Genetic algorithm: Difference between revisions

Revision as of 19:39, 12 December 2024

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

Introduction

Algorithm Discussion

Numerical Example

1. Simple Example

We aim to maximize $f(x)=x^{2}$ , 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	$x$	$f(x)=x^{2}$
10010	18	324
00111	7	49
11001	25	625
01001	9	81

Total Fitness $=324+49+625+81=1079$

@@ Line 7: / Line 7: @@
 == Algorithm Discussion ==
+== Numerical Example ==
+=== 1. Simple Example ===
+We aim to maximize <math>f(x) = x^2</math>, where <math>x \in [0, 31]</math>. 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:
+{| class="wikitable"
+|+
+!Chromosome (Binary)
+!x (Decimal)
+|-
+|10010
+|18
+|-
+|00111
+|7
+|-
+|11001
+|25
+|-
+|01001
+|9
+|}
+==== 1.2 Generation 1 ====
+===== 1.2.1 Evaluation =====
+Calculate the fitness values:
+{| class="wikitable"
+|+
+!Chromosome
+!<math>x</math>
+!<math>f(x) = x^2</math>
+|-
+|10010
+|18
+|324
+|-
+|00111
+|7
+|49
+|-
+|11001
+|25
+|625
+|-
+|01001
+|9
+|81
+|}
+'''Total Fitness <math>=324+49+625+81=1079</math>'''