Facility Location with Tree Topology and Radial Distance Constraints

Algorithm 3

Simulated annealing-based metaheuristic.

	Data: input matrices and and input graph .
	Result: a feasible solution for .
	Step 1:;
	Set and ;
	while loop as in Step 1 of Algorithm 2;
	and ;
	Step 2:;
	while () do
	Set and ;
	for each () do
	Draw a random number r from ;
	if then
	and ;
	Remove all neighbors of from W;
	while ( is not empty and ) do
	Chose a vertex randomly from W;
	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 ;
	if (A better solution is found) then
	Save it in and set and ;
	else
	Compute as the difference between the current objective value minus the previous one;
	Draw a random number r from ;
	Compute ;
	if then
	Accept the new solution and save it in ;
	else
	;
	and ;
	if () then
	;
	if () then
	;
	else
	;
	Return best solution found and its objective function value;