The two-machine flowshop scheduling problem with sequence-independent setup times: New lower bounding strategies

The two-machine flowshop environment with sequence-independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature. Nevertheless, very scant attention has been devoted to deriving effective lower bounding strategies. In this paper, we propose new lower bounds for the total completion time minimization criterion. These bounds are based on three relaxation schemes, namely the waiting time-based relaxation scheme, the single machine-based relaxation scheme, and the Lagrangian relaxation scheme. Extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time-based bounding strategy within the Lagrangian relaxation framework yields the best performance while requiring negligible CPU time.     

Comparison of non-sequential sets of protein residues

A methodology for performing sequence-free comparison of functional sites in protein structures is introduced. The method is based on a new notion of similarity among superimposed groups of amino acid residues that evaluates both geometry and physico-chemical properties. The method is specifically designed to handle disconnected and sparsely distributed sets of residues. A genetic algorithm is employed to find the superimposition of protein segments that maximizes their similarity. The method was evaluated by performing an all-to-all comparison on two separate sets of ligand-binding sites, comprising 47 protein-FAD (Flavin-Adenine Dinucleotide) and 64 protein-NAD (Nicotinamide-Adenine Dinucleotide) complexes, and comparing the results with those of an existing sequence-based structural alignment tool (TM-Align). The quality of the two methodologies is judged by the methods’ capacity to, among other, correctly predict the similarities in the protein-ligand contact patterns of each pair of binding sites. The results show that using a sequence-free method significantly improves over the sequence-based one, resulting in 23 significant binding-site homologies being detected by the new method but ignored by the sequence-based one.     

Lifting inequalities: a framework for generating strong cuts for nonlinear programs

In this paper, we introduce the first generic lifting techniques for deriving strong globally valid cuts for nonlinear programs. The theory is geometric and provides insights into lifting-based cut generation procedures, yielding short proofs of earlier results in mixed-integer programming. Using convex extensions, we obtain conditions that allow for sequence-independent lifting in nonlinear settings, paving a way for efficient cut-generation procedures for nonlinear programs. This sequence-independent lifting framework also subsumes the superadditive lifting theory that has been used to generate many general-purpose, strong cuts for integer programs. We specialize our lifting results to derive facet-defining inequalities for mixed-integer bilinear knapsack sets. Finally, we demonstrate the strength of nonlinear lifting by showing that these inequalities cannot be obtained using a single round of traditional integer programming cut-generation techniques applied on a tight reformulation of the problem.