Self-organized modularization in evolutionary algorithms

The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization. Based on a combination of two formalizations by Radcliffe and Altenberg, some quantitative measures of modularity are introduced. Particularly, we distinguish Built-in Modularity as an inherent property of a genotype and Effective Modularity, which depends on the rest of the population. These measures can easily be applied to a wide range of present Evolutionary Computation models. It will be shown, both theoretically and by simulation, that under certain conditions, Effective Modularity (as defined within this paper) can be a selection factor. This causes Self-Organized Modularization to take place. The experimental observations emphasize the importance of Effective Modularity in comparison with Built-in Modularity. Although the experimental results have been obtained using a minimalist toy model, they can lead to a number of consequences for existing models as well as for future approaches. Furthermore, the results suggest a complex self-amplification of highly modular equivalence classes in the case of respected relations. Since the well-known Holland schemata are just the equivalence classes of respected relations in most Simple Genetic Algorithms, this observation emphasizes the role of schemata as Building Blocks (in comparison with arbitrary subsets of the search space).     

Crystal Structure and High-Temperature Thermoelectric Properties of the Mo<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript>Ru<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Sb<Subscript>7</Subscript> Compounds

Zintl phases are currently receiving great attention for their thermoelectric potential typified by the discovery of a high ZT value in Yb₁₄MnSb₁₁-based compounds. Herein, we report on the crystallographic characterization via neutron and x-ray diffraction experiments, and on the thermoelectric properties measured in the 300 K to 1000 K temperature range, of Mo₃Sb₇ and its isostructural compounds Mo_3−x Ru _x Sb₇. Even though Mo₃Sb₇ displays rather high ZT values given its metallic character, the partial substitution of Mo by Ru substantially improves its thermoelectric properties, resulting in a ZT value of ∼0.45 at 1000 K for x = 0.8.     

Influence of ZnO Inclusions on the Low-Temperature Thermoelectric Properties of CoSb3

CoSb₃ composites with different amounts of ZnO nanoparticles (2?wt.% to 12?wt.%) were prepared from nanosized ZnO (commercial) and micron-sized CoSb₃ (obtained via solid-state reaction) particles mixed in solution and freeze dried. The resulting powders were densified by spark plasma sintering. The samples were characterized by x-ray diffraction and scanning electron microscopy. It was found that ZnO forms micron-sized clusters at the grain boundaries of the matrix material. The thermoelectric properties (electrical resistivity, thermopower, and thermal conductivity) were measured in the 2?K to 300?K temperature range. Both the electrical and thermal conductivities were observed to decrease with increasing ZnO content. The dimensionless figure of merit ZT was improved by up to 30% at 300?K for the sample containing 2?wt.% ZnO.     

High temperature thermoelectric properties of CoSb3 skutterudites with PbTe inclusions

Nanostructured thermoelectric materials generally exhibit enhanced properties. PbTe–CoSb₃ thermoelectric composites (0–8 wt% of PbTe) have been successfully prepared by freeze-drying nanoparticles of PbTe (6 nm in diameter, synthesized by laser fragmentation of micron-sized particles in water) with micron-sized skutterudite CoSb₃ powders (~5 μm in diameter, synthesized by powder metallurgy), followed by spark plasma sintering. X-ray diffraction analyses and scanning electron microscopy observations have been performed. Microstructures reveal an agglomeration of the PbTe particles at the grain boundaries of CoSb₃. Electrical resistivity, thermopower, and thermal conductivity measurements have been performed in the 300–800 K temperature range. The composites exhibit n-type conduction whereas the reference CoSb₃ skutterudite is p-type. This change of conduction mode is attributed to substitution of Sb for a minute amount of Te in the composites. The influence of both PbTe nanoparticules and Te on the thermoelectric properties is discussed in detail.     

Optimization of Bulk Thermoelectrics: Influence of Cu Insertion in Ag3.6Mo9Se11

Currently, there is a resurgence of interest in thermoelectric materials with enhanced efficiency. Among investigated classes of bulk thermoelectrics such as partially filled skutterudites, Zn₄Sb₃-based materials, and clathrates, novel polycrystalline Mo₉ cluster-based chalcogenides were reported recently. Among those, Chevrel phase-derived Ag _y Mo₉Se₁₁ (with 3.4????y????3.9) compounds have shown interesting thermoelectric properties, in particular extremely low thermal conductivity allowing improved thermoelectric efficiency compared with reported Chevrel phases. They also possess a complex crystallographic structure where stacked Mo₉Se₁₁ units leave channels occupied by Ag atoms. Analysis of the structural determinants of the thermoelectric properties of Ag _y Mo₉Se₁₁ suggested that performance improvements could result from further Cu insertion. In this paper, we describe the synthesis route we used for preparing quaternary Ag-Cu-Mo-Se compositions by a combination of powder metallurgy and spark plasma sintering techniques. Characterization by x-ray diffraction, scanning electron microscopy, and electrical and thermal measurements has been performed. The results obtained for two compounds (Ag_3.6Cu_0.2Mo₉Se₁₁ and Ag_3.6Cu_0.4Mo₉Se₁₁) are discussed and compared with those of the parent ternary compound Ag_3.6Mo₉Se₁₁.