An improved linearization technique for a class of quadratic 0-1 programming problems

The recent research on linearization techniques for solving 0-1 quadratic programming problems focuses on providing concise models and tightening constraint bounds. In this paper, we propose a computational enhancement for a linearization technique to make the linearized model much faster to solve. We investigate the computational performance of the proposed approach, by comparing it with other linearization techniques on a class of 0-1 quadratic programming problems. We can further speed up the proposed technique by heuristically tightening the constraint bounds, as demonstrated by solving the uncapacitated single allocation p-hub median problem using the Civil Aeronautics Board data.

[1]  Panos M. Pardalos,et al.  Construction of test problems in quadratic bivalent programming , 1991, TOMS.

[2]  Hanif D. Sherali,et al.  An improved linearization strategy for zero-one quadratic programming problems , 2006, Optim. Lett..

[3]  Fred W. Glover,et al.  Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs , 2004, Discret. Optim..

[4]  Warren P. Adams,et al.  A simple recipe for concise mixed 0-1 linearizations , 2005, Oper. Res. Lett..

[5]  M. O'Kelly,et al.  A quadratic integer program for the location of interacting hub facilities , 1987 .

[6]  Morton E. O'Kelly,et al.  Hub‐and‐Spoke Networks in Air Transportation: An Analytical Review , 1999 .

[7]  Andreas T. Ernst,et al.  Hub location problems , 2002 .

[8]  Jitamitra Desai,et al.  A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times , 2006 .

[9]  Warren P. Adams,et al.  A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems , 1986 .

[10]  Lawrence J. Watters.  Letter to the Editor - Reduction of Integer Polynomial Programming Problems to Zero-One Linear Programming Problems , 1967, Oper. Res..

[11]  Andreas T. Ernst,et al.  Efficient algorithms for the uncapac-itated single allocation p-hub median problem , 1996 .

[12]  D. Skorin-Kapov,et al.  Tight linear programming relaxations of uncapacitated p-hub median problems , 1996 .

[13]  Fred W. Glover,et al.  Technical Note - Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program , 1974, Oper. Res..

[14]  W. Art Chaovalitwongse,et al.  A new linearization technique for multi-quadratic 0-1 programming problems , 2004, Oper. Res. Lett..

[15]  L. Kaufman,et al.  An algorithm for the quadratic assignment problem using Bender's decomposition , 1978 .

[16]  F. Glover.  IMPROVED LINEAR INTEGER PROGRAMMING FORMULATIONS OF NONLINEAR INTEGER PROBLEMS , 1975 .

[17]  Willard I. Zangwill,et al.  Media Selection by Decision Programming , 1976 .

[18]  James F. Campbell,et al.  Integer programming formulations of discrete hub location problems , 1994 .

[19]  Fred W. Glover,et al.  Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems , 1973, Oper. Res..

[20]  Éric Soutif,et al.  Decomposition and Linearization for 0-1 Quadratic Programming , 2000, Ann. Oper. Res..