<form action="/action_page.php">
   <select class="form-control select2" multiple="" id="source" name="source[]" style="width: 250px;">

      <optgroup label="Group1">
         <option>x1</option>
         <option>x2</option></optgroup>
         <optgroup label="Group2">
            <option>y1</option>
            <option>y2</option></optgroup>
         </select>
         <script type="text/javascript">
            $(".select2").select2({
            tags: true
            });
         </script>
         <script type="text/javascript">
         string = source.join()
         </script>
         type='hidden' name='string' ></input>
         <br><br>
         <input type="submit">
      </form>