Intelligent Critical Path Computation Algorithm Utilising Ant Colony Optimisation for Complex Project Scheduling

Algorithm 1

The intelligent critical path computation algorithm steps utilising ant colony optimisation.

(1)	Initialization process: let ; / is the time counter /
	;/ is the loop counter /
	; /let the initial value of pheromone intensity for each path be /
	; /let the initial value of incremental pheromone intensity be 0/
	; / in critical path∗/
	; /the table is empty in the initial phase /
	The m ants were randomly placed on n events
(2)	Let /s is the table index, placing the initial event of each ant in the current table /
	For to do;
	For to do;
	; / placing the initial event of the k^th ant in the current table /
(3)	Repeating the following steps until the table is full. /∗ This step is going to be repeated times/
	Let ;
	For to do;
	For to do;
	The next event is selected with probability , whose probability is specifically given by equation (5);
	At time t, the k^th ant transfer to event j at event ;
	Add the event j to .
(4)	Whether the table is full?
(5)	For to do
	The k^th ant transfer from to , and the ant returns to the starting event after one cycle;
	Calculate the distance travelled by the k^th ant;
	Update the longest travel path found
(6)	For each path ;
	For to do;
	is calculated according to equation (3).
(7)	For each path
	The pheromone intensity is calculated according to equation (2);
	Let ;
	;
	Let for each path .
(8)	If
	Clear all table;
	Return to step (2);
(9)	Else
	Output the longest path, the critical path.