A.8.10 CLP(B) predicate index
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Availability::- use_module(library(clpb)).
Source[multi]weighted_maximum(+Weights, +Vs, -Maximum)
Enumerate weighted optima over admissible assignments. Maximize a linear objective function over Boolean variables Vs with integer coefficients Weights. This predicate assigns 0 and 1 to the variables in Vs such that all stated constraints are satisfied, and Maximum is the maximum of sum(Weight_i*V_i) over all admissible assignments. On backtracking, all admissible assignments that attain the optimum are generated.

This predicate can also be used to minimize a linear Boolean program, since negative integers can appear in Weights.

Example: 

?- sat(A#B), weighted_maximum([1,2,1], [A,B,C], Maximum).
A = 0, B = 1, C = 1, Maximum = 3.