Novel Degree Constrained Minimum Spanning Tree Algorithm Based on an Improved Multicolony Ant Algorithm

Algorithm 1

Input:

 : a complete graph with weight;

 : function to calculate weight;

 : degree constraint of vertex, ;

 MA: the amount of ant colonies

Output:

 A degree constrained minimum spanning tree

Begin

 //Initialization

 Create the Multiple set of ants of size with the number of colonies

 InitAntsEdges(, , )

    ConstructSpanningTree()

 while   and   do

  for     to   MA   do

   AntsMove //Exploration

    Calculation Entropy

      ConstructSpanningTree()

   If     then

   //local optimization

      2-EdgeReplacement()

      1-EdgeReplacement()

  If     then

  foreach     do //enhance

   e⋅⋅phm

  if   () >   then

   Restart(

  if   mod gap(s) = 0  then

   ExchangePheromone()

  ResetAnts()

  Update parameters and

 return