Thomas L. Morin

Fixed Order Branch-and-Bound Methods for Mixed-Integer Programming: The zoom System

A branch-and-bound algorithm for mixed-integer programming (MIP) is presented in which a different integer variable is designated for branching at each depth in the search tree. This is done in order to achieve economies of scale in solving the linear programming relaxations to obtain bounds for the (MIP) algorithm. This algorithm is the foundation for the zoom software system, which is briefly described. Illustrative computational experience is included. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

The imbedded state space approach to reducing dimensionality in dynamic programs of higher dimensions

By exploiting discontinuity properties of the maximal convolution it is possible to drastically reduce dimensionality in finite dynamic programs. In fact, we show how the search over the usual M-dimensional state space can be reduced to a one-dimensional search over an imbedded state space. The versatility of our approach is illustrated on a number of example problems.

SOLUTION OF SOME COMBINATORIAL OPTIMIZATION PROBLEMS ENCOUNTERED IN WATER RESOURCES DEVELOPMENT

The solution of some constrained combinatorial optimization problems encountered in the preinvestment planning of large-scale water resources systems is discussed. Mathematical structures are formulated for several problems involving the optimal selection, sequencing and timing of a set of water resources development projects which, in the aggregate, must satisfy a number of continuous time demand projections at every point in a finite planning horizon. An overview of four different solution techniques is also given. Specifically, myopic decision rules, integer programming formulations, and both implicit enumeration by branch-and-bound algorithms and dynamic programming algorithms are discussed. A computational comparison of these solution techniques on a number of real-world water resources problems of various sizes is also reported.