Fundamenta Informaticae - Volume 122, issue 3

Authors: Ma, Zhanshan Sam

Article Type: Research Article

Abstract: Natural populations are dynamic in both time and space. In biological populations such as insects, spatial distribution patterns are often studied as the first step to characterize population dynamics. In nature, the spatial distribution patterns of insect populations are considered as the emergent expression (property) of individual behaviors at population levels and are fine-tuned or optimized by natural selection. This inspiration prompts us to investigate the possibly similar mechanisms in Genetic Algorithms (GA) populations. In this study, we introduce the mathematical models for the spatial distribution patterns of insect populations to GA with the conjecture that the emulation of biological …populations in nature may lead to computational improvement. In particular, we introduce three modeling approaches from the research of spatial distribution patterns of insect populations: (i) probability distribution modeling approach, (ii) aggregation index approach, and (iii) Taylor's (1961, 1977) Power Law, Iwao's (1968, 1976) Mean Crowding Model and Ma's (1991c) population aggregation critical density (PACD), to characterize populations in GA. With these three approaches, we investigate four mappings from the research field of insect spatial distribution patterns to GA populations in order to search for possible counterpart mechanisms or features in GA. They are: (i) mapping insect spatial distribution patterns to GA populations or allowing GA populations to be controlled by stochastic distribution models that describe insect spatial distributions; (ii) mapping insect population distribution to GA population fitness distribution via Power Law and PACD modeling; (iii) mapping population aggregation dynamics to GA fitness progression across generations (or fitness aggregation dynamics in GA) via insect population aggregation index; (iv) mapping insect population sampling model to optimal GA population sizing. With regard to the mapping (i), the experiment results show the significant improvements in GA computational efficiency in terms of the reduced fitness evaluations and associated costs. This prompts us to suggest using probability distribution models, or what we call stochastic GA populations, to replace the fixed-size population settings. We also found the counterpart for the second mapping, the wide applicability of Power Law and Mean Crowding model to the fitness distribution in GA populations. The testing of the third and fourth mappings is very preliminary; we use example cases to suggest two further research problems: the potential to use fitness aggregation dynamics for controlling the number of generations iterated in GA searches, and the possibility to use fitness aggregation distribution parameters [(obtained in mapping (ii)] in determining the optimum population size in GA. A third interesting research problem is to investigate the relationship between mapping (i) and (iii), i.e., the controlling of both population sizes and population generations. Show more

Keywords: Genetic Algorithm (GA), Spatial Distribution Pattern, Power Law, Dynamic Population, Fitness Distribution, Fitness Aggregation, Fitness Aggregation Dynamics, Insect Population Dynamics

DOI: 10.3233/FI-2013-787

Citation: Fundamenta Informaticae, vol. 122, no. 3, pp. 173-206, 2013

Authors: Fashandi, Homa | Peters, James F.

Article Type: Research Article

Abstract: This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a means of dealing with imperfections and small errors, especially in cases such as digital images where boundaries of subsets of an image are not crisp. The properties of the new operators are presented. Applications of the proposed operators are given in …terms of rough sets and mathematical morphology. Show more

Keywords: Crisp topology, Fuzzy topology, Inclusion degree, Interior operator, Closure operator, Rough set, Mathematical morphology

DOI: 10.3233/FI-2013-788

Citation: Fundamenta Informaticae, vol. 122, no. 3, pp. 207-225, 2013

Authors: Langmaack, Hans | Salwicki, Andrzej

Article Type: Research Article

Abstract: In [14] an axiomatic approach towards the semantics of FJI, Featherweight Java with Inner classes, essentially a subset of the Java-programming language, is presented. In this way the authors contribute to an ambitious project: to give an axiomatic definition of the semantics of programming language Java. At a first glance the approach of reducing Java's semantics to that of FJI seems promising. We are going to show that several questions have been left unanswered. It turns out that the theory how to elaborate or bind types and thus to determine direct superclasses as proposed in [14] has different models. Therefore …the suggestion that the formal system of [14] defines the (exactly one) semantics of Java is not justified. We present our contribution to the project showing that it must be attacked from another starting point. Quite frequently one encounters a set of inference rules and a claim that a semantics is defined by the rules. Such a claim should be proved. One should present arguments: 1° that the system has a model and hence it is a consistent system, and 2° that all models are isomorphic. Sometimes such a proposed system contains a rule with a premise which reads: there is no proof of something. One should notice that this is a metatheoretic property. It seems strange to accept a metatheorem as a premise, especially if such a system does not offer any other inference rules which would enable a proof of the premise. We are going to study the system in [14]. We shall show that it has many non-isomorphic models. We present a repair of Igarashi's and Pierce's calculus such that their ideas are preserved as close as possible. Show more

Keywords: object oriented programming, semantics, inheritance, inner classes, direct superclass, static semantics analysis, static binding, derivation calculus, model, minimal resp. least model

DOI: 10.3233/FI-2013-789

Citation: Fundamenta Informaticae, vol. 122, no. 3, pp. 227-274, 2013