strip the "[]" from the php code:
change:
<input <?php if (!(strcmp(((isset($_POST["search_usage[]"]))?$_POST["search_usage[]"]:""),1))) {echo "checked=\"checked\"";} ?> type="checkbox" name="search_usage[]" id="search_usage_0" value="1" />
Light</label>
to:
<input <?php if (!(strcmp(((isset($_POST["search_usage"]))?$_POST["search_usage"]:""),1))) {echo "checked=\"checked\"";} ?> type="checkbox" name="search_usage[]" id="search_usage_0" value="1" />
Light</label>