Exact solutions to generalized vertex covering problems: a comparison of two models
نویسندگان
چکیده
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 edgeweights in the objective function. Due to reported difficulties in finding good solutions for even modest sized problems via the use of exactmethods (CPLEX), heuristic solutions obtained from a customized genetic algorithm (GA)were reported byMilanovic (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 formany largeGVCPproblems.Moreover, our quadraticmodel dramatically G. Kochenberger (B) Business Analytics Department, School of Business Administration, University of Colorado at Denver, Denver, CO 80217, USA e-mail: [email protected] M. Lewis Craig School of Business, Missouri Western State University, St Joseph, MO 64507, USA e-mail: [email protected] F. Glover OptTek Inc, Boulder, CO 80302, USA e-mail: [email protected] H. Wang IB&TS Division, Sanchez School of Business, Texas A&M International University, Laredo, TX 78041, USA e-mail: [email protected]
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عنوان ژورنال:
- Optimization Letters
دوره 9 شماره
صفحات -
تاریخ انتشار 2015