%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/lp_qap15
% name: LPnetlib/lp_qap15
% [Netlib LP problem qap15: minimize c'*x, where Ax=b, lo<=x<=hi]
% id: 661
% date: 
% author: T. Johnson
% ed: R. Bixby, M. Saltzman, T. Johnson
% fields: title name A b id aux kind date author ed notes
% aux: c lo hi z0
% kind: linear programming problem
%-------------------------------------------------------------------------------
% notes:
% A Netlib LP problem, in lp/generators/qap.  For more information          
% send email to netlib@ornl.gov with the message:                           
%                                                                           
% 	 send index from lp                                                      
% 	 send readme from lp/data                                                
% 	 send readme from lp/generators/qap                                      
%                                                                           
% This copy of QAP15 was created by the QAP generator program,              
% on an Sun UltraSparc, on May 15, 1997.                                    
%                                                                           
% The following are relevant excerpts from lp/data/readme (by David M. Gay):
%                                                                           
% The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude  
% slack and surplus columns and the right-hand side vector, but include     
% the cost row.  We have omitted other free rows and all but the first      
% right-hand side vector, as noted below.  The byte count is for the        
% MPS compressed file; it includes a newline character at the end of each   
% line.  These files start with a blank initial line intended to prevent    
% mail programs from discarding any of the data.  The BR column indicates   
% whether a problem has bounds or ranges:  B stands for "has bounds", R     
% for "has ranges".                                                         
%                                                                           
% The optimal value is from MINOS version 5.3 (of Sept. 1988)               
% running on a VAX with default options.                                    
%                                                                           
%                        PROBLEM SUMMARY TABLE                              
%                                                                           
% Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value         
% QAP15      6331  22275   110700 (see NOTES)       1.0409940410E+03        
%                                                                           
% Problems QAP8, QAP12, and QAP15 are from a generator by Terri             
% Johnson (communicated by a combination of Bob Bixby, Matt Saltzman, and   
% Terri Johnson).                                                           
%                                                                           
% Source for Terri Johnson's generator and input data                       
% for producing MPS files for QAP8, QAP12, and QAP15 appear in directory    
% lp/generators/qap.                                                        
%                                                                           
% Added to Netlib on 12 April 1996.                                         
%                                                                           
% The following are relevant excerpts from lp/generators/qap/readme         
% (by Terri Johnson):                                                       
%                                                                           
%         The Quadratic Assignment Problem (Problem QAP) is a specially-    
% structured zero-one quadratic programming problem.  While having          
% received considerable attention since its introduction into the           
% literature over 30 years ago, and while many applications exist in        
% various disciplines, this problem has resisted exact solution             
% procedures.  Only for smaller-size problems can optimal solutions be      
% obtained and verified.  The solution strategies for Problem QAP           
% developed by Johnson (Ph.D.  dissertation, Clemson University, 1992)      
% and Adams and Johnson (Improved Linear Programming-based Lower Bounds     
% for the Quadratic Assignment Problem, DIMACS:  Quadratic Assignment       
% and Related Problems, Vol. 16 (1994), 43-75) are based on a new,          
% equivalent, mixed- integer linear reformulation, Problem LP.              
%         The traditional , nonlinear formulation of Problem QAP has a      
% quadratic objective function, 2m constraints and m^2 binary variables.    
% The linearized version of concern, Problem LP, on the other hand, has     
% 2m^2(m-1) + m^2(m-1)^2/2 + 2m constraints, in addition to non-            
% negativity restrictions on all the variables, and m^2 binary variables    
% and m^2(m-1)^2 continuous variables.  The continuous relaxation of        
% Problem LP, obtained by omitting the x binary restrictions, possesses     
% a special block diagonal structure which readily lends itself to          
% decomposition techniques.  However, the inherent degeneracy makes this    
% a formidable program for problems as small in size as m=15 to 20.  A      
% smaller reformulation, which reduces the number of constraints and        
% variables each by m^2(m-1)^2/2, can be obtained via an appropriate        
% substitution of variables, but such a substitution forfeits the           
% problem structure.  It has been amply demonstrated that this              
% formulation serves as a unifying and dominating entity with respect to    
% the different linear reformulations of Problem QAP, as well as with       
% respect to a variety of bounding procedures.  Consequently, the           
% ability to quickly solve this linear formulation holds the promise of     
% being able to solve larger-sized QAP's.                                   
%         Provided here is Fortran source, newlp.f, for a program that      
% generates MPS files for the linearized QAP with the substitution of       
% variables.  Under the assumption that the test problem is symmetric,      
% the generator reads the problem size, m, and an mxm matrix with the       
% original distances in the upper half of the matrix and the original       
% flows in the lower half of the matrix.  All diagonal entries are 0.       
% Using this input, the generator program computes the objective            
% function coefficients for the quadratic terms, and automatically          
% computes the constraints.  The objective function is assumed to           
% contain no linear terms since such values can be easily incorporated      
% into the quadratic terms.                                                 
%         Input files qap8.dat, qap12.dat, and qap15.dat cause the          
% generator program to emit MPS files for well-known test problems of       
% Nugent, C.E., T.E. Vollmann, and J. Ruml, An Experimental Comparison      
% of Techniques for the Assignment of Facilities to Locations,              
% Operations Research, Vol. 16, No. 1 (1968), 150-173, of sizes m=8, 12,    
% and 15 for the linearization.                                             
%                                                                           
%                                                                           
% PROBLEM:  M = 15		No. of Variables	No. of Constraints                     
%                                                                           
% 	QAP				225			  30                                                        
% 	LP (with substitution)	      22275			6330                                
% 	Optimal value: 1.0409940410e+3                                           
%                                                                           
% For more information, please contact Terri Johnson at:                    
% 	johnsont@numen.elon.edu                                                  
%-------------------------------------------------------------------------------
