Multi-Project Scheduling using Competent Genetic Algorithms

m Number of projects n Total number of activities n h Number of activities in project h h Index of Project V z Set of activities {a(1)…a(n h)} in project h d i Processing time for activity i i→j Predecessor relationship Pred(i) Set of predecessors for activity i k R Set of renewable resources of type k ihk r Per period usage of activity i of resource k in project h K h Number of types of resources used by project h θ Set of feasible schedules θ T Set of precedent feasible schedules θ R Set of resource feasible schedules C max Vector of task completion times ARLF Average Resource Loading Factor AUF Average Utilization Factor CP h Non-resource-constrained critical path duration of project h X iht Boolean variable, true (equal to 1) if activity i of project h is active at time t Z iht Equal to-1 if the part of activity i of project h is active at time t ≤ CP l / 2; otherwise equal to 1 S Number of time intervals spanning a problem Nomenclature (Genetic Algorithm) SGA Simple Genetic Algorithm CGA Competent Genetic Algorithm BB Building Block c Constant factor k BB Order or size of BBs l Current chromosome/problem length m BB Number of BBs n pop Population size p cut Cut probability p κ Bitwise cut probability p m Mutation probability p s Slice probability s Size of tournament used in the Tournament Selection phase μ Calibration coefficient Φ p Phenotypic search space Φ g Genotypic search space ABSTRACT In a multi-project environment, many projects are to be completed that rely on a common pool of scarce resources. In addition to resource constraints, there exist precedence relationships among activities of individual projects. This project scheduling problem is NP-hard and most practical solutions that can handle large problem instances rely on priority-rule heuristics and meta-heuristics rather than optimal solution procedures. In this paper, a Competent Genetic Algorithm (CGA), hybridized with a local search strategy, is proposed to minimize the overall duration or makespan of the resource constrained multi-project scheduling problem (RCMPSP) without violating inter-project resource constraints or intra-project precedence constraints. The proposed Genetic Algorithm (GA) with several varied parameters is tested on sample scheduling problems generated according to two popular multi-project summary measures, Average Utilization Factor (AUF) and Average Resource Load Factor (ARLF). The superiority of the proposed CGA over simple GAs …