Safety Harness Toddler

My son has just turned two - i thought i had already experienced the 'terrible two's !!". All of a sudden now he just throws himself on the floor if he doesn't get what he wants and now runs off on my in public, eg supermarket or when we are having a something to eat in a cafe together. Any suggestions. I am now thinking of a safety harness as today he made onto the road and also i have a 5 month year old who i am watching when we are going out to.
Question for Gothica: i have read your answer thanks for you contribution however i must disagree with you. if i was not to take my son out to the shops as an outing how can any parent socialise their child to surrounding areas such as shops, learning how to cross the road, deal with people and teach them stranger danger. I enjoy taking my child out on outings (despite problems i have encountered) however i don't think keeping a child confined at home with a babysitter is the best solution either. What do others think?