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    Solving Mixed-Integer Linear Programs With MATLAB

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    Mahfuzulhoq Chowdhury
    This document provides instructions for solving mixed-integer linear programs using MATLAB and the optimization toolbox. It begins by explaining how to install MATLAB, YALMIP, which is a modeling environment for optimization problems, and the optimization toolbox. It then provides an example of using YALMIP to model and solve a simple mixed-integer linear program. Finally, it presents a more complex unit commitment example to illustrate modeling a real-world problem with YALMIP.

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    Solving Mixed-Integer Linear Programs With MATLAB

    Uploaded by

    Mahfuzulhoq Chowdhury
    38 views19 pages
    This document provides instructions for solving mixed-integer linear programs using MATLAB and the optimization toolbox. It begins by explaining how to install MATLAB, YALMIP, which is a modeling environment for optimization problems, and the optimization toolbox. It then provides an example of using YALMIP to model and solve a simple mixed-integer linear program. Finally, it presents a more complex unit commitment example to illustrate modeling a real-world problem with YALMIP.

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    Matlab_mip

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    This document provides instructions for solving mixed-integer linear programs using MATLAB and the optimization toolbox. It begins by explaining how to install MATLAB, YALMIP, which is a modeling environment for optimization problems, and the optimization toolbox. It then provides an example of using YALMIP to model and solve a simple mixed-integer linear program. Finally, it presents a more complex unit commitment example to illustrate modeling a real-world problem with YALMIP.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    38 views19 pages

    Solving Mixed-Integer Linear Programs With MATLAB

    Uploaded by

    Mahfuzulhoq Chowdhury
    This document provides instructions for solving mixed-integer linear programs using MATLAB and the optimization toolbox. It begins by explaining how to install MATLAB, YALMIP, which is a modeling environment for optimization problems, and the optimization toolbox. It then provides an example of using YALMIP to model and solve a simple mixed-integer linear program. Finally, it presents a more complex unit commitment example to illustrate modeling a real-world problem with YALMIP.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 19

    Solving Mixed-Integer Linear

    Programs with MATLAB


    Bowen Hua
    Department of Electrical and Computer Engineering
    The University of Texas at Austin
    November 2018
    Outline
    • Install MATLAB and YALMIP
    • Example problem
    • Example unit commitment problem
    Outline
    • Install MATLAB and YALMIP
    • Example problem
    • Example unit commitment problem
    Install MATLAB and YALMIP
    • Cockrell School provides licenses for MATLAB.
    • http://www.engr.utexas.edu/itg/products/8017-matlab
    • Remember to install the optimization toolbox.
    • Download YALMIP and install it.
    • https://yalmip.github.io/download/
    • https://yalmip.github.io/tutorial/installation/
    • Unzip the downloaded file into a folder ~/YALMIP-master.
    • Add the folder with all its subfolders to your MATLAB path
    • See next slide for detailed instructions
    Add YALMIP to MATLAB Path
    • Click “Set Path” on the MATLAB toolbar

    • Click “Add with Subfolders”


    • Add the above-mentioned folder
    • Run yalmiptest in MATLAB to test the installation
    What is YALMIP?
    • YALMIP is a modeling environment for
    optimization problems.
    • It allows a user to describe an optimization
    problem by writing algebraic equations.
    • It then translate the optimization problem
    into a form that is recognizable by a solver.
    • The solver then finds the solution to the
    problem.
    Outline
    • Install MATLAB and YALMIP
    • Example problem
    • Example unit commitment problem
    Describe the problem with YALMIP
    • Declare variables
    • Define constraints
    • Define the objective function
    • Solve
    Example Problem

    • Problem (4.45) in Section 4.8.3 on page 143 of Section 4.


    • Mathematical formulation of the problem:
    Declare variables
    • Code: • binvar(1,1)defines a binary
    z = binvar(1,1); variable.
    x = sdpvar(1,1); • sdpvar(1,1)defines a
    continuous variable.
    Define constraints
    • Put all constraints in a list:
    constr = [-x == -3];
    constr = [constr, 2*z <= x <= 4 * z];
    • Double-sided inequality constraints are supported.
    Define objective function
    Objective = 4*z + x;
    Solve
    options = sdpsettings('verbose',1,'solver','INTLINPROG');
    sol = optimize(constr,Objective,options);
    • We use the built-in mixed-integer linear program solve of MATLAB, intlinprog.
    • To see the optimal objective function value, we can use:
    • value(Objective)
    • To see the optimal value of the decision variables, we can use:
    • value(x)
    • value(z)
    Outline
    • Install MATLAB and YALMIP
    • Example problem
    • Example unit commitment problem
    Example unit
    commitment problem
    • Unit Commitment Example in
    Section 10.8.1 on page 126 of
    Section 10.
    • Mathematical formulation of
    the problem:
    Declare variables
    • Code: • binvar(2,1)defines a 2-
    z1 = binvar(2,1); column-vector of binary
    z2 = binvar(2,1); variables.
    u1 = binvar(2,1); • sdpvar(2,1)defines a 2-
    u2 = binvar(2,1); column-vector of continuous
    P1 = sdpvar(2,1); variables.
    P2 = sdpvar(2,1);
    • z1, u1, P1 are variables for
    generator 1.
    Define constraints
    • Bounds for power outputs. These constraints are defined in vector form:
    private_constr = [0 <= P1 <= 100 * z1];
    private_constr = [private_constr, 0 <= P2 <= 50 * z1];
    • Logical constraints between startup and on/off variables:
    private_constr = [private_constr, u1(1) == z1(1) - 1];
    private_constr = [private_constr, u1(2) == z1(2) - z1(1)];
    private_constr = [private_constr, u2(1) == z2(1)];
    private_constr = [private_constr, u2(2) == z2(2) - z2(1)];
    • Power balance constraints:
    power_balance = [P1(1) + P2(1) == 110];
    power_balance = [power_balance, P1(2) + P2(2) == 125];
    Define objective function
    Objective = 1000 * (sum(u1) + sum(u2)) + 25 * sum(P1) + 35 * sum(P2);
    Solve
    options = sdpsettings('verbose',1,'solver','INTLINPROG');
    sol = optimize([private_constr, power_balance],Objective,options);
    • To see the optimal objective function value, we can use:
    • value(Objective)
    • To see the optimal value of the decision variables, we can use:
    • value(P1)

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