Magento 2 – By Default Checked Checkbox in Admin Form

Update the code as below,

   $fieldset->addField('city', 'checkboxes', array(
                    'label' => $this->__('City'),
                    'name' => 'city[]',
                    'required' => true,
                    "checked" => $city,
                    'values' => $this->getOptionValues($city),
                    'onclick' => "",
                    'onchange' => "",
                    'disabled' => false,
                    'value'  => '1',
                    'tabindex' => 1
                ));

Create a new function to get the option values,

 public function getOptionValues($city)

     $result = array();

     $selectedvalues =  $city; //exploded array

     $optionslists = array(
                            array('value' => '0', 'label' => 'aaaaa'),
                            array('value' => '1', 'label' => 'bbbbbbb'),
                            array('value' => '2', 'label' => 'ccccccc'),
                            array('value' => '3', 'label' => 'dddddddd'),
                            array('value' => '4', 'label' => 'eeeeeeee')
                        );

    if(count($selectedvalues)>1){
        foreach($selectedvalues as $selectedvalue ){
                foreach($optionslists as $optionslist)
                {
                    if(in_array($selectedvalue, $optionslist))
                    {
                        $result[] = $optionslist;
                    }

                }
            }
    }
    else{
       $result = $optionslists; 
    }
    return $result;

You have to add below code in form file

app\code\Vendor\ModuleName\Block\Adminhtml\ModuleName\Edit\Form.php

    $model->setData('test', 'female');

Example of form file:

<?php
namespace Mystore\Slider\Block\Adminhtml\Slider\Edit;

/**
 * Adminhtml blog post edit form
 */
class Form extends \Magento\Backend\Block\Widget\Form\Generic
{

    /**
     * @var \Magento\Store\Model\System\Store
     */
    protected $_systemStore;

    /**
     * @param \Magento\Backend\Block\Template\Context $context
     * @param \Magento\Framework\Registry $registry
     * @param \Magento\Framework\Data\FormFactory $formFactory
     * @param \Magento\Cms\Model\Wysiwyg\Config $wysiwygConfig
     * @param \Magento\Store\Model\System\Store $systemStore
     * @param array $data
     */
    public function __construct(
        \Magento\Backend\Block\Template\Context $context,
        \Magento\Framework\Registry $registry,
        \Magento\Framework\Data\FormFactory $formFactory,
        \Magento\Store\Model\System\Store $systemStore,
        array $data = []
    ) {
        $this->_systemStore = $systemStore;
        parent::__construct($context, $registry, $formFactory, $data);
    }

    /**
     * Init form
     *
     * @return void
     */
    protected function _construct()
    {
        parent::_construct();
        $this->setId('mystore_slider_form');
        $this->setTitle(__('Slider Information'));
    }

    /**
     * Prepare form
     *
     * @return $this
     */
    protected function _prepareForm()
    {
        /** @var \Ashsmith\Blog\Model\Post $model */
        $model = $this->_coreRegistry->registry('mystore_slider');

        if ($model->getId()) {
            $model->setData('test', 'female');
        }

        /** @var \Magento\Framework\Data\Form $form */
        $form = $this->_formFactory->create(
            ['data' => ['id' => 'edit_form', 'action' => $this->getData('action'), 'method' => 'post', 'enctype' => 'multipart/form-data']]
        );

        $form->setHtmlIdPrefix('mystore_slider_');

        $fieldset = $form->addFieldset(
            'base_fieldset',
            ['legend' => __('General Information'), 'class' => 'fieldset-wide']
        );

        if ($model->getSliderId()) {
            $fieldset->addField('slider_id', 'hidden', ['name' => 'slider_id']);
        }

        $fieldset->addField(
            'slider_title',
            'text',
            ['name' => 'slider_title', 'label' => __('Slider Title'), 'title' => __('Slider Title'), 'required' => true]
        );

        $fieldset->addField(
            'url',
            'text',
            [
                'name' => 'url',
                'label' => __('Slider URL'),
                'title' => __('Slider URL'),
                'required' => true,
                'class' => 'validate-xml-identifier'
            ]
        );

        $fieldset->addField(
            'image',
            'image',
            [
                'name' => 'image',
                'label' => __('Slider Image'),
                'title' => __('Slider Image'),
                'required' => true
            ]
        );


        $fieldset->addField(
            'test', 
            'radios',
            [
                'label' => __('test'),
                'title' => __('test'),
                'name' => 'test',
                'required' => true, 
                'values' => array(
                        array('value'=>'male','label'=>'Male'),
                        array('value'=>'female','label'=>'Female'),
                   )
            ]
        );

        /**
         * Check is single store mode
         */
        if (!$this->_storeManager->isSingleStoreMode()) {
            $field = $fieldset->addField(
                'store_id',
                'multiselect',
                [
                    'name' => 'stores[]',
                    'label' => __('Store View'),
                    'title' => __('Store View'),
                    'required' => true,
                    'values' => $this->_systemStore->getStoreValuesForForm(false, true)
                ]
            );
            $renderer = $this->getLayout()->createBlock(
                'Magento\Backend\Block\Store\Switcher\Form\Renderer\Fieldset\Element'
            );
            $field->setRenderer($renderer);
        } else {
            $fieldset->addField(
                'store_id',
                'hidden',
                ['name' => 'stores[]', 'value' => $this->_storeManager->getStore(true)->getId()]
            );
            $model->setStoreId($this->_storeManager->getStore(true)->getId());
        }

        $fieldset->addField(
            'is_active',
            'select',
            [
                'label' => __('Status'),
                'title' => __('Status'),
                'name' => 'is_active',
                'required' => true,
                'options' => ['1' => __('Enabled'), '0' => __('Disabled')]
            ]
        );        

        $form->setValues($model->getData());
        $form->setUseContainer(true);
        $this->setForm($form);

        return parent::_prepareForm();
    }
}