Problem Description

This project aims to find the solution of a specific mathematical equation using Genetic Algorithm (GA).

The given equation is a mathematical expression containing variables x and arimethic operations, trigonometric function, exponential functions and other calculations.

You can find the rules for input here: Input Syntax

For example, we have an expression:

$f(x) = x^2 + log_{50}(\frac{x}{5} + \frac{1}{x}) + sin(x^2+1) - 5.5x$

The goal is to find the value of variable $x$ such that the function $f(x)$ approaches 0. Here, we find that if $x=x_0$ then $f(x_0) \approx 1.38 \times 10^{-9}$, so we can conclude $x_0$ is a solution.

Input

• String of the function. The user have to follow the function entry rules in the section Input Syntax

• Example:

  x^2 + log((x/5 + 1/x), 50) + sin(x^2 + 1) + sqrt(x^2 + 1) - 5.5 * x

Output

• If we find the value $x_0$ such that $f(x_0) \approx 0$ or $f(x_0) < 10^{-8}$ then we can conclude that $x_0$ is 1 solution of $f(x)$.

• Otherwise, we conclude there is no solution of the given equation.

Input Syntax

Function	Description
+, -, *, /	Add, Minus, Product, Divide respectively
a ^ n, a ** n	a to the power n
e	Return Euler's number (2.7182...)
pi	Return PI (3.1415...)
sin(x)	Return the sine of a number x
cos(x)	Return the cosine of a number x
tan(x)	Return the tangent of a number x
cot(x)	Return the cotangent of a number x
log(x, base)	Return the logarithm of a number x to base. The default base is 10
arcsin(x)	Return the arc sine of a number x
arccos(x)	Return the arc cosine of a number x
arctan(x)	Return the arc tangent of a number x
arccot(x)	Return the arc cotangent of a number x
ln(x)	Return the natural logarithm of a number x
sqrt(x)	Return the square root of a number x
nroot(x, nth)	Return the $n^{th}$ root of a number x
abs(x)	Return the absolute value of a number x
factorial(n)	Return the factorial of a number x (equal to n!)

Genetic Algorithm

flowchart TD;
    A[Start]
    B[Initialization]
    C[Selection]
    D[Quiet?]
    E[Crossover]
    F[Mutation]
    G[End]

    A --> B
    B --"Initial Population"--> C
    C --"New Population"--> D
    D --"Yes"--> G
    D --"No"--> E
    E --> F
    F --"Old Population"--> C
    F --> G

Installation

• Open the terminal clone the project using command:

  git clone https://github.com/dtruong46me/genetic-solver-equation.git
  

• Go to repository

  cd genetic-solver-equation
  

• Execute program

  python run.py
  

Contributions

• Instructor: Assoc. Prof. Tran Dinh Khang

• Students:

  No.	Name	Student ID	Email
  1	Dinh Nguyen Cong Quy	20214927	quy.dnc214927@sis.hust.edu.vn
  2	Nguyen Trung Truc	20214936	truc.nt214936@sis.hust.edu.vn
  3	Phan Dinh Truong	20214937	truong.pd214937@sis.hust.edu.vn