Integer linear programming models for the weighted total domination problem

Exact and heuristic algorithms for the weighted total domination problem

“…A genetic algorithm (GA) is also developed, which is based on a greedy randomized adaptive search procedure (GRASP) version of our starting heuristic. We carry out a computational study to assess the performance of our new approaches in comparison to the previous work by [22]. The study reveals that our algorithms are up to 500 times faster and instances with up to 125 vertices can be solved to optimality within a timelimit of 1800 seconds.…”

“…The WTDP was recently introduced in [22], where three Mixed-Integer Programming (MIP) formulations to solve the problem were presented and evaluated in a computational study. In this paper, we present two new MIP models for the problem, and design solution frameworks based on them.…”

“…The paper is organized as follows. In the reminder of this section, we give a short overview of the models introduced in [22]. In Section 2 we present our two new MIP models, together with valid inequalities.…”

“…1.1 Revisiting the models of [22] In the following, we give a brief overview of the three formulations for the WTDP presented in [22] (we denote them as (MA1), (MA2), (MA3)). We re-implemented these models and included them in our computational study, see Section 5.…”

“…We note that in the WTDP, we are not just concerned with the concept of domination, but with the stronger concept of total domination, which imposes that for each vertex v ∈ D, there is also a neighbor of v in D (i.e., the vertices of D also need to be dominated by D). The WTDP was introduced in [22] an is an extension of the (unweighted) total domination problem (TDP), resp., the vertex-weighted total domination problem. In the TDP, the objective function has w i = 1 for all i ∈ V , and c e = 0 for all e ∈ E. The optimal solution of the TDP for a given graph is called its total domination number.…”