Related Posts based on Nick Croft's http://designsbynickthegeek.com/tutorials/related-posts-genesis, modified from Andrea Whitmer's https://gist.github.com/nutsandbolts/467a6bcdef875303afce by Chinmoy Paul. Live Demo.: http://thedailydoll.com/soartificiallysweet/

related-posts.php

<?php
/**
 * Related Posts Methods.
 *
 * @package     Daily Doll
 * @subpackage  Genesis
 * @copyright   Copyright (c) 2014, The Blog Maven
 * @license     GPL-2.0+
 * @since       2.0.0
 */

// Exit if accessed directly
if ( ! defined( 'ABSPATH' ) ) exit;

//* Add related posts image size
add_image_size( 'related', 300, 0, true );

add_action( 'wp_enqueue_scripts', 'dailydoll_masonry_script' );
function dailydoll_masonry_script() {
	if ( is_singular( 'post' ) ) {
		wp_enqueue_script( 'masonry-init', get_stylesheet_directory_uri().'/js/related-init.js', array( 'jquery-masonry' ), '1.0', true );		
	}
}

add_action( 'genesis_before_comments', 'someday_related_posts', 12 );
/**
 * Outputs related posts with thumbnail
 *
 * @author Nick the Geek
 * @url http://designsbynickthegeek.com/tutorials/related-posts-genesis
 * @global object $post
 */
function someday_related_posts() {
  global $do_not_duplicate;
	if ( ! is_singular ( 'post' ) ) {
		return;
	}
	$count = 0;
	$related = '';
  $do_not_duplicate = array();
	$tags = wp_get_post_tags( get_the_ID() );
	$cats = wp_get_post_categories( get_the_ID() );
	// If we have some tags, run the tag query.
	if ( $tags ) {
		$query    = someday_related_tag_query( $tags, $count );
		$related .= $query['related'];
		$count    = $query['count'];
	}
	// If we have some categories and less than 12 posts, run the cat query.
	if ( $cats && $count <= 11 ) {
		$query    = someday_related_cat_query( $cats, $count );
		$related .= $query['related'];
		$count    = $query['count'];
	}
	// End here if we don't have any related posts.
	if ( ! $related ) {
		return;
	}
	// Display the related posts section.
	echo '<div class="related">';
		echo '<h3 class="related-title">You might also enjoy...</h3>';
		echo '<div class="related-posts-list" data-columns>' . $related . '</div>';
	echo '</div>';
}

function someday_related_tag_query( $tags, $count ) {

  global $do_not_duplicate;
  
	if ( ! $tags ) {
		return;
	}
	$postIDs = array( get_the_ID() );

	foreach ( $tags as $tag ) {
		$tagID[] = $tag->term_id;
	}
	$tax_query = array(
		array(
			'taxonomy'  => 'post_format',
			'field'     => 'slug',
			'terms'     => array(
				'post-format-link',
				'post-format-status',
				'post-format-aside',
				'post-format-quote'
				),
			'operator' => 'NOT IN'
		)
	);
	$args = array(
		'tag__in'               => $tagID,
		'post__not_in'          => $postIDs,
		'showposts'             => 12,
		'ignore_sticky_posts'   => 1,
		'tax_query'             => $tax_query,
	);

	$related  = '';
	$tag_query = new WP_Query( $args );
	if ( $tag_query->have_posts() ) {
		while ( $tag_query->have_posts() ) {
			$tag_query->the_post();
      
      $do_not_duplicate[] = get_the_ID();
      
			$count++;

			$title = genesis_truncate_phrase( get_the_title(), 35 );

			$related .= '<div class="related-post">';
			$related .= '<a class="related-post-title" href="' . get_permalink() . '" rel="bookmark" title="Permanent Link to ' . $title . '">' . $title . '</a>';
			$related .= '<a class="related-image" href="' . get_permalink() . '" rel="bookmark" title="Permanent Link to ' . $title . '">' . genesis_get_image( array( 'size' => 'related' ) ) . '</a>';
			$related .= '</div>';
		}
	}
	wp_reset_postdata();
	$output = array(
		'related' => $related,
		'count'   => $count
	);
	return $output;
}

function someday_related_cat_query( $cats, $count ) {
  global $do_not_duplicate;
  
	if ( ! $cats ) {
		return;
	}
	$postIDs = array_merge( array( get_the_ID() ), $do_not_duplicate );
	$catIDs = array();
	foreach ( $cats as $cat ) {
		if ( 6 == $cat ) {
			continue;
		}
		$catIDs[] = $cat;
	}
	$showposts = 12 - $count;
	$tax_query = array(
		array(
			'taxonomy'  => 'post_format',
			'field'     => 'slug',
			'terms'     => array(
				'post-format-link',
				'post-format-status',
				'post-format-aside',
				'post-format-quote'
				),
			'operator' => 'NOT IN'
		)
	);
	$args = array(
		'category__in'          => $catIDs,
		'post__not_in'          => $postIDs,
		'showposts'             => $showposts,
		'ignore_sticky_posts'   => 1,
		'orderby'               => 'rand',
		'tax_query'             => $tax_query,
	);

$related  = '';

	$cat_query = new WP_Query( $args );
	if ( $cat_query->have_posts() ) {
		while ( $cat_query->have_posts() ) {
			$cat_query->the_post();

			$count++;

			$title = genesis_truncate_phrase( get_the_title(), 35 );

			$related .= '<div class="related-post">';
			$related .= '<a class="related-post-title" href="' . get_permalink() . '" rel="bookmark" title="Permanent Link to ' . $title . '">' . $title . '</a>';
			$related .= '<a class="related-image" href="' . get_permalink() . '" rel="bookmark" title="Permanent Link to ' . $title . '">' . genesis_get_image( array( 'size' => 'related' ) ) . '</a>';
			$related .= '</div>';

		}
	}
	wp_reset_postdata();
	$output = array(
		'related' => $related,
		'count'   => $count
	);
	return $output;
}