CoeffMatrix

Julia Module to Extract the Coefficient Matrix in Standard LP or MILP Problem

This repo has been archived On Aug 11, 2019. New update will be made to edxu96/MatrixOptim, which is the aggregation of robust optimization and decomposition.

To use the algorithms like Benders Decomposition in edxu96/MatrixOptim for better solving MILP or stochastic programming, you have to convert the problem into standard form. The way to find the coefficient matrix for continuous variables and integer variables is trivial and easy to make a mistake. This module can help you to generate the coefficient matrix by sequential calculation.

Algorithm Description

How it works

function updateRow(; mat_coeff = 0, add = false, num_m, num_n, mat_a,
    vec_i_x, vec_j_x, vec_i_a = vec_i_x, vec_j_a = vec_j_x, inverse = false)

Default double-script order: | n(j)| |m(i) * |

The default single-script order: (To bottom, then right)

k = (j - 1) * m + i

To convert back to double-script order:

i = k % m
j = Int8((k - i) / m)

The inversed single-script order: (To right, then bottom)

k = (i - 1) * n + j
j = k % n
i = Int8((k - j) / n)

Examples

For example, to generate a coefficient matrix with one row:

mat_a = [99.74  99.21  100.21  99.76  100.48  100.7  99.42  99.11  97.69  98.94  97.22  98.99;
         1.89   2.02   1.95    2.16   2.16    2.08   2.08   2.09   1.97   1.99   1.89   1.95;
         15.58  15.11  14.93   14.86  15.06   15.51  14.41  14.96  15.62  14.4   15.64  14.52]
(mat_coeff, mat_a_cal) = updateRow(num_m = 3, num_n = 12, mat_a = - hcat(mat_a[:,1]),
    vec_i_x = [1 2 3], vec_j_x = [1])
(mat_coeff, mat_a_cal) = updateRow(add = 1, mat_coeff = mat_coeff, num_m = 3, num_n = 12,
    mat_a = - mat_a, vec_i_x = [1 2 3], vec_j_x = collect(2: 1: 12))
(mat_coeff, mat_a_cal) = updateRow(add = 1, mat_coeff = mat_coeff, num_m = 3, num_n = 12,
    mat_a = mat_a, vec_i_x = [1 2 3], vec_j_x = collect(1: 1: 11), vec_j_a = collect(1: 1: 11) .+ 1)

which is the matrix form of the following constraint:

@constraint(model, - sum(mat_a[i, 1] * x[i, 1] for i = 1: 3) - sum((x[i,t] - x[i, t-1]) * mat_a[i, t]
	for i = 1: 3, t = 2: 12) == 0)

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Edward J. Xu
[email protected]
Version: 2.0
Date: April 7th, 2019