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‎codes/chapter3/GenerateRandomLPs.m

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function GenerateRandomLPs
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% Filename: GenerateRandomLPs.m
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% Description: Custom menu for creating random LPs
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% Authors: Ploskas, N., & Samaras, N.
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%
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% Syntax: GenerateRandomLPs
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%
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% Input: None
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%
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% Output: files that store the generated random LPs
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choice = 0;
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while choice ~= 4
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% show menu
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choice = menu('Generate Random LPs', ...
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'Generator Initialization', 'Dense Random LPs', ...
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'Sparse Random LPs', 'Exit');
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if choice == 1 % initialize generator
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seedNumber = input('Please give the seed number: ');
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rand('state', seedNumber);
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sprand('state');
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elseif choice == 2 % create dense random LPs
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m = input('Please give the number of constraints: ');
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n = input('Please give the number of variables: ');
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denseMenu(m, n);
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elseif choice == 3 % create sparse random LPs
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m = input('Please give the number of constraints: ');
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n = input('Please give the number of variables: ');
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sparseMenu(m, n);
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elseif choice == 4 % exit
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return;
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end
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end
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end

‎codes/chapter3/denseMenu.m

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function denseMenu(m, n)
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% Filename: denseMenu.m
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% Description: Custom menu for creating dense random LPs
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% Authors: Ploskas, N., & Samaras, N.
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%
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% Syntax: denseMenu(m, n)
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%
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% Input:
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% -- m: the number of constraints of the generated random LPs
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% -- n: the number of variables of the generated random LPs
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%
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% Output: files that store the generated dense random LPs
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% read the directory to store the LPs
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pathName = input(['Please give the path where you want ' ...
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'to store the generated LPs: ']);
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% read the number of the LPs to generate
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nOfProblems = input(['Please give the number of the LPs ' ...
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'that you want to create: ']);
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% read the ranges of the values for matrix A
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Alu = input(['Please give the range of the values for ' ...
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'matrix A: ']);
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% read the ranges of the values for vector c
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clu = input(['Please give the range of the values for ' ...
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'vector c: ']);
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% read the type of optimization
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optType = input(['Please give the type of optimization ' ...
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'(0 min, 1 max, 2 random): ']);
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% read if all LPs will be optimal
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optimality = input(['Do you want all the LPs to be ' ...
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'optimal (1 yes, 2 no): ']);
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if optimality == 1 % optimal LPs
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% read the center of the circle
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center = input(['Please give the center of the circle: ']);
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% read the radius of the circle
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R = input(['Please give the radius of the circle ' ...
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'(must be less than the center of the circle: ']);
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while R >= center % read R
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R = input(['Please give the radius of the circle ' ...
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'(must be less than the center of the circle: ']);
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end
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% create nOfProblems dense random optimal LPs
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for i = 1:nOfProblems
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[A, c, b, Eqin, MinMaxLP] = denseRandomOptimal(m, n, ...
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optType, Alu, clu, center, R);
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s1 = num2str(m);
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s2 = num2str(n);
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k = num2str(i);
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fname = [pathName '/' 'fdata' k '_' s1 'x' s2];
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Name = ['fdata' k '_' s1 'x' s2];
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R = [];
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BS = [];
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NonZeros = nnz(A);
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c0 = 0;
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c00 = 0;
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% save variables in a MAT file
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eval(['save ' fname '.mat A c b Eqin MinMaxLP Name ' ...
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'R BS NonZeros c0 c00']);
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end
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else % not optimal LPs
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% read the ranges of the values for vector b
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blu = input(['Please give the range of the values for ' ...
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'vector b: ']);
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% read the ranges of the values for vector Eqin
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Eqinlu = input(['Please give the range of the values ' ...
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'for vector Eqin (0 - equality constraints, 1 - ' ...
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' less than or equal to inequality constraints, ' ...
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' 2 - greater than or equal to inequality ' ...
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'constraints: ']);
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for i = 1:nOfProblems % create nOfProblems dense random LPs
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[A, c, b, Eqin, MinMaxLP] = denseRandom(m, n, ...
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optType, Alu, clu, blu, Eqinlu);
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s1 = num2str(m);
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s2 = num2str(n);
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k = num2str(i);
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fname = [pathName '/' 'fdata' k '_' s1 'x' s2];
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Name = ['fdata' k '_' s1 'x' s2];
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R = [];
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BS = [];
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NonZeros = nnz(A);
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c0 = 0;
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c00 = 0;
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% save variables in a MAT file
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eval(['save ' fname '.mat A c b Eqin MinMaxLP Name ' ...
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'R BS NonZeros c0 c00']);
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end
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end
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end
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function denseMenu(m, n)
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% Filename: denseMenu.m
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% Description: Custom menu for creating dense random LPs
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% Authors: Ploskas, N., & Samaras, N.
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%
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% Syntax: denseMenu(m, n)
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%
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% Input:
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% -- m: the number of constraints of the generated random LPs
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% -- n: the number of variables of the generated random LPs
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%
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% Output: files that store the generated dense random LPs
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% read the directory to store the LPs
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pathName = input(['Please give the path where you want ' ...
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'to store the generated LPs: ']);
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% read the number of the LPs to generate
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nOfProblems = input(['Please give the number of the LPs ' ...
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'that you want to create: ']);
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% read the ranges of the values for matrix A
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Alu = input(['Please give the range of the values for ' ...
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'matrix A: ']);
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% read the ranges of the values for vector c
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clu = input(['Please give the range of the values for ' ...
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'vector c: ']);
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% read the type of optimization
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optType = input(['Please give the type of optimization ' ...
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'(0 min, 1 max, 2 random): ']);
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% read if all LPs will be optimal
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optimality = input(['Do you want all the LPs to be ' ...
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'optimal (1 yes, 2 no): ']);
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if optimality == 1 % optimal LPs
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% read the center of the circle
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center = input(['Please give the center of the circle: ']);
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% read the radius of the circle
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R = input(['Please give the radius of the circle ' ...
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'(must be less than the center of the circle: ']);
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while R >= center % read R
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R = input(['Please give the radius of the circle ' ...
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'(must be less than the center of the circle: ']);
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end
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% create nOfProblems dense random optimal LPs
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for i = 1:nOfProblems
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[A, c, b, Eqin, MinMaxLP] = denseRandomOptimal(m, n, ...
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optType, Alu, clu, center, R);
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s1 = num2str(m);
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s2 = num2str(n);
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k = num2str(i);
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fname = [pathName '/' 'fdata' k '_' s1 'x' s2];
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Name = ['fdata' k '_' s1 'x' s2];
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R = [];
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BS = [];
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NonZeros = nnz(A);
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c0 = 0;
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c00 = 0;
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% save variables in a MAT file
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eval(['save ' fname '.mat A c b Eqin MinMaxLP Name ' ...
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'R BS NonZeros c0 c00']);
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end
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else % not optimal LPs
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% read the ranges of the values for vector b
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blu = input(['Please give the range of the values for ' ...
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'vector b: ']);
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% read the ranges of the values for vector Eqin
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Eqinlu = input(['Please give the range of the values ' ...
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'for vector Eqin (0 - equality constraints, 1 - ' ...
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' less than or equal to inequality constraints, ' ...
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' 2 - greater than or equal to inequality ' ...
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'constraints: ']);
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for i = 1:nOfProblems % create nOfProblems dense random LPs
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[A, c, b, Eqin, MinMaxLP] = denseRandom(m, n, ...
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optType, Alu, clu, blu, Eqinlu);
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s1 = num2str(m);
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s2 = num2str(n);
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k = num2str(i);
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fname = [pathName '/' 'fdata' k '_' s1 'x' s2];
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Name = ['fdata' k '_' s1 'x' s2];
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R = [];
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BS = [];
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NonZeros = nnz(A);
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c0 = 0;
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c00 = 0;
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% save variables in a MAT file
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eval(['save ' fname '.mat A c b Eqin MinMaxLP Name ' ...
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'R BS NonZeros c0 c00']);
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end
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end
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end

‎codes/chapter3/denseRandom.m

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function [A, c, b, Eqin, MinMaxLP]= denseRandom(m, n, ...
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optType, Alu, clu, blu, Eqinlu)
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% Filename: denseRandom.m
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% Description: Creates dense random LPs
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% Authors: Ploskas, N., & Samaras, N.
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%
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% Syntax: [A, c, b, MinMaxLP, Eqin]= denseRandom(m, n, ...
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% minCard, Alu, clu, blu, Eqinlu)
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%
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% Input:
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% -- m: the number of constraints of the generated random
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% LPs
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% -- n: the number of variables of the generated random
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% LPs
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% -- optType: the type of optimization (0 min, 1 max, 2
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% random)
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% -- Alu: the ranges of the values for matrix A
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% (size 1 x 2)
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% -- clu: the ranges of the values for vector c
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% (size 1 x 2)
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% -- blu: the ranges of the values for vector b
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% (size 1 x 2)
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% -- Eqinlu: the ranges of the values for vector Eqin
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% (size 1 x 2)
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%
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% Output:
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% -- A: matrix of coefficients of the constraints
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% (size m x n)
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% -- c: vector of coefficients of the objective function
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% (size n x 1)
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% -- b: vector of the right-hand side of the constraints
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% (size m x 1)
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% -- Eqin: vector of the type of the constraints
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% (size m x 1)
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% -- MinMaxLP: the type of optimization
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Al = Alu(1); % get the lower bound of A
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Au = Alu(2); % get the upper bound of A
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% create matrix A
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A = floor((Au - Al + 1) * rand(m, n)) + Al;
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cl = clu(1); % get the lower bound of c
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cu = clu(2); % get the upper bound of c
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% create vector c
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c = floor((cu - cl + 1) * rand(n, 1)) + cl;
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bl = blu(1); % get the upper bound of b
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bu = blu(2); % get the upper bound of c
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% create vector b
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b = floor((bu - bl + 1) * rand(m, 1)) + bl;
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eqinl = Eqinlu(1); % get the lower bound of Eqin
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eqinu = Eqinlu(2); % get the upper bound of Eqin
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% create vector Eqin
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Eqin = floor((eqinu - eqinl + 1) * rand(m, 1)) + eqinl;
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% less than or equal to inequality constraints
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Eqin(Eqin == 1) = -1;
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% greater than or equal to inequality constraints
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Eqin(Eqin == 2) = 1;
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if optType == 0 % minimization
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MinMaxLP = -1;
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elseif optType == 1 % maximization
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MinMaxLP = 1;
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else % pick random optimization type
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MinMaxLP = -1;
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if randi(2) < 2
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MinMaxLP = 1;
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end
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end
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end

‎codes/chapter3/denseRandomOptimal.m

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function [A, c, b, Eqin, MinMaxLP] = ...
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denseRandomOptimal(m, n, optType, Alu, clu, center, R)
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% Filename: denseRandomOptimal.m
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% Description: Creates dense random optimal LPs
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% Authors: Ploskas, N., & Samaras, N.
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%
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% Syntax: [A, c, b, Eqin, MinMaxLP] = ...
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% denseRandomOptimal(m, n, optType, Alu, clu, center, R)
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%
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% Input:
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% -- m: the number of constraints of the generated random
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% LPs
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% -- n: the number of variables of the generated random
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% LPs
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% -- optType: the type of optimization (0 min, 1 max, 2
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% random)
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% -- Alu: the ranges of the values for matrix A
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% (size 1 x 2)
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% -- clu: the ranges of the values for vector c
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% (size 1 x 2)
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% -- center: the center of the circle
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% -- R: the radius of the circle
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% Output:
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% -- A: matrix of coefficients of the constraints
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% (size m x n)
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% -- c: vector of coefficients of the objective function
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% (size n x 1)
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% -- b: vector of the right-hand side of the constraints
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% (size m x 1)
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% -- Eqin: vector of the type of the constraints
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% (size m x 1)
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% -- MinMaxLP: the type of optimization
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%
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cl = clu(1); % get the lower bound of c
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cu = clu(2); % get the upper bound of c
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% create vector c
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c = round((cu - cl + 1) * randn(n, 1)) + cl;
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Al = Alu(1); % get the lower bound of A
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Au = Alu(2); % get the upper bound of A
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A = zeros(m, n);
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b = zeros(m, 1);
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k = ones(1, n) * center;
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for i = 1:m % create matrix A and vector b
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% create a row of matrix A
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a = round((Au - Al + 1) * rand(1, n)) + Al;
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% calculate the hyperplane that is tangent
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% in a random point of the sphere
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y = k + r * (a / norm(a));
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b0 = a * y';
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b(i, 1) = b0; % add the point to vector b
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A(i, :) = a; % add the row to matrix A
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end
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% create vector Eqin
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Eqin(1:m, 1) = -1;
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if optType == 0 % minimization
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MinMaxLP = -1;
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elseif optType == 1 % maximization
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MinMaxLP = 1;
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else % pick random optimization type
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MinMaxLP = -1;
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if randi(2) < 2
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MinMaxLP = 1;
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end
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end
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end

‎codes/chapter3/example1_1.mps

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NAME EXAMPLE1_1
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ROWS
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N OBJ
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G R1
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E R2
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L R3
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E R4
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G R5
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G R6
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L R7
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COLUMNS
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X1 R2 4
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X1 R3 -3
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X1 R4 4
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X1 R5 1
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X1 OBJ -2
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X2 R1 2
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X2 R2 -3
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X2 R3 2
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X2 OBJ 4
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X3 R1 3
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X3 R2 8
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X3 R4 -1
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X3 R6 1
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X3 R7 1
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X3 OBJ -2
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X4 R2 -1
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X4 R3 -4
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X4 R4 4
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X4 OBJ 2
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RHS
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RHS1 R1 6
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RHS1 R2 20
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RHS1 R3 -8
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RHS1 R4 18
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RHS1 R5 1
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RHS1 R6 2
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RHS1 R7 10
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BOUNDS
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FR BND1 X1
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FR BND1 X3
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ENDATA

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