Genetic Algorithm: Evolving a Route

Evolving Population

Population size 80

Mutation rate 0.02

Crossover rate 0.85

Generations / sec 6

Generation

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Best tour

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Avg tour

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Stall gens

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How it works

Each individual is a permutation of the cities — one candidate tour. Fitness is the inverse of its total round-trip length: shorter tours score higher. Every generation, the single fittest individual survives unchanged (elitism); the rest of the next generation is built by picking parents through tournament selection, recombining them with order crossover (which copies a slice from one parent and fills the remaining cities in the order the other parent visits them, so every child stays a valid permutation), then swap-mutating a few genes to keep exploring new orderings.

fitness(tour) = 1 / Σ dist(cityᵢ, cityᵢ₊₁)
parent = fittest of k random individuals   (tournament)
child = OX(parentA, parentB)               (order crossover)
child = swap(i, j) with prob. mutationRate (per gene)

Population size — more candidate tours explored per generation, at the cost of more work per step.
Mutation rate — how often two stops in a child tour get swapped; too low and the population stagnates on a mediocre tour, too high and good tours keep getting scrambled.
Crossover rate — the chance two parents recombine at all; below that chance a parent is copied through unchanged.
Generations / sec — how fast the evolutionary loop advances; slow it down to watch a single generation's selection and crossover play out on the routes below.

Real-world relevance: this is the same selection–crossover–mutation loop used to search huge combinatorial spaces — vehicle routing, job-shop scheduling, circuit layout and neural-architecture search — where the search space is too large and too non-differentiable for gradient-based optimization.

Best route 2nd best 3rd best

Fitness convergence

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