Some straightforward but unconventional strategies are proposed for implementing branch and bound methods. These include 'shrinking' the branch and bound tree and instituting 'branch reversals' by reference to the notion .of the relative influence of particular branches in the current solution. An attractive feature of these strategies is their ease of implementation, and the fact that they fre...

We introduce new lower bounds for the minimum graph bisection problem. Within a branch-and-bound framework, they enable the solution of a wide variety of instances with tens of thousands of vertices to optimality. Our algorithm compares favorably with the best previous approaches, solving long-standing open instances in minutes.

In chemical engineering and other areas of engineering and science, high performance computing is providing the capability to: ¯ Solve problems faster.

We propose the use of logic-based preference representation languages based on weighted propositional formulas for specifying bids in a combinatorial auction. We then develop several heuristics for a branch-and-bound search algorithm for determining the winning bids in this framework and report on their empirical performance. The logic-based approach is attractive due to its high degree of flex...

Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is i...

We present a new method for solving nonlinear integer arithmetic constraints. The method relies on the MCSat approach to solving nonlinear constraints, while using branch and bound in a conflict-directed manner. We report encouraging experimental results where the new procedure outperforms state-of-the-art SMT solvers based on bit-blasting.

The Multi-Story Space Assignment Problem (MSAP) is an innovative formulation of the multi-story facility assignment problem that allows one to model the location of departments of unequal size within multi-story facilities as a Generalized Quadratic 3-dimensional Assignment Problem (GQ3AP). Not only can the MSAP generate the design of the location of the departments in the facility, the MSAP al...

In this short paper we present a brief exposition of a composite decision process our unifying formulation of search procedures which provides new insights concerning the relationships among heuristic search, dynamic programming and branch and bound procedures.

Precise constraint satisfaction modeling requires specific knowledge acquired from multiple past cases. We address this issue with a general branch-and-bound algorithm that learns the parameters of a given global constraint from a small set of positive solutions. The idea is to cleverly explore the possible combinations taken by the constraint’s parameters without explicitly enumerating all com...

The problem of determining the largest order nd,k of a graph of maximum degree at most d and diameter at most k is well known as the degree/diameter problem. It is known that nd,k Md,k where Md,k is the Moore bound. For d = 4, the current best upper bound for n4,k is M4,k − 1. In this paper we study properties of graphs of order Md,k − 2 and we give a new upper bound for n4,k for k 3. © 2007 El...