1. Open phone's settings
2. open battery
3. open menu and select "battery optimization"
4. from the dropdown menu select "all apps"
5. select the app you want to whitelist
6. select "don't optimize"

Now this app will show under not optimized apps.

An app can check whether it's whitelisted by calling isIgnoringBatteryOptimizations()

Whitelisting won't disable the doze mode for your app, but you can do that by using network and hold-wake locks.

Whitelisting an Android application programmatically can be done as follows:

boolean isIgnoringBatteryOptimizations = pm.isIgnoringBatteryOptimizations(getPackageName());
if(!isIgnoringBatteryOptimizations){
    Intent intent = new Intent();
    intent.setAction(Settings.ACTION_REQUEST_IGNORE_BATTERY_OPTIMIZATIONS);
    intent.setData(Uri.parse("package:" + getPackageName()));
    startActivityForResult(intent, MY_IGNORE_OPTIMIZATION_REQUEST);
}

The result of starting the activity above can be verfied by the following code:

@Override
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
    if (requestCode == MY_IGNORE_OPTIMIZATION_REQUEST) {
        PowerManager pm = (PowerManager)getSystemService(Context.POWER_SERVICE);
        boolean isIgnoringBatteryOptimizations = pm.isIgnoringBatteryOptimizations(getPackageName());
        if(isIgnoringBatteryOptimizations){
            // Ignoring battery optimization
        }else{
           // Not ignoring battery optimization
        }
    }
}