Benders algorithm to solve mixed integer linear programming, especially stochastic programming in seconds!
This repo has been archived in 190728. New update will be made to edxu96/MatrixOptim, which is the aggregation of robust optimization and matrix optimization. It's in matrix form as well, and there is a new function tool to convert the model to matrix form.
According to wikipedia:
Benders decomposition (or Benders' decomposition) is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure. This block structure often occurs in applications such as stochastic programming as the uncertainty is usually represented with scenarios. The technique is named after Jacques F. Benders.
https://en.wikipedia.org/wiki/Benders_decomposition
There are two algorithms, with one for standard MILP, and the other one specifically for stochastic programming without integer variables in second stage.
For detailed explanation, refer to Cookbook for Benders Decomposition, EDXU.
Put the file Benders.jl, Benders_milp.jl and Benders_lshaped.jl in your working folder. Write the following code
in your file:
using Benders
Bender.milp(n_x, n_y, vec_min_y, vec_max_y, vec_c, vec_f,
vec_b, mat_a, mat_b, epsilon, timesIterationMax)3. L-Shaped Benders Decomposition for Stochastic Programming without Integer Variables in Second Stage
Bender.lshaped(n_x, n_y, vec_min_y, vec_max_y, vec_f,
vec_pi, mat_c, mat_h, mat3_t, mat3_w, epsilon, timesIterationMax)Edward J. Xu (edxu96@outlook.com) (edxu96.github.io)
Version: 2.1
Date: July 28th, 2019