Optimize for happiness and equality

Question

I'm trying to solve an optimization problem:

There are $N$ students who can choose to enroll into $C$ courses, each of them has a set of 3 preferences $P = \{c_1, c_2, c_3\}$ about the courses they would like to enroll into (in order of preference). Each student must enroll in two courses. However, each course $c_i$ has a fixed capacity $k_i$.

Since I suppose it's a NP problem, I would like to solve it using Local Search, but I don't know how to optimize for happiness and equality (minimize variance) between students at the same time. Thanks

Answer 1

I chose a fitness function f such that f(students) = average(happiness(students)) + minimum(happiness(students))