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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook offers a step-by-step tutorial on utilizing EvoX to optimize the Ackley function through the Particle Swarm Optimization (PSO) algorithm. Both the PSO algorithm and the Ackley optimization problem are integrated as built-in components within the EvoX framework.\n",
    "\n",
    "First, we should import all necessary modules including `PSO` (algorithm), `Ackley` (problem) and `StdWorkflow` & `EvalMonitor` (workflow)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "from evox.algorithms import PSO\n",
    "from evox.problems.numerical import Ackley\n",
    "from evox.workflows import StdWorkflow, EvalMonitor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we instantiate the [`PSO`](#evox.algorithms.so.pso_variants.pso.PSO) algorithm. We specify the following settings:\n",
    "\n",
    "- `pop_size`: The size of the particle swarm (population).\n",
    "- `lb` and `ub`: The lower and upper bounds for each dimension in the search space.\n",
    "- Other parameters are all default. Please refer to the detailed API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the algorithm\n",
    "algorithm = PSO(pop_size=100, lb=-32 * torch.ones(10), ub=32 * torch.ones(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we choose the [`Ackley`](#evox.problems.numerical.basic.Ackley) function in EvoX' s numerical problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the problem\n",
    "problem = Ackley()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We creat an [`EvalMonitor`](#evox.workflows.eval_monitor.EvalMonitor) instance to track necessary information during the optimization procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the monitor\n",
    "monitor = EvalMonitor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [`StdWorkflow`](#evox.workflows.std_workflow.StdWorkflow) class provides a standardized process to integrate the algorithm, problem, and monitor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the workflow\n",
    "workflow = StdWorkflow(algorithm=algorithm, problem=problem, monitor=monitor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calling `setup()` initializes the components so that the workflow is ready to perform optimization steps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run the optimization for a certain number of iterations (100 in this example). In each iteration, the `step()` method updates the PSO algorithm, evaluates new candidate solutions on the Ackley function, and tracks their fitness via the monitor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform the Ackley function optimization procedure\n",
    "for _ in range(100):\n",
    "    workflow.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we retrieve the [`monitor`](#StdWorkflow.get_submodule) submodule from the workflow to access the top solutions found so far (`topk_solutions`) and their corresponding objective values (`topk_fitness`). We then print the best result and the associated solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best solution is:\n",
      "tensor([[ 2.9274e-06, -6.9952e-05, -9.1939e-06, -1.6155e-05,  2.9382e-06,\n",
      "          2.8082e-05, -3.1130e-05, -3.7086e-05, -1.1396e-05,  3.6595e-05]]),\n",
      "with the minimum value:\n",
      "tensor([0.0001])\n"
     ]
    }
   ],
   "source": [
    "# Get the best solution and its fitness\n",
    "population = monitor.topk_solutions\n",
    "fitness = monitor.topk_fitness\n",
    "print(f\"The best solution is:\\n{population},\\nwith the minimum value:\\n{fitness}\")"
   ]
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