A memetic algorithm based on multiple learning procedures for global optimal design of composite structures

The mechanical properties of composite structures are sensitive to the choice of the material systems, the distribution of laminates on the structure, and the sizing at the laminate level. This sensitivity depends on many variables. To overcome the difficulties in attaining a global solution for the optimisation problem of composite structures, a new strategy is proposed based on the hybridisation of the memetic algorithm (MA) and the selfish gene (SG) algorithm. Instead of a local search, as performed in MAs, the selfish gene (SG) theory is applied, which follows a different learning scheme in which the conventional population of the individuals is replaced by a virtual population of alleles. The proposed approach, which is called the memetic-based selfish gene algorithm (MA + SG), is a mixed model that applies multiple learning procedures to explore the synergy of different cultural transmission rules in the evolutionary process. The principal aspects of the approach are as follows: co-evolution of multiple populations, species conservation, migration rules, self-adaptive multiple crossovers, local search in hybrid crossover with local genetic improvements, controlled mutation, individual age control, and feature-based allele statistical analysis. To discuss the capabilities of the proposed approach, numerical examples are represented to compare the results of MA + SG with those obtained using genetic algorithms (GA) and MA. The numerical results of the comparison tests showed that the GA and the MA maintained long periods without the evolution of the best-fitted individual/solutions. This behaviour during evolution is associated with the slow maturation of the elite group of populations in the GA and MA approaches. This behaviour is avoided when the MA + SG proposed approach is used with computational cost benefits.     

Imaginary quadratic function fields

In Bautista-Ancona and Diaz-Vargas (2006) [B-D] a characterization and complete listing is given of the imaginary quadratic extensions K of k(x), where k is a finite field, in which the ideal class group has exponent two and the infinite prime of k(x) ramifies. The objective of this work is to give a characterization and list of these kind of extensions but now considering the case in which the infinite prime of k(x) is inert in K. Thus, we get all the imaginary quadratic extensions of k(x), in which the ideal class group has exponent two.     

Delta shock wave for a 3 × 3 hyperbolic system of conservation laws

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. The system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that models viscoelastic fluids. An important issue is that the considered 3×3 system is such that every characteristic field is linearly degenerate. We study theRiemann problemfor this system and under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta shock type solutions are established.