{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(user_guide_optimization_ga_tuning)="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selection Strategies and Population Diversity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This page continues the {doc}`bga` walkthrough, again minimizing the Rosenbrock function, and looks at two knobs for tuning convergence behaviour: the selection strategy and the diagnostic `diversity` metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Iterable\n",
    "from numbers import Number\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sigmaepsilon.math.optimize import BinaryGeneticAlgorithm as BGA\n",
    "\n",
    "\n",
    "def Rosenbrock(x: Iterable[Number], a: Number = 1, b: Number = 100) -> float:\n",
    "    return (a - x[0]) ** 2 + b * (x[1] - x[0] ** 2) ** 2\n",
    "\n",
    "\n",
    "ranges = [[-2, 2], [-1, 3]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Selection strategies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The winners of each generation (beyond the automatically-surviving elite) are picked by a pluggable {py:class}`~sigmaepsilon.math.optimize.selection.SelectionStrategy`, injected via the `selection_strategy` constructor argument. Three are built in: {py:class}`~sigmaepsilon.math.optimize.selection.TournamentSelection` (the default), {py:class}`~sigmaepsilon.math.optimize.selection.RouletteSelection` (fitness-proportionate) and {py:class}`~sigmaepsilon.math.optimize.selection.RankSelection`. \ud83d\udcd6 {ref}`Selection strategies API Reference <api_optimization_GA>`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sigmaepsilon.math.optimize import TournamentSelection, RouletteSelection, RankSelection\n",
    "\n",
    "for strategy in [TournamentSelection(), RouletteSelection(), RankSelection()]:\n",
    "    bga = BGA(\n",
    "        Rosenbrock,\n",
    "        ranges,\n",
    "        length=12,\n",
    "        nPop=100,\n",
    "        minimize=True,\n",
    "        seed=0,\n",
    "        selection_strategy=strategy,\n",
    "    )\n",
    "    result = bga.solve()\n",
    "    print(f\"{type(strategy).__name__:<20} fitness={result.fitness:.6g}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Population diversity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `diversity` property (and the `state.diversity` snapshot updated after every `evolve` call) measures how spread out the current population still is (the mean, per-dimension standard deviation of the phenotypes). A value close to zero, alongside a champion that hasn't improved in a while, is a sign of premature convergence \u2014 in addition to `champion.age`, it's a second, independent signal you can use to tune `maxage`, `p_m`, or the selection strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "bga = BGA(Rosenbrock, ranges, length=12, nPop=100, minimize=True, seed=0)\n",
    "\n",
    "fitness_history = []\n",
    "diversity_history = []\n",
    "\n",
    "for _ in range(60):\n",
    "    bga.evolve(1)\n",
    "    fitness_history.append(bga.champion.fitness)\n",
    "    diversity_history.append(bga.state.diversity)\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(8, 4))\n",
    "ax1.plot(fitness_history, color=\"tab:blue\")\n",
    "ax1.set_xlabel(\"generation\")\n",
    "ax1.set_ylabel(\"best fitness\", color=\"tab:blue\")\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(diversity_history, color=\"tab:orange\")\n",
    "ax2.set_ylabel(\"diversity\", color=\"tab:orange\")\n",
    "plt.title(\"Best fitness and population diversity over generations\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "sigmaepsilon-math-NMVzm02N-py3.12",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}