🧬 GA Notes — Full Explanation

What is GA?

Imagine natural evolution (survival of the fittest). In nature, strong individuals survive, mate with other strong individuals, and produce even stronger babies. Sometimes a random mutation gives a baby a superpower. GA uses this exact same concept to solve math problems by breeding "chromosomes" representing solutions!

How is GA different from PSO & ACO?

	GA	PSO	ACO
Inspired by	Evolution / Genetics	Birds flocking	Ants finding food
Mechanism	Crossover & Mutation	Velocity updates	Pheromone deposits
Representation	Binary strings (0101)	Continuous numbers	Discrete choices
Memory	None (only current pop)	Remembers Personal Best	Pheromone memory

Key Terms Explained

Term	Symbol	Simple Meaning
Chromosome / Genotype	-	A single solution encoded as a binary string (e.g., `101011`). Think of it as a person's DNA.
Phenotype	x	The real, decoded value of the chromosome (e.g., length = 15.5m).
Gene / Allele	-	A single bit (0 or 1) inside the chromosome.
Population Size	m	The number of chromosomes (solutions) currently alive in a generation.
Fitness Function	F(x)	How "good" a solution is. Better fitness = more likely to survive and reproduce.
Penalty Function	P(x)	If a solution breaks a rule (e.g., stress is too high), we subtract a massive penalty from its fitness so it dies out.
Crossover Prob.	p_c	Mating chance. How often parents swap DNA to create babies (usually 80-90% or 0.8-0.9).
Mutation Prob.	p_m	Random flip chance. Tiny chance (e.g., 1-5%) a bit flips (0→1). Prevents inbreeding and getting stuck.
Bits per Variable	L	How many 0s and 1s represent one variable. More bits = higher accuracy (e.g., 4 bits max = 15, 8 bits max = 255).

Step-by-Step Walkthrough with Example

Step 1: Encoding & Initialization

Convert the continuous range (e.g., 0.15 to 0.40) into binary. Let's use 4 bits (max value = 15). We generate a random population:

Formula: Real Value = Min + Decimal × (Max - Min) / (2^bits - 1)

Parent 1: 1010 (Decimal 10) → Value = 0.15 + 10 × (0.25) / 15 = 0.3167

Parent 2: 0011 (Decimal 3) → Value = 0.15 + 3 × (0.25) / 15 = 0.2000

Parent 3: 1111 (Decimal 15) → Value = 0.15 + 15 × (0.25) / 15 = 0.4000

Step 2 & 3: Evaluation and Roulette Wheel Selection

Let's say their fitness scores are: P1 = 10, P2 = 20, P3 = 50. (Total = 80)

Probability = Fitness / Total
P1 (10) → 10/80 = 0.125  (12.5% chance)
P2 (20) → 20/80 = 0.250  (25.0% chance)
P3 (50) → 50/80 = 0.625  (62.5% chance)

Now we map these to a Cumulative Probability Line (Roulette Wheel) from 0 to 1:

0       0.125         0.375                           1.000
|---P1---|------P2------|---------------P3--------------|
   12%         25%                      62%

We generate a random number r between 0 and 1 to pick parents:

If r = 0.250 → Falls in P2's range (0.125 to 0.375) → Parent 2 is selected!
If r = 0.810 → Falls in P3's range (0.375 to 1.000) → Parent 3 is selected!

Step 4: Crossover (Mating)

We take selected Parent 2 and Parent 3, pick a random cut point (e.g., after the 2nd bit), and swap their tails:

Parent 2: 00 | 11
Parent 3: 11 | 11

Child 1 : 00 | 11  (Took head of P2, tail of P3)
Child 2 : 11 | 11  (Took head of P3, tail of P2)

Step 5: Mutation

We check every bit of Child 1 (0011). Let's say the 3rd bit gets lucky and mutates (flips):

Child 1 (Before): 0011
Child 1 (After) : 0001   (The '1' flipped to '0')

Step 6: Repeat

The mutated children replace the old parents to form Generation 2. We repeat Steps 1-5 until the maximum number of generations is reached or the best fitness stops improving.

GA Optimizer

Variables

Define variable min and max value (e.g. b_min=0.15, b_max=0.40)

Calculations & Logic

Intermediate Calculations (JS)

Fitness Function Formula Return higher value to maximize.

GA Parameters

Pop Size m (Population Size)

Generations imax (Maximum Generations)

Crossover Prob pc (Crossover Probability)

Mutation Prob pm (Mutation Probability)(thump rule suggest 1/total bits=1/32=0.03125)

Bits / Var how much accuracy need for eg 0.40-0.15=0.25 then 0.25/15 = 16.67mm accuracy its 4bits only/////if takes 8 bits then 0.25/255= 0.98mm accuracy//16 bits 0.25/65535=0.00000381 m accuracy

Convergence SF sf_max (Convergence Factor)

Optimization Dashboard

Ready

Best Feasible Solution

Run the optimization to see results.

Convergence Log

Gen	Best Fitness	Best Values	SF (Std Dev)

Detailed Calculations (Generation 1 Step-by-Step)

All Generations Population Details

Run the optimization to see population details for all generations.