Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms

We study five penalty function-based constraint handling techniques to be used with genetic algorithms in global optimization. Three of them, the method of superiority of feasible points, the method of parameter free penalties and the method of adaptive penalties have already been considered in the literature. In addition, we introduce two new modifications of these methods. We compare all the five methods numerically in 33 test problems and report and analyze the results obtained in terms of accuracy, efficiency and reliability. The method of adaptive penalties turned out to be most efficient while the method of parameter free penalties was the most reliable.     

Interactive Solution Approach to a Multiobjective Optimization Problem in a Paper Machine Headbox Design

A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented.     

Concluding the Amyloid Formation Pathway of a Coiled‐Coil‐Based Peptide from the Size of the Critical Nucleus

The size of the critical nucleus acting as intermediate in the amyloid formation of a model peptide is calculated. The theoretical approach is based on experimentally determined amyloid formation rates and gives new insights into the amyloid formation pathway.     

Finite Element Approximation of Hemivariational Inequalities

The paper deals with a finite element approximation of elliptic and parabolic variational inequalities. Elliptic hemivariational inequalities are equivalently expressed as a system consisting of one equation and one inclusion for a couple of unknowns, namely a primal variable u and an element belonging to a multivalued mapping at u. Both components of the solution are approximated independently each other by a finite element method. Parabolic inequalities are transformed into a system of elliptic ones by using an appropriate time discretization. A numerical experiment is realized by using non-smooth optimization methods.     

Molecular structure determination of Ni(II) diimine complex and DMA analysis of Ni(II) diimine‐based polyethenes

Dynamic mechanical thermoanalysis showed that polyethene, prepared under suitable polymerization conditions with the Brookhart‐type catalyst dibromo‐N,N′‐1,2‐acenaphthylenediylidenebis[2,6‐bis(1‐methylethyl)benzeneamine]Ni(II)/methylaluminoxane (MAO), behaved like an elastomer, even though no comonomer was added. A structural characterization showed that the polymers contained methyl to hexyl branches and some longer branches. The effect of the polymerization conditions on branching was investigated through variations in the pressure and temperature of the polymerization. Depending on the degree and type of branching, polyethene was either quite amorphous or highly crystalline with a high melting temperature. The solid‐state structure of the catalyst dibromo‐N,N′‐1,2‐acenaphthylenediylidenebis[2,6‐bis(1‐methylethyl)benzeneamine]Ni(II) consisted of two centrosymmetrically related monomeric moieties, where Ni atoms were bridged by two bromide ligands. The Ni atom was five‐coordinated, with a square pyramidal coordination polyhedron. The sixth coordination site of the octahedral geometry was effectively blocked by the isopropyl groups of the 2,6‐C₆H₃(i‐Pr) substituents of the diimine ligand. In solution in the presence of MAO, the longer bridging Ni? Br bonds broke, and the complex dissociated to a monomeric species. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1426–1434, 2001     

Unitarity bounds for inelastic diffraction

Unitarity in the s-channel is invoked to derive an upper bound for the inelastic diffractive cross-section as a function of impact parameter. The application of this bound to high-energy proton-proton scattering strongly suggests that inelastic diffraction should be peripheral in the impact parameter space.     

Hysteresis and Hemivariational Inequalities: Semilinear Case

In this paper we consider semilinear parabolic boundary value problems having nonsmooth and nonmonotone behaviour and memory effects. The mathematical problem can be formulated and studied by using the notions of hemivariational inequality (based on the generalized gradient in the sense of F.H. Clarke) and the hysteresis operator. We establish two general existence results for such problems. Applications from mechanics illustrate the theory.