Walter H. Kohler
Abstract
Branch-and-bound implicit enumeration algorithms for permutation problems (discrete optimization problems where the set of feasible solutions is the permutation group Sn) are characterized in terms of a sextuple (Bp S,E,D,L,U), where (1) Bp 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.
- 1 AGIN, N. Optimum seeking with branch and bound. Manag. Sci. I~, 4 (Dec. 1966), B 176- B 185.Google Scholar
- 2 BAL~s, E. A note on the branch-and-bound principle. Opcr. Res. 16, 2 (March-April 1968), 442-444; Errata, Oper. Res. I6, 4 (1968), 886.Google Scholar
- 3 BntTNO, J.,ANDSTEIGLITz, K. The expressi on of algorithms by charts. J. ACM 19,3 (July 1972), 517-525. Google Scholar
- 4 Fox, B. L., AND SCHRAGE, L.E. The value of various strategies in branch-and-bound. Unpublished rep., June 1972.Google Scholar
- 5 GEOFFRION, A. M., AND MARSTEN, R.E. Integer programming algorithms: A framework and state of the art survey. Manag. Sci. I8, 9 (May 1972), 465-491.Google Scholar
- 6 HELD, M., AND KARP, R. A dynamic programming approach to sequencing problems. J. SIAM 10, 1 (March 1962), 196-210.Google Scholar
- 7 HELD, M., AND KAaP, R. The traveling-salesman problem and minimum spanning trees: Part iI. Mathematical Programming I, 1 (Oct. 1971), 6-25.Google Scholar
- 8 IGNALL, E., AnD SCHRAGE, L. Application of branch and bound technique to some flow-shop scheduling problems. Oper. Res. I8, 3 (May-June 1965), 400-412.Google Scholar
- 9 KOHLER, W.H. Exact and approximate algorithms for permutation problems. Ph.D. Diss., Princeton U., Princeton, N.J., 1972. Google Scholar
- 10 LAWLER, E. L., AND WOOD, D. E. Branch-and-bound methods: A survey. Oper. Res. 14, 4 (July-Aug. 1966), 699-719.Google Scholar
- 11 MITTEN, L.G. Branch-and-bound methods: General formulation and properties. Oper. Res. 18, 1 (Jan.-Feb. 1970), 24-34.Google Scholar
- 12 NOLLnMEIEn, H. Ein branch-and-bound-verfahren-generator. Computing 8 (1971), 99-106.Google Scholar
- 13 PIEacE, J. F., AND CROWSTON, W.B. Tree-search algorithms for quadratic assignment problems. Naval Res. Logislics Quart. 18, 1 (March 1971), 1-36.Google Scholar
- 14 RoY, B. Procedure d'exploration par sdparation et dvaluation. Rev. Francaise d'Informatique et de Recherche Opdrationelle, 6 (1969), 61-90.Google Scholar
- 15 SC~RAGE, L. Solving resource-constrained network problems by implicit enumeration~non* preemptive case. Oper. Res. 18, 2 (March-April 1970), 263-278.Google Scholar
- 16 SCHRAGE, L. Solving resource-constrained network problems by implicit enumeration~preemptive case. Oper. Res. 20, 3 (May-June 1972), 668-677.Google Scholar
Index Terms
- Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems
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