Search-Based Software Project Scheduling Francisco Chicano joint - PowerPoint PPT Presentation

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Search-Based Software Project Scheduling Francisco Chicano joint work with E. Alba, A. Cervantes, D. González-Álvarez, F. Luna, A. J. Nebro, G. Recio, R. Saborido, M. A. Vega-Rodríguez First International Summer School on SBSE, Cádiz, june/july 2016 1 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Introduction • Current software projects are very complex • They can involve hundreds of people and tasks • An efficient way of assigning employees to tasks is required • An automatic software tool can assist to the software project manager • Problem: assign employees to tasks with a given dedication degree Employee Task Salary Effort Maximum dedication Required skills Skills TPG First International Summer School on SBSE, Cádiz, june/july 2016 2 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Introduction • Several authors proposed different formulations in the literature First International Summer School on SBSE, Cádiz, june/july 2016 3 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work First International Summer School on SBSE, Cádiz, june/july 2016 4 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: duration • Project duration (computation) Task TPG duration T1 T2 T3 T4 T5 T6 E1 0.3 0.2 0.5 0.7 1.0 0.0 E2 0.0 0.0 0.2 0.1 0.5 0.8 E3 0.2 0.0 0.0 0.6 1.0 1.0 Gantt diagram of the project E4 0.4 0.6 0.0 0.0 0.0 1.0 ∑ 0.8 Project duration T1 T2 T3 T4 Effort T2 T5 = Duration T2 T6 Time First International Summer School on SBSE, Cádiz, june/july 2016 5 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: cost • Project cost (computation) T1 T1 T1 T2 T2 T2 T3 T3 T3 T4 T4 T4 T5 T5 T5 T6 T6 T6 ∑ = time the employee Salary of E3 Cost of employee E1 due E1 E1 E1 0.3 0.3 0.3 0.2 0.2 0.2 0.5 0.5 0.5 0.7 0.7 0.7 1.0 1.0 1.0 0.0 0.0 0.0 spends on the project to its participation Dur. Dur. T1 Dur. T2 Dur. T3 Dur. T4 Dur. T5 Dur. T6 Cost of employee E2 due E2 E2 E2 0.0 0.0 0.0 0.0 0.2 0.2 0.1 0.1 0.5 0.5 0.8 0.8 T4 to its participation × × × × × × × Cost of employee E3 due E3 E3 0.2 0.2 0.0 0.0 0.0 0.0 0.6 0.6 1.0 1.0 1.0 1.0 E3 0.2 0.0 0.0 0.6 1.0 1.0 to its participacion Cost of employee E4 due E4 E4 0.4 0.4 0.6 0.6 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 E4 0.4 0.6 0.0 0.0 0.0 1.0 to its participacion Time employee E3 spends on task T4 ∑ = Project cost First International Summer School on SBSE, Cádiz, june/july 2016 6 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: constraints • Constraints T1 T2 T3 T4 T5 T6 � � E1 E1 0.3 0.2 0.5 0.7 1.0 0.0 � � E2 0.0 0.0 0.2 0.1 0.5 0.8 E3 E3 0.2 0.0 0.0 0.6 1.0 1.0 E4 E4 0.4 0.6 0.0 0.0 0.0 1.0 ∑ 0.9 > 0 � � � C2. The union of the work team skills must include the required , skills of the task they perform � � � C1. All tasks must be performed First International Summer School on SBSE, Cádiz, june/july 2016 7 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: constraints • Constraints (cont.) T1 T2 T3 T4 T5 T6 E1 0.3 0.2 0.5 0.7 1.0 0.0 Project duration T1 T2 T3 T4 T5 T6 Time Overwork Maximum dedication Dedication C3. No employee must exceed her/his maximum dedication Time First International Summer School on SBSE, Cádiz, june/july 2016 8 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: fitness Peso Valor  1 /q if the solution is feasible  w cost 10 -6  ) = w dur 0.1 1 / ( q + p ) otherwise   w penal 100 Project duration w undt 10 w reqsk 10 w over 0.1 Project cost Overwork Undone tasks Required skills First International Summer School on SBSE, Cádiz, june/july 2016 9 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: algorithm & representation • Steady State GA with binary representation • Maximum dedication set to 1.0 for all employees → x ij ∈ [0,1] • Matrix elements are discretized to eight values (3 bits per element) T1 T2 T3 T4 T5 T6 T1 T2 T3 T4 T5 T6 E1 0,3 0,2 0,5 0,7 1,0 0,0 E1 010 001 100 101 110 000 E2 0,0 0,0 0,2 0,1 0,5 0,8 E2 000 000 001 001 100 110 E3 0,2 0,0 0,0 0,6 1,0 1,0 E3 001 000 000 100 111 111 E4 0,4 0,6 0,0 0,0 0,0 1,0 E4 010 100 000 000 000 111 2D recombination Chromosome 010001100101110000000000… First International Summer School on SBSE, Cádiz, june/july 2016 10 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: experiments • 48 generated instances in 5 groups • In the first three groups (12 instancias) only one parameter change v Employees (5, 10, 15, 20) v Tasks (10, 20, 30) v Skills of employees (2, 4, 6, 8, 10) • Fourth and fifth groups: all parameters simultaneously change • 100 independent runs GA param. Value Population 64 Selection Binary tournament Recombination 2D crossover Mutation Bit flip (p m =1/length) Replacement Elitist Stop condition 5000 generations First International Summer School on SBSE, Cádiz, june/july 2016 11 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Basic Problem Formulation: experiments Fourth group of instances Hit rate Project duration decreases 6 with more employees Duration 43 94 97 97 Cost 4-5 skills per employee First International Summer School on SBSE, Cádiz, june/july 2016 12 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work First International Summer School on SBSE, Cádiz, june/july 2016 13 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Multi-Objective Problem Formulation • Multi-Objective Software Project Scheduling Employee Task Solution Salary Effort Max dedication Required skills Skills TPG • Objectives T1 T2 T3 T4 T5 T6 – Minimize the project cost E1 0.3 0.2 0.5 0.7 1.0 0.0 – Minimize the project duration E2 0.0 0.0 0.2 0.1 0.5 0.8 • Constraints E3 0.2 0.0 0.0 0.6 1.0 1.0 – C1: All tasks must be performed by E4 0.4 0.6 0.0 0.0 0.0 1.0 some employee – C2 : The union of the employees skills must include Dedication of E1 to T4 the required skills of the task they perform – C3 : No employee exceeds his/her maximum dedication First International Summer School on SBSE, Cádiz, june/july 2016 14 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Multi-Objective Problem Formulation T1 T2 T3 T4 T5 T6 E1 0.3 0.2 0.5 0.7 1.0 0.0 E2 0.0 0.0 0.2 0.1 0.5 0.8 E3 0.2 0.0 0.0 0.6 1.0 1.0 E4 0.4 0.6 0.0 0.0 0.0 1.0 First International Summer School on SBSE, Cádiz, june/july 2016 15 / 47

Conclusions Basic Multi-Objective Robust Preference-Based Introduction Formulation Formulation Formulation Formulation & Future Work Multi-Objective Problem Formulation: quality indicators • Hypervolume (HV) – Volume covered by members of the non-dominated set of solutions – Measures both convergence and diversity in the Pareto front – Larger values are better 1.0 1.0 1.0 1.0 75%-EAS • Attainment surfaces 0.8 0.8 0.8 0.8 – Localization statistics for fronts 50%-EAS 0.6 0.6 0.6 0.6 – The same as the median and the interquartile range in the 0.4 0.4 0.4 0.4 mono-objective case 25%-EAS 0.2 0.2 0.2 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 0.0 0.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 First International Summer School on SBSE, Cádiz, june/july 2016 16 / 47