An Improved Implicit Enumeration Approach for Integer Programming

A generalized implicit enumeration algorithm for a class of integer nonlinear programming problems

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...

Integer Programming by Implicit Enumeration and Balas' Method

A zero one programming model for RNA structures with arclength ≥ 4

In this paper, we consider RNA structures with arc-length 4 . First, we represent these structures as matrix models and zero-one linearprogramming problems. Then, we obtain an optimal solution for this problemusing an implicit enumeration method. The optimal solution corresponds toan RNA structure with the maximum number of hydrogen bonds.

Resolution Search and Dynamic Branch-and-Bound

A novel approach to pure 0-1 integer programming problems called Resolution Search has been proposed by Chvatal (l997) as an alternative to implicit enumeration, with a demonstration that the method can yield more effective branching strategies. We show that an earlier method called Dynamic Branch-and-Bound (DB&B), due to Glover and Tangedahl (1976), yields the same branching strategies as Reso...

An Integer Programming Model and a Tabu Search Algorithm to Generate α-labeling of Special Classes of Quadratic Graphs

First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...