This document discusses using genetic algorithms to solve linear systems of equations. It explains that genetic algorithms can be used as an alternative to conventional numerical methods like Gaussian elimination to find optimal values for unknown variables. The key steps are: (1) creating a genetic class with genes representing each unknown variable containing possible values, (2) defining a fitness function that substitutes gene values into the equations, (3) running the genetic algorithm to find values that minimize the fitness value and solve the system of equations. The genetic algorithm approach avoids rounding errors of mathematical methods and can solve large matrix systems.

1. SOLVING
LINEAR
EQUATIONS
WITH GENETIC
SUBMITTED TO: DR ALI
MUHAMMAD LATIF
PRESENTED: SAJID ALI
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2. Basic concept of Linear Equation in GA:
 For solving linear system of equations iterative algorithms are used.
 GA in finding optimal solution of systems of simultaneous linear equations.
 Conventional numerical methods such as Gaussian Elimination method produce a set of solutions for a
particular system of simultaneous linear equations
 GA includes a search for optimal values for the unknown variables in the equation that best fit the
system of linear equation. In mathematics solving for avoid the rounding errors(big dis-advantage of
mathematical solving systems) and inverting large matrices.
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3. How genetic algorithms can be used to find the unknowns in a
system of linear equations?
We want to figure out which x and y values we can use to solve both equations
simultaneously
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4. Creating Class, Gens
we can do with our genetic
engine using one gene for
each unknown and a gene set
containing all numbers in the
range of expected values
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5. Fitness Function
we can substitute the gene values directly into x and y
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6. Fitness Class
With Fitness defined as:
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7. Optimal fitness
That means the optimal fitness value in our test is going to be zero.
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8. Display
In display, we can write out the x and y values
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9. Final Part Just Running
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