algorithm - Special combinations with score in Java -

i have k time intervals calls epochs (e.g epoch1, epoch2,.., epochk). have set s of n elements (e.g a, b, c, d, e, f).

i have assign each epoch elemnt of powerset(s) every elements in powerset(s) have score depends on epoch.

for example in epoch1 have score = 5, in epoch2 have score = 4.

i need assign epochs element of powerset(s), there problem. have global score sum of epochs score minus number of change between contiguos epochs multiplied parameter lambda.

for example if have:

epoch1 = ab score 5; epoch2 = score 6; epoch3= c score 4 

i have 1 change betwenn epoch1 , epoch2 (remove b), 2 change between epoch3 , epoch2 (remove , add c), global score 6+5+4 - 3*lambda.

for reason can't maximum of each epochs. 1 solutions make combination, if |s| = 30, |powerset(30)| = 2^30, suppose have c'(2^30, k) combinations repetitions.

there method maximum without compute combination ?

my idea algorithm finds local optima:

treat epoch configurations 1 long string, use genetic algorithm find local optimum of configuration.

i feel making problem hard, instead of viewing problem "find best set of sets e1{a,b,c....}, e2{...} etc., see 1 big set e{a1,b1,a2,c3}, try find maximum on space. said, genetical algorithm might work ok.

maybe view can model differently, maybe linear mixed integer optimization problem if relations between variables , scores can expressed in such way. if can model in such way, can globally optimal result. can't more modeling though, since didn't how compute epoch score.