它的工作在搜索和多选selectpiker：

<select id="mySelect" class="selectpicker show-menu-arrow" multiple data-live-search="true" title="Persons"
            data-selected-text-format="static" data-actions-box="true">
 </select>

<script>
        $(document).ready(function () {
            for (let i = 0; i < 20; i++) 
                $("#mySelect").append(
                    `<option value="${i}">person ${i}</option>`
                );
            
            $("#mySelect").selectpicker("refresh");
            $('.bs-select-all').html("All");
            $('.bs-deselect-all').html("Nothing");
        });
    </script>

您可以使用jQuery select2.Eg轻松地完成此操作。

<select class="form-control" id="tagsExample">
  <option selected="selected">orange</option>
  <option>white</option>
  <option>purple</option>
</select>

$("#tagsExample").select2({
  tags: true
});

参考：https://select2.org/tagging

您有一个打字错误。而不是：

$('#myselect').append('<option val="'+newitemnum+'">'+newitemdesc+'</option>');

您需要：

$('#myselect').append('<option value="'+newitemnum+'">'+newitemdesc+'</option>');

下面是一个JSFiddle演示：http://jsfiddle.net/xbr5agqt/
"添加并选择"酱油"选项"按钮执行以下操作：

$("#myselect").append('<option value="'+newitemnum+'">'+newitemdesc+'</option>');
$("#myselect").val(4);
$("#myselect").selectpicker("refresh");

一种稍微快一点的方法（由"Add and select 'Relish' option"按钮使用）是在新元素后面附加已经应用的selected属性： element with the selected attribute already applied:

$("#myselect").append('<option value="'+newitemnum+'" selected="">'+newitemdesc+'</option>');
$("#myselect").selectpicker("refresh");

用于在bootstrap-selectpicker中动态添加options，append将option添加到select，refresh将selectpicker添加到

$(document).on('click','#addOptions',function(){
  var newitemnum = Math.floor(Math.random() * 100) + 1;
  var newitemdesc = "Item "+ newitemnum;
  
  // Append the option to select
  $('#myselect').append('<option value="'+newitemnum+'">'+newitemdesc+'</option>');
  
  // Set the select value with new option
  $("#myselect").val(newitemnum);
  
  // Refresh the selectpicker
  $("#myselect").selectpicker("refresh");
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<link rel="stylesheet" type="text/css" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" />
<script type="text/javascript" src="https://maxcdn.bootstrapcdn.com/bootstrap/3.4.0/js/bootstrap.min.js"></script>


<!-- Latest compiled and minified CSS -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/bootstrap-select@1.13.9/dist/css/bootstrap-select.min.css">

<!-- Latest compiled and minified JavaScript -->
<script src="https://cdn.jsdelivr.net/npm/bootstrap-select@1.13.9/dist/js/bootstrap-select.min.js"></script>

<select name="myselect[]" class="selectpicker" id="myselect">
  <option value="A1">Anatomy</option>
  <option value="A2">Anesthesia</option>
  <option value="A3">Biochemistry</option>
  <option value="A4">Community Medicine</option>
  <option value="A5">Dermatology</option>
  <option value="A6">ENT</option>
</select>

<button id="addOptions" class="btn btn-success">Add</button>

为了更好地执行此操作，请在append选项中添加selected属性

// Append the option to select
$('#myselect').append('<option value="'+newitemnum+'" selected>'+newitemdesc+'</option>');