## Welcome to the world of Optimizations

In this blog concepts of conventional and unconventional optimization techniques are discussed.

# What is Scilab?

Developed at INRIA, Scilab has been developed for system control and signal processing applications. It is freely distributed in source code format (see the copyright file).
A key feature of the Scilab syntax is its ability to handle matrices:
Polynomials, polynomials matrices and transfer matrices are also defined and the syntax used for manipulating these matrices is identical to that used for manipulating constant vectors and matrices.
Scilab provides a variety of powerful primitives for the analysis of non-linear systems. Integration of explicit and implicit dynamic systems can be accomplished numerically.
The scicos(similar to simulink) toolbox allows the graphic definition and simulation of complex interconnected hybrid systems.
There exist numerical optimization facilities for non linear optimization (including non differentiable optimization), quadratic optimization and linear optimization.
Scilab has an open programming environment where the creation of functions and libraries of functions is completely in the hands of the user.
Finally, Scilab is easily interfaced with Fortran or C subprograms. This allows use of standardized packages and libraries in the interpreted environment of Scilab.

The site gives detailed documentation also.

I will post some programs in scilab  to solve some optimization problems soon.

Download scilab and install it. All the best

## Wednesday, December 8, 2010

### Binary integer programming.

Integer programming is one of the important branch of optimization where some of the variables are bound to be integers.
The integer linear programming is described as follows.
min f'*X
Subject to:  A*X <= b,
Aeq*X = beq,
Where the elements of X are integers.
There are two types of integer programming problems.
1. Binary integer programming.
2. Mixed integer Programming
The mixed integer programming can be modeled as binary integer programming by making some simplifications.
Solving a binary integer programming problem.
To solve binary integer programming problem in Matlab the routine “bintprog” is used
[X FVAL] = bintprog(f,A,b,Aeq,beq,X0) sets the starting point to X0. The   starting point X0 must be binary integer and feasible, or it will   be ignored.

This routine returns the value of the objective function at
FVAL = f'*X.
Example
Minimize -9x1-5x2-6x3-4x4
Subject to
6x1+3x2+5x3+2x4<9
x3+x4  <1
-x1+x3   <   0
-x2 +  x4<  0

Program
Clear;
clc;
f = [-9; -5; -6; -4];
A = [6 3 5 2; 0 0 1 1; -1 0 1 0; 0 -1 0 1];
b = [9; 1; 0; 0];
[X F] = bintprog(f,A,b)
l=[0 0 0 0]';
u=[1 1 1 1]';
[X1 F1]=linprog(f,A,b,[],[],l,u)
Results
Binary integer programming
X =

1
1
0
0
F =  -14
Linear programming
X1 =
0.6667
1.0000
0.0000
1.0000
F1 = -15.0000
It can be observed that function value in integer programming is little more.
Rounding off the linear programming results does not yield the integer programming results.