How to set selected value on select using selectpicker plugin from bootstrap

$('select[name=selValue]').val(1);
$('.selectpicker').selectpicker('refresh');

This is all you need to do. No need to change the generated html of selectpicker directly, just change the hidden select field, and then call the selectpicker('refresh').

$('.selectpicker').selectpicker('val', YOUR_VALUE);

No refresh is needed if the "val"-parameter is used for setting the value, see fiddle. Use brackets for the value to enable multiple selected values.

$('.selectpicker').selectpicker('val', [1]); 

The value is correctly selected, but you didn't see it because the plugin hide the real select and show a button with an unordered list, so, if you want that the user see the selected value on the select you can do something like this:

//Get the text using the value of select
var text = $("select[name=selValue] option[value='1']").text();
//We need to show the text inside the span that the plugin show
$('.bootstrap-select .filter-option').text(text);
//Check the selected attribute for the real select
$('select[name=selValue]').val(1);

Edit:

Like @blushrt points out, a better solution is:

$('select[name=selValue]').val(1);
$('.selectpicker').selectpicker('refresh')

Edit 2:

To select multiple values, pass the values as an array.