I am a Non EU citizen and got L Permit to join duty on 01-06-10. I applied for a visa to start my journey on 28-05-10 and enter switzerland on the same day. My air ticket for 28-05-10 also booked.
Now my visa has been issued for the period from 01-06-10 to 31-08-10. So whther i my travel on 28-05-10 so as to join duty on 01-06-10.

You need to speak to the swiss embassy/ consulate general in your home country. You cannot enter early without a visa. If your entry permit says you have to enter between x date and y date, then you must do that.

The swiss embassy are the only ones who can tell you what you must do - and even if they aren't too worried, it is the airline that will get a big fine if they allow you to travel without the correct paperwork...so you might find you have serious problem when you try to check in at the airport.

I have a little bit different question. I've been admitted to the Doctoral Program at EPFL. Now I have to apply for a visa and in my application form I have to designate the entry date. I know that e.g. in the US one can enter the US no earlier than 30 days before the start date. So, my question is: how earlier can I enter Switzerland before official enrolment date at EPFL?

Check here at the Department for Foreign Affairs - but ultimately the embassy should tell you...

Ok, I've been in the embassy and they told me that there are no restrictions on the earliest permissible date (at least in my case), but I need to show that I have sufficient funds to live in Switzerland before the official enrolment date.