Showing papers on "Bounding overwatch published in 1982"

The power of upper and lower bounding functions in branch-and-bound algorithms

Abstract: In a branch-and-bound algorithm, a partial problem Pi is terminated if the lower bound of the optimal value of Pj is greater (in case all optimal solutions are sought) or not smaller (in case a single optimal solution is sought) than the least upper bound on the optimal value of the original minimization problem Po currently available. Although it seems obvious that tighter lower bounding function and upper bounding function always improve the efficiency of a branch-and-bound algorithm, counterexamples can be easily constructed. In this paper, therefore, it is extensively studied when such improvement is guaranteed, for typical search strategies such as heuristic search, best-bound search and depth-first s(,arch. The model of branch-and-bound algorithms used for investigation is quite general in the sense that it allows the dominance test as well as the lower bound test mentioned above. The efficiency is measured by the number of partial problems decomposed in the execution of the algorithm.