This article presents the preliminary results on a new branch-and-bound algorithm proposed for the single machine total tardiness problem with arbitrary release dates. The algorithm relies on dominance properties from the literature as well as a new branching condition. A new lower bounding technique for the problem is also introduced. The performance of the algorithm is compared to the perform...

Single round robin tournaments are a well-known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated with each possible match. Moreover, stadium availability, fixed matches, and regions’ capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasi...

We present a Branch and Bound approach for the resource constrained project scheduling problem where activity durations are assumed to be random according to independent probability distributions. Our aim is to compute an optimal scheduling policy that minimize the expected project cost with respect to some regular measure of performance.

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...