add an OR condition to the if statement:
<input <?php if(((isset($_POST["search_usage"])) && (is_array($_POST["search_usage"])) && (in_array("1",$_POST["search_usage"]))) || (!isset($_POST["search_usage"]))) {echo "checked=\"checked\"";} ?> type="checkbox" name="search_usage[]" id="search_usage_0" value="1" />