An Effective Hybrid Algorithm Based on Particle Swarm Optimization with Migration Method for Solving the Multiskill Resource-Constrained Project Scheduling Problem

Table 2

The notations.

Ci	The set of tasks need to be completed before task i can be executed
S	The set of all resource’s skills S^i: the subset of skills owned by the resource i, S^i ⊆ S
Si	The skill i
tj	The duration of task j
L	The resources used to execute tasks of the project
L^k	The subset of the resources which can perform task k; L^k ⊆ L
Li	The resource i
W	The tasks that the project needs to do
W^k	The subset of task which can be executed by the resource k, W^k ⊆ W
Wi	The task i
r^i	The subset of the skill required by task i. A resource has the same skill and skill level equal to or greater than the requirement that can be performed
Bk, Ek	The begin time and end time of the task k
Au,v^t	The variable to identify the resource is running task u at time t; 1: yes, 0: no
hi	The skill level i
	Type of skill i
m	Makespan of the schedule
P	The feasible solution
Pall	The set of all solution
f(P)	The function to calculate the makespan of P solution
n	Task number
z	Resource number