Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems

Branch-and-bound implicit enumeration algorithms for permutation problems (discrete optimization problems where the set of feasible solutions is the permutation group S n ) are characterized in terms of a sextuple ( B p S,E,D,L,U ), where (1) B p is the branching rule for permutation problems, (2) S is the next node selection rule, (3) E is the set of node elimination rules, (4) D is the node dominance function, (5) L is the node lower-bound cost function, and (6) U is an upper-bound solution cost. A general algorithm based on this characterization is presented and the dependence of the computational requirements on the choice of algorithm parameters, S, E, D, L, and U is investigated theoretically. The results verify some intuitive notions but disprove others.