Degree-Constrained -Minimum Spanning Tree Problem

Algorithm 6

Ant-Q algorithm for the DCMST problem.

	Data: an instance of the DCMST problem using degree .
	Result: a feasible solution and its objective function value.
	Step 1
	Initialize parameters , , , , , , and the set of ants ()
	, , ,
	, ,
	Step 2
	While () do
	Construct ant tours
	ForEachdo
	Randomly choose a node
	,
	For to do
	ForEachdo
	Ifthen
	Randomly choose an unvisited node of the ant and add it to .
	Else
	Update AQ-values
	Find best solution
	ForEachdo
	Denote by the length of consecutive nodes in starting from node
	Compute
	If () then
	Set and save the best tour of length in
	, ,
	Reinforcement of ant tours
	ForEachdo
	,
	Reinforcement of best solution
	ForEachdo
	,
	Delayed reinforcement of AQ values
	ForEachdo
	For to do
	,
	Ifthen
	Return best feasible solution found and its objective function value