLE Consider a software development project scheduling problem (SDPSP) having employee(s), considered under employee set ‘E’, that covers some or all activities of a software website to be developed as per client’s requirements by the available employee(s) of the software company. The efficient set of employee(s) is chosen by the project manager or scheduler in such a manner that overall project’s time duration and cost will be minimized. In this section, we demonstrate the key steps for the proposed ACO-SDPSP algorithm by using the simplistic example. The SDPSP have the employee set ‘E’ as shown in the Table 1, containing eight employees as; E = {E1, E2, E3, E4, E5, E6, E7, E8}. The prerequisite for the example assumes that all the eight employee(s) posses some skills to do the given ten activities as; A = {A1, A2, A3, A4, A5, A5, A6, A7, A8, A9, A10} to develop the software website as per Table 1. The activities covered by employee(s) and time taken by them to complete the activities are shown in Table 1. Employee E1 can do four activities {A2, A4, A7, A9} in 7 days, employee E2 covers two activities {A1 and A3} in 4 days, employee E3 covers four activities {A1, A5, A7, A8} in 5 days, employee E4 can do three activities {A2, A4, A9} in 4 days, employee E5 can do activities {A3, A6, A10} in 4 days, employee E6 covers activities {A1 and A7} in 5 days, employee E7 covers


three activities {A3, A6, A8} in 4 days and employee E8 covers two activities {A2 and A10} in 2 days. TABLE 1: Employee(s) with corresponding activities and time taken by them to complete particular activity Number of Employee available

A1

A2

A3

A4

A5

A6

A7

A8

A9

A10

To do the Project E1 E2 E3 E4 E5 E6 E7 E8

9 9 9

9

9

9

9 9 9

9

9

9 9

9 9

9

9

9 9

9

9

9

9

Time Taken By Employee To cover Activities (in days)

Figure 5. Graph showing pheromone depositions after 2nd iteration for the given example (Minimum Total time taken is 17 days for this iteration).

7 4 5 4 4 5 4 2

TABLE 2: Result after four stochastic iterations by using elitist ACO on SDPSP Iteration number That contains minimum of overall time for the project

Ants (Employee) having minimum time for the given random example

Employee(s) chosen randomly by ants That covers all Activities With minimum time

Time taken for completing an Activity (in days)

Activities covered by Ants (Employee(s))

1

A4

E4 E6 E3 E5 E7 E8 E1 E3 E2 E3 E5 E4 E3 E5 E4 E4 E5 E3 E3 E5 E4 E5 E3 E2 E4

4 5 5 4 4 2 7 5 4 5 4 4 5 4 4 4 4 5 5 4 4 4 5 4 4

2,4,9 1,7 1,5,7,8 3,6,10 3,6,8 2,10 2,4,7,9 1,5,7,8 1,3 1,5,7,8 3,6,10 2,4,9 1,5,7,8 3,6,10 2,4,9 2,4,9 3,6,10 1,5,7,8 1,5,7,8 3,6,10 2,4,9 3,6,10 1,5,7,8 1,3 2,4,9

A7

2

3

A2

A3 A4

4

A3 A5

Overall time taken for completing all activities (in days)

18

18

Figure 6. Graph showing pheromone depositions after 3rd iteration for the given example (Minimum Total time taken is 17 days for this iteration).

ACO-SDPSP algorithm stops executing after 4th iteration as time constraint limit exceeds TC=85 time units [28, 33] and all the activities of the SDPSP will be covered. The best path is discovered after 4th iteration, that is, {A3, A5, and A4} and the minimum time taken (in days) has been calculated to be 16. This path is comparable to the optimal path that can be obtained for this example.

17

17 17 16 16

Total time limit assumed to be 85 days [28, 33] for the examined example. This is the stopping criteria for execution of ACO-SDPSP algorithm. All employees have Rs. 4000 as per day salary.

Figure 4. Graph showing pheromone depositions after 1st iteration for the given example (Minimum Total time taken is 18 days for this iteration).

Figure 7. Graph showing pheromone depositions after 4th and final iteration for the given example (Minimum Total time taken is 16 days for this iteration).

Figures 4 to 7 shows graphs four iterations. Pheromone deposition on the best path can be figure out from the graphs. Hence, it can be concluded by the graphs that after fourth iteration, the ant will give best path having maximum pheromone content and covers all the ten activities to develop the software website with minimum, that is, three employees {E3, E4, E5}, minimizing the project’s cost and time duration. All the three employees, E3, E4, and E5 takes Rs. 4000 *16 (i.e. current number of days in which project get completed * employees’ per day salary) = Rs. 64000 salary, which is minimized from Rs. 4000*85 (i.e. total allocated number of days to complete the project) = Rs.340000. Hence, an inference can be made that the proposed methodology minimizes the overall cost and duration of a given software project.


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X. SUMMARY The paper summarizes the application of Ant Colony Optimization (ACO) based solution for Software Development Project Scheduling Problem (SDPSP) in a parameter-constrained environment. An ‘Elitist-Behavior’ version of the optimization is proposed and applied on the stated problem taking project’s cost and duration into consideration. A Flowchart of the solution approach is presented with an illustrative example to show its effectiveness endowing good results. XI. CONCLUSION AND FUTURE PROSPECT Ant colony optimization is a promising approach for solving software development project scheduling problem. In this paper, an ACO-SDPSP approach using elitist behavior of ants has been proposed which can give results that can be obtained in the close proximity to the optimal results. The problem is clearly stated and explained with necessary diagrams and an example. The simplistic example shows the key steps of the proposed algorithm. This approach and developed algorithm can be utilized by software project managers as a standalone application for small software projects. Additionally, in future we plan to apply the methodology to more complex tasks and projects making it a web based application by considering more parameters. This can be done by hybridizing the proposed algorithm with other evolutionary algorithms. Experimental results are very encouraging and inferences that the methodology is promising in achieving the desired results. REFERENCES J.M. Odut, Solving the software project scheduling problem with metaheuristics, Masterthesis, Universidad De Malaga, E.T.S. Ingenieria Informatica; September 2012. [2] B. Hughes, M. Cotterell, Software project management (Fourth edition, Tata McGraw- Hill Edition, 2006). [3] GR Heerkens, editor (McGraw- Hill, 2002). [4] J. Xiao, X. T. Ao, Y. Tong, “Solving software project scheduling problem with ant colony optimization,” Elsevier: Computers and operation research, 40(2013) 33-46. [5] E. Alba, J.F. Chicano, “Software project management with GAs,” Information sciences, 2007; 177(11): 2380-401. [6] Wikipedia; http://en.wikipedia.org/wiki/Swarm_intelligence. [7] T. Gonsalves, A. Ito, R.Kawabata, K.Toh, “Swarm intelligence in the optimization of software development project schedule,” Annual IEEE International computer software and applications conference, 07303157/08; 2008. [8] T. Bakshi, B. Sarkar, S.K. Sanyal, “An evolutionary algorithm for multicriteria resource constrained project scheduling problem based on PSO,” SciVerse Science Direct, Procedia technology, 6(2012) 231-238. [9] M. Rabbani, M.A. Bajestani, G.B. Khoshkhou, “A multi- objective particle swarm optimization for project scheduling problem,” Expert systems with applications, 37(2010) 315-321. [10] P. Brucker, A. Drexl, R. Mohring, K. Neumann, E. Pesch, “Resourceconstrained project scheduling: notation, classification, models and methods,” European journal of operational research 1999; 112(1): 341. [11] S. Hartmann, D. Briskorn, “A survey of variants and extensions of the resource-constrained project scheduling problem,” European journal of operational research 2010; 207(1):1-14. [12] W. Herroelen, B.D. Reyck, E. Demeulemeester, “Resource-constrained project scheduling, a survey of recent developments,” Computers and operations research 1998, 13(4): 279-302. [1]

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