jQuery Simple Example

HTML

<script src="//www.addressfinder.co.nz/assets/v2/widget.js"></script>
<div class="col-sm-8">
   <select name="leave_type" class="select2-container form-control" id="leave_type_edit">
      <option></option>
      <option value="val1">val 1</option>
      <option value="val2">val 2</option>
      <option value="val3">val 3</option>
      <option value="val4">val 4</option>
      <option value="val5">val 5</option>
    </select>
</div>

<button id="btn_change">
  Change
</button>

CSS

body {
    padding: 5px;
}

label {
    font-weight: bold;
}

input[type=text] {
    width: 20em
}

p {
    margin: 1em 0 0;
}

JavaScript

var leaveTypeId = 'val2';
$(document).on('click', '#btn_change', function() {
	$('#leave_type_edit option[value= '+leaveTypeId+' ]').attr('selected', 'selected');
});