We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables.

Statistical analysis is a powerful tool to apply when evaluating the performance of computer implementations of algorithms and heuristics. Yet many computational studies in the literature do not use this tool to maximum effectiveness. This paper examines the types of data that arise in computational comparisons and presents appropriate techniques for analyzing such data sets. Case studies of computational tests from the open literature are re-evaluated using the proposed methods in order to illustrate the value of statistical analysis for gaining insight into the behavior of the tested algorithms.

No abstract

No abstract

No abstract