On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

This paper addresses the solution of a cardinality boolean quadratic programming problem using three different approaches. The first transforms the original problem into six Mixed-Integer Linear Programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/20072013) under grant agreement n. PCOFUND-GA-2009-246542 and from the Fundação para a Ciência e Tecnologia, Portugal, under grant agreement n. DFRH/WIIA/67/2011. Ricardo M. Lima Computer, Electrical and Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. E-mail: [email protected] Tel.: +966 12 808 0434 Ignacio E. Grossmann Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. E-mail: [email protected] Manuscript Click here to download Manuscript Lima_Grossmann_COA_Springer_Review_v3.pdf Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 Ricardo M. Lima, Ignacio E. Grossmann