Decentralized Algorithms for Weapon-Target Assignment in Swarming Combat System

Algorithm 2

The improved task swap algorithm DWLCC.

(1)	Initialize the dual variables , the reduced cost ;
(2)	Let be the set of candidate source nodes;
(3)	While do
(4)	is voted among neighbors as the source node; ; if , the assignment cannot be improved, then Algorithm 2 terminates;
(5)	Let be the set of the candidate nodes to be added to the swap chain, let be the set of the nodes that joined the swap chain (leaf nodes);
(6)	Let be the distance from node to the source node, let be ’s predecessor node; initialize , , and ;
(7)	While do
(8)	;
(9)	; ;
(10)	For each node on outgoing edge of do
(11)	If then
(12)	//This step is termed as the relaxation operation.
(13)	; set ;
(14)	End if
(15)	If and the distance is smaller than its previous value then
(16)	If then
(17)	Change the source node: ; ;
(18)	Go to step 5;
(19)	Else
(20)	Go to step 3;
(21)	End if
(22)	End if
(23)	If there exists a loop with between the source node and a leaf node then
(24)	If then
(25)	The valid task swap loop is found, and Algorithm 2 terminates.
(26)	End if
(27)	End if
(28)	End for
(29)	End while
(30)	End while