Facility Location with Tree Topology and Radial Distance Constraints

Algorithm 2

Guided local search-based metaheuristics.

	Data: input matrices and and input graph .
	Result: a feasible solution for .
	Step 1:;
	Set and ;
	while ( is not empty) do
	Let be the vertex with minimum degree in ;
	and ;
	Remove all neighbors of from W;
	Find the minimum spanning tree formed with nodes in S using the Kruskal algorithm;
	Assign each user to its nearest facility in S and compute the objective function value of ;
	Save the current solution found in if its objective function value is less than the best found so far;
	;
	Step 2:;
	while () do
	Update degree vector according to the indices of each element in as ;
	Set and ;
	while ( is not empty and ) do
	Let be the vertex with minimum value in ;
	and ;
	Remove all neighbors of from W;
	Find the minimum spanning tree formed with nodes in S using the Kruskal algorithm;
	Assign each user to its nearest facility in S and compute the objective function value of ;
	Save the current solution found in if its objective function value is less than the best found so far. If a better solution is found, set ; ;
	If () then
	;
	else
	;
	Return best solution found and its objective function value;