Exact solutions to generalized vertex covering problems: a comparison of two models

Gary Kochenberger, Mark Lewis, Fred Glover, Haibo Wang
Optimization Letters, In Press

The generalized vertex cover problem (GVCP) was recently introduced in the literature and modeled as a binary linear program. GVCP extends classic vertex cover problems to include both node and edge weights in the objective function. Due to reported difficulties in finding good solutions for even modest sized problems via the use of exact methods (CPLEX), heuristic solutions obtained from a customized genetic algorithm (GA) were reported by Milanovic (Comput Inf 29:1251–1265, 2010). In this paper we consider an alternative model representation for GVCP that translates the constrained linear (binary) form to an unconstrained quadratic binary program and compare the linear and quadratic models via computations carried out by CPLEX’s branch-and-cut algorithms. For problems comparable to those previously studied in the literature, our results indicate that the quadratic model efficiently yields optimal solutions for many large GVCP problems. Moreover, our quadratic model dramatically outperforms the corresponding linear model in terms of time to reach and verify optimality and in terms of the optimality gap for problems where optimality is unattained.