HYBRID EVOLUTIONARY AND ANNEALING ALGORITHMS FOR NONLINEAR DISCRETE CONSTRAINED OPTIMIZATION

This paper presents a procedural framework that unifies various mechanisms to look for discrete-neighborhood saddle points in solving discrete constrained optimization problems (DCOPs). Our approach is based on the necessary and sufficient condition on local optimality in discrete space, which shows the one-to-one correspondence between the discrete-space constrained local minima of a problem and the saddle points of the corresponding Lagrangian function. To look for such saddle points, we study various mechanisms for performing ascents of the Lagrangian function in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our results show that CSAEA, a combined constrained simulated annealing and evolutionary algorithm, performs well when using mutations and crossovers to generate trial points and accepting them based on the Metropolis probability. We apply iterative deepening to determine the optimal number of generations in CSAEA and show that its performance is robust with respect to changes in population size. To test the performance of the procedures developed, we apply them to solve some continuous and mixed-integer nonlinear programming (NLP) benchmarks and show that they obtain better results than those of existing algorithms.

TUNING STRATEGIES IN CONSTRAINED SIMULATED ANNEALING FOR NONLINEAR GLOBAL OPTIMIZATION

This paper studies various strategies in constrained simulated annealing (CSA), a global optimization algorithm that achieves asymptotic convergence to constrained global minima (CGM) with probability one for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and sufficient condition for discrete constrained local minima (CLM) in the theory of discrete Lagrange multipliers and its extensions to continuous and mixed-integer constrained NLPs. The strategies studied include adaptive neighborhoods, distributions to control sampling, acceptance probabilities, and cooling schedules. We report much better solutions than the best-known solutions in the literature on two sets of continuous benchmarks and their discretized versions.

Molecular modeling of the oxytocin receptor/bioligand interactions.

Oxytocin is a nonapeptide hormone (CYIQNCPLG-NH2, OT), controlling labor and lactation in mammalian females, via interactions with specific cellular membrane receptors (OTRs). The native hormone is cyclized via a 1-6 disulfide and its receptor belongs to the GTP-binding (G) protein-coupled receptor (GPCR) family, also known as heptahelical transmembrane (7TM) or serpentine receptors. Using a technique combining multiple sequence alignments with available experimental constraints, a reliable OTR model was built. Subsequently, the OTR complexes with a selective agonist [Thr4,Gly7]OT, a selective cyclohexapeptide antagonist L-366,948 and oxytocin itself were modeled and relaxed using a constrained simulated annealing (CSA) protocol. All three ligands seem to prefer similar modes of binding to the receptor, manifested by repeating receptor residues which directly interact with the ligands. Those involved in the three complexes are putative helices: TM3: R113, K116, Q119, M123; TM4: Q171, and TM5: I201 and T205. Most of them are the equivalent residues/positions to those found in our earlier studies, regarding related vasopressin V2 receptor/bioligand interactions.

Elucidation of neurophysin/bioligand interactions from molecular modeling.

This is a review of our recent modeling work aimed at: (i) development and assessment of techniques for reliable refinement of low-resolution protein structures and (ii) using these techniques, at solving specific problems pertinent to neurophysin-bioligand interactions. Neurophysins I and II (NPI and NPII) serve in the neurosecretory granules of the posterior pituitary as carrier proteins for the neurophyseal hormones oxytocin (OT) and vasopressin (VP), respectively, until the latter are released into blood. NPs are homologous two-domain, sulphur rich small proteins (93-95 residues, 7 disulphide bridges per monomer), capable of being aggregated. The C2 symmetrical NPI2 and NPII2 homodimers, and the (NPI/OT)2 and (NPII/VP)2 heterotetramers, all believed to be the smallest functional units, were modeled using low-resolution structure information, i.e. the C alpha-carbon coordinates of the homologous NPII/dipeptide complex as a template. The all-atom representations of the models were obtained using the SYBYL suite of programs (by Tripos, Inc.). Subsequently, they were relaxed, using a constrained simulated annealing (CSA) protocol, and submitted to about 100 ps molecular dynamics (MD) in water, using the AMBER 4.1 force field. The (NPI/OT)2 and (NPII/VP)2 structures, averaged after the last 20 ps of MD, were remarkably similar to those recently reported either for NPII/dipeptide or NPII/oxytocin complex in the solid state (Chen et al., 1991, Proc. Natl. Acad. Sci., U.S.A. 88, 4240-4244; Rose et al., 1996, Nature Struct. Biol. 3, 163-169). The results indicate that the 3(10) helices (terminating the amino domains) and the carboxyl domains are more mobile than the remainder of the NP monomers. The hormones become anchored by residues 1-3 and 6 to the host, leaving residues 4-5 and 7-9 exposed on the surface and free to move. A cluster of attractive interactions, extending from the ligand binding site, Tyr-24-Ile-26 of unit 1(2), to the inter-monomer interface Val-36 of unit 1(2), Cys-79 and Ile-72 of unit 2(1), is clearly seen. We suggest that both these interactions as well as the increased mobility of the 3(10) helix and the carboxyl domain may contribute to the allosteric communication between the ligand and the unit1-unit2 interface.