Advanced Search (Search Api Solr)
I built a form like this for a website. If I wanted to I'm pretty sure I could use the same principle to build a form like Google Advanced Search. Whether it's the best approach or not I'm not sure.  

Which sits on the front page of the websites and then sends to the search page from there. 

What I'm doing is recreating the URL thats being created on the search page.  like 'search/applications?f[0]=field_location%3A2439' 


I created a Custom Module
used hook_block_info to create a block
used hook_block_view to create a block view - assigned the form to its content
Example of the form code -> 

function search_applications_form($form, &amp;$form_state) {
$locations = db_query("SELECT tid, name FROM {taxonomy_term_data} WHERE vid     = 5")-&gt;fetchAllKeyed();  // vid will be the id of the location taxonomy data

$form['locations'] = array(
   "#type" =&gt; "select",
   '#multiple' =&gt; TRUE,
   "#title" =&gt; t(""),
   '#required' =&gt; FALSE,
   '#default_value' =&gt; 'Select Application Locations',
   '#options' =&gt; $locations,
   );
 return $form;
 }



And in the submit 

function search_applications_submit($form, &amp;$form_state) {
     global $base_url;


     $search = $form_state['values']['search_applications'];

     $i = 0;

     if($form_state['values']['locations'] != NULL &amp;&amp; $form_state['values']['searchlocations'] != '0' &amp;&amp; $form_state['values']['locations'] != 'none'){

     $tid = $form_state['values']['locations'];

     $addlocationsearch = '&amp;f['.$i.']=field_job_location%3A'.$tid;
      $i++;
     } 
     else {
     $addlocationsearch = NULL;
     }

     $searchUrl = $base_url.'/search/applications?'.$addlocationsearch;

     $form_state['redirect'] = $searchUrl;
     }


I think the logic used here could be used to make a much better module. If you've a plan for some development I'd be happy to join in a project.