This paper presents a multi-objective post enrolment course timetabling problem as a new case study. We added a new soft constraint to the original single objective problem to both increase the complexity and represent a real world course timetabling problem. The new soft constraint introduced here attempts to minimize the total number of waiting timeslots in between courses for every student in a day. We proposed a Non-dominated Sorting Genetic Algorithm-II with a variable population size, called NSGA-II VPS, based on a given lifetime for each individual that is evaluated at the time of its birth. The algorithm was tested on the standard benchmark problems and experimental results show that the proposed method demonstrably improved upon the original approach (NSGA-II).