Optim Lett DOI 10.1007/s11590-015-0851-1 ORIGINAL PAPER Exact solutions to generalized vertex covering problems: a comparison of two models Gary Kochenberger · Mark Lewis · Fred Glover · Haibo Wang Received: 11 May 2013 / Accepted: 7 January 2015 © Springer-Verlag Berlin Heidelberg 2015 Abstract 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 G. Kochenberger (B ) Business Analytics Department, School of Business Administration, University of Colorado at Denver, Denver, CO 80217, USA e-mail: gary.kochenberger@cudenver.edu M. Lewis Craig School of Business, Missouri Western State University, St Joseph, MO 64507, USA e-mail: mlewis14@missouriwestern.edu F. Glover OptTek Inc, Boulder, CO 80302, USA e-mail: glover@opttek.com H. Wang IB&TS Division, Sanchez School of Business, Texas A&M International University, Laredo, TX 78041, USA e-mail: hwang@tamiu.edu 123