Genetic algorithm

Author: Yunchen Huo (yh2244), Ran Yi (ry357), Yanni Xie (yx682), Changlin Huang (ch2269), Jingyao Tong (jt887) (ChemE 6800 Fall 2024)

Stewards: Nathan Preuss, Wei-Han Chen, Tianqi Xiao, Guoqing Hu

Numerical Example

1. Simple Example

We aim to maximize Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = x^2} , where $x\in [0,31]$. Chromosomes are encoded as 5-bit binary strings since the binary format of the maximum value 31 is 11111.

1.1 Initialization (Generation 0)

The initial population is randomly generated:

Chromosome (Binary)	x (Decimal)
10010	18
00111	7
11001	25
01001	9

1.2 Generation 1

1.2.1 Evaluation

Calculate the fitness values:

Chromosome	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = x^2}
10010	18	324
00111	7	49
11001	25	625
01001	9	81

Total Fitness Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =324+49+625+81=1079}