The branch-and-bound algorithm is stated in general i ty, and i l l us t ra ted by two applications, unidirect ional graph search, and reducing a sparse matrix to i t s minimal band form. The algorithm is then generalised to mult iple par t i t ions , applied to bid i rect ional graph searching for both heurist ic and non-heuristic searches, and further extended to graph searches and problem so...

This work addresses the correction and improvement of Mavrotas and Diakoulaki’s branch and bound algorithm for mixed 0-1 MOLP. We first develop about the issues encountered by the original algorithm and propose and corrected version for the biobjective case. We then introduce several improvements about the bounds and end with the proposition of a new algorithm based on the two phase method and ...

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges (i.e., the number of edges that cut a line between consecutive vertices) is minimized. This paper starts by reviewing previous exact approaches for special classes of graphs as well as a linear integer formulation for the general problem. We propose a branch and bound algorit...

4 A single product maritime inventory routing problem in which the production and con5 sumption rates vary over the planning horizon is studied. The problem includes a heteroge6 neous fleet and multiple production and consumption ports with limited storage capacity. 7 Two discrete time formulations are developed. One is a standard formulation and the other 8 is a fixed charge network flow refor...

Difficult discrete optimization problems are often solved using a Branch and Bound approach. Resolution search is an alternate approach proposed by Chvátal for 0-1 problems, allowing more flexibility in the search process. In this paper, we generalize the Resolution Search to any discrete problem.

We propose an exact branch-and-bound algorithm for the problem of maximizing the minimum machine completion time on identical parallel machines. The proposed algorithm is based on tight lower and upper bounds aswell as an effective symmetry-breaking branching strategy. Computational results performed on a large set of randomly generated instances attest to the efficacy of the proposed algorithm.

This paper reviews tools which have great potential for reducing the difficulty of solving IP (and also MIP) problems, if well implemented in solvers. Recent experiments with Branch and Bound solvers, in connection with “Short Start Features”, have shown that implementations need and can still be improved. Concepts which are likely to be specially important for (0,1) MIP are pointed out.

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...

Booth and Cox proposed the E(s) criterion for constructing twolevel supersaturated designs. Nguyen [Technometrics 38 (1996) 69– 73] and Tang and Wu [Canad. J. Statist 25 (1997) 191–201] independently derived a lower bound for E(s). This lower bound can be achieved only when m is a multiple of N − 1, where m is the number of factors and N is the run size. We present a method that uses difference...