Experimental Results on the New Techniques for Integer Programming Formulations

We present experimental results on some new formulations of problems as mixed integer programmes.On a family of small problems involving ‘either/or’ constraints, the newer formulations performed distinctly better than does a ‘textbook formulation’, with an advantage that increases with problem size. On a second set of small problems involving separable programmes with fixed charges imposed on a piecewise-linear functions, the advantage of the newer formulations was again evident.

[1]  R. R. Meyer,et al.  Mixed integer minimization models for piecewise-linear functions of a single variable , 1976, Discret. Math..

[2]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[3]  Toshimde Ibaraki.  Integer programming formulation of combinatorial optimization problems , 1976, Discret. Math..

[4]  Susan Powell,et al.  Fortran codes for mathematical programming: linear, quadratic and discrete , 1973 .

[5]  H. P. Williams,et al.  Model Building in Mathematical Programming , 1979 .

[6]  H. P. Williams.  Experiments in the formulation of integer programming problems , 1974 .

[7]  R. R. Meyer.  A theoretical and computational comparison of “equivalent” mixed‐integer formulations , 1981 .

[8]  R. R. Meyer,et al.  Rational Mixed-Integer Minimization Models. , 1976 .

[9]  L. A. Oley,et al.  Automatic reformulation of mixed and pure integer models to reduce solution time in apex IV , 1983, SMAP.

[10]  Ellis L. Johnson,et al.  Solving Large-Scale Zero-One Linear Programming Problems , 1983, Oper. Res..

[11]  R. D. Young.  Hypercylindrically Deduced Cuts in Zero-One Integer Programs , 1971, Oper. Res..

[12]  Fred W. Glover.  New results on equivalent integer programming formulations , 1975, Math. Program..

[13]  Fred W. Glover,et al.  Polyhedral annexation in mixed integer and combinatorial programming , 1975, Math. Program..

[14]  Robert G. Jeroslow,et al.  Cutting-Plane Theory: Disjunctive Methods , 1977 .

[15]  R. Meyer.  Integer and mixed-integer programming models: General properties , 1975 .

[16]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[17]  J. K. Lowe.  Modelling with Integer Variables. , 1984 .

[18]  E. Balas.  DISJUNCTIVE PROGRAMMING: CUTTING PLANES FROM LOGICAL CONDITIONS , 1975 .

[19]  Charles E. Blair,et al.  A converse for disjunctive constraints , 1978 .