Genetic Algorithm Solver Calculator

Calculator Inputs

Use the settings below to search for the best candidate solution across your chosen interval.

Objective Function

f(x) = A·x² + B·x + C

Optimization Goal

Chromosome Bits

Lower Bound

Upper Bound

Population Size

Generations

Crossover Rate

Mutation Rate

Elite Count

Tournament Size

Coefficient A

Coefficient B

Coefficient C / Shift

Coefficient D / Linear Term

Coefficient E / Constant

Example Data Table

These examples illustrate typical solver configurations and representative outputs.

Example	Function	Goal	Range	Population	Generations	Sample Best x	Sample Best f(x)
1	f(x) = -x² + 6x - 2	Maximize	[-10, 10]	60	80	≈ 3.0000	≈ 7.0000
2	f(x) = x³ - 4x² + x + 5	Minimize	[-3, 5]	90	120	≈ 2.5350	Illustrative
3	f(x) = 5sin(2x) + 0.5x	Maximize	[0, 8]	70	100	Depends on phase	Illustrative

Formula Used

1. Chromosome decoding
Each binary chromosome maps to a real value using:
x = lower + (decimal / (2^bits - 1)) × (upper - lower)

2. Objective evaluation
The decoded value is inserted into the selected function. Supported models include quadratic, cubic, quartic, sinusoidal-linear, and gaussian-linear forms.

3. Fitness transformation
For maximization, fitness is raw - min(raw) + ε.
For minimization, fitness is max(raw) - raw + ε.

4. Genetic operators
Tournament selection chooses stronger parents. Single-point crossover mixes chromosomes. Mutation flips bits using the chosen mutation rate. Elitism preserves top solutions between generations.

How to Use This Calculator

Select an objective function model that matches your equation structure.
Choose whether you want to maximize or minimize the objective.
Set the lower and upper bounds for the search interval.
Enter genetic settings such as population size, generations, crossover rate, mutation rate, tournament size, and elitism.
Enter coefficients A through E based on the selected function family.
Press Run Genetic Algorithm Solver to see the best solution, optimization metrics, convergence chart, and downloadable reports.

FAQs

1. What does this calculator optimize?

It searches a bounded interval for the best real-valued x that maximizes or minimizes your chosen objective model using a genetic algorithm.

2. Why use a genetic algorithm instead of direct calculus?

Genetic algorithms work well when derivatives are unavailable, the landscape is noisy, or multiple local optima make conventional methods harder to apply reliably.

3. What does chromosome bit length change?

More bits increase search resolution and enlarge the search space. That can improve precision, but it may require more generations or a larger population.

4. How should I choose mutation and crossover rates?

Use moderate crossover for mixing strong solutions and low mutation for controlled exploration. Very high mutation can destroy progress, while very low mutation can stall diversity.

5. What does elitism do here?

Elitism copies the best chromosomes into the next generation unchanged. This helps preserve strong candidates and usually stabilizes convergence speed.

6. Why does the result vary slightly between runs?

The algorithm starts with random populations and random genetic events. Different runs can explore different regions before converging toward strong candidates.

7. Can I use this for minimization problems?

Yes. Choose the minimize option. The calculator transforms raw objective values into positive selection fitness while still reporting the original objective output.

8. What do the convergence chart lines mean?

The chart shows best objective, average objective, and population diversity by generation. Together they reveal progress, stability, and exploration balance.