How to add option to select optgroup in jquery?

I'm trying to fill an html select with javascript. Now I simply do:

function addRow(selectID, testName) {
    var x = document.getElementById(selectID);
    var option = document.createElement("option");
    option.text = testName;
    x.add(option);
}    

for (var x = 0; x < testSet.length; x++) {
    addRow('select', testSet[x]);
}

where testSet is an array of string. In this way I have the filled select. Now I want to upgrade the fill of select using optgroup so, in my html code, I have

<select onchange="selectionChanged()" 
style="width: 400px; height: 20px; vertical-align: middle;"
id="select"><optgroup label="OptionSet1"></optgroup>
<optgroup label="OptionSet2"></optgroup>
<optgroup label="OptionSet3"></optgroup>
</select>

Now to fill with my options I think I must do something like that

for (var x = 0; x < testSet.length; x++) {
    if(testSet[x].indexOf("string1") != -1){
       // Add testSet[x] in OptionSet1
    }
    if(testSet[x].indexOf("string2") != -1){
       // Add testSet[x] in OptionSet2
    }
    if(testSet[x].indexOf("string3") != -1){
        // Add testSet[x] in OptionSet3
    }
}

What I must do to "Add testSet[x] in OptionSet"? I readed something on the web, but I cannot find anything that seems to work for me.

Thank you.

Solution

Maybe this give you little idea

on how to do it

<html>
<head>
    <style>
        .overlay {
            background-color: rgba(0,0,0,0.5);
            width: 100%;
            height: 100%
        }
    </style>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
</head>

<body>
    <select class="selectgroup" 
    style="width: 400px; height: 20px; vertical-align: middle;"
    id="select">
    <optgroup id="optgroup1" label="OptionSet1">
    </optgroup>
    <optgroup id="optgroup2" label="OptionSet2">
    </optgroup>
    <optgroup id="optgroup3" label="OptionSet3">
    </optgroup>
    </select>


    <script type="text/javascript">

        //create a option with a key name pertaining to the id of the optgroup
        //and set its value to array with a list of options

        var options = {
            "optgroup1" : new Array('red', 'blue', 'red'),
            "optgroup2" : new Array('thin', 'thick'),
            "optgroup3" : new Array('pencil', 'ballpen')
        };

        $(document).ready(function(){
            // loop all the options created
            for (var i in options) {
                // get value
                var elements = options[i];
                // get optgroup to insert new option
                var parentgroup = $('#' + i);
                // iterate and insert new option to optgroup
                for (var j = 0; j < elements.length; j++) {
                    parentgroup.append('<option>' + elements[j]+ '</option>')
                };

            }

        });

    </script>

</body>
</html>

You can improve the code to make it more meaning full to your usage

thanks