**2017**

*A discrete representation of dicomplemented lattices*

Ivo Düntsch [1], Léonard Kwuida and Ewa Orlowska, March 2017. [PDF [2]] [abstract [3]] [close [4]]Dicomplemented lattices were introduced as an abstraction of Wille’s concept algebras which provided negations to a concept lattice. We prove a discrete representation theorem for the class of dicomplemented lattices. The theorem is based on a topology free version of Urquhart’s representation of bounded general lattices.

**2016**

*Mixed algebras and their logics*

Ivo Düntsch [1], Ewa Orlowska and Tinko Tinchev, January 2016. [PDF [5]] [abstract [6]] [close [7]]We investigate complex algebras of the form <2

^{X}, <R>, [[S]]> arising from a frame <X, R, S> where S ⊆ R, and exhibit their abstract algebraic and logical counterparts.*Online Image Classification Using Graphics Processing Unit-Based Genetic Programming*

Mehran Maghoumi, Brian J. Ross [8], August 2016. [PDF [9]] [abstract [10]] [close [11]]A texture classification vision system implemented with Graphics Processing Unit-based genetic programming is described. An online learning environment is implemented, in which genetic programming is automatically invoked when un-classified texture instances are present in an image stream. Once a segment is positively classified, the genetic programming classifier expression is reapplied to frames of the image stream. System performance is enhanced using population-parallel evaluation on a graphics processing unit. Various experiments with textures of varying difficulty were performed. Real-time performance was often seen in cases using 4-segments of texture data, as correct classifiers were evolved within seconds. In all cases, once evolved, classifiers were easily applied to the image stream in real-time. This research shows that high-performance real-time learning environments for image classification are attainable with genetic programming.

**2015**

*Simplifying contextual structures*

Ivo Düntsch [1] and Günther Gediga, January 2015. [PDF [12]] [abstract [13]] [close [14]]We present a method to reduce a formal context while retaining much of its information content. Although simple, our ICRA approach offers an effective way to reduce the complexity of concept lattices and / or knowledge spaces by changing only little information in comparison to a competing model which uses fuzzy K-Means clustering.

*Rough set clustering*

Ivo Düntsch [1] and Günther Gediga, January 2015. [PDF [15]] [abstract [16]] [close [17]]We present a survey of clustering methods based on rough set data analysis.

*A relational logic for spatial contact based on rough set approximation*

Ivo Düntsch [1] and Ewa Orloska, Hui Wang, November 2015. [PDF [18]] [abstract [19]] [close [20]]In previous work we have presented a class of algebras enhanced with two contact relation used in spatial reasoning on the basis of rough sets. In this paper we present a relational logic for such structures in the spirit of Rasiowa -- Sikorki proof systems.

**2014**

*Virtual Photography Using Multi-Objective Particle Swarm Optimization*

William Barry and Brian J. Ross [8], January 2014. [PDF [21]] [abstract [22]] [close [23]]Particle swarm optimization (PSO) is a stochastic population-based search algorithm that is inspired by the flocking behaviour of birds. Here, a PSO is used to implement swarms of cameras flying through a virtual world in search of an image that satisfies a set of compositional constraints, for example, the rule of thirds and horizon line rules. To effectively process these multiple, and possible conflicting, criteria, a new multi-objective PSO algorithm called the sum of ranks PSO (SR-PSO) is introduced. The SR-PSO is useful for solving high-dimensional search problems, while discouraging degenerate solutions that can arise with other approaches. Less user intervention is required for the SR-PSO, as compared to a conventional PSO. A number of problems using different virtual worlds and user-supplied constraints were studied. In all cases, solution images were obtained that satisfied the majority of given constraints. The SR-PSO was shown to be superior to other algorithms in solving the high-dimensional virtual photography problems studied.

*Passive Solar Building Design Using Genetic Programming*

Mohammad Mahdi Oraei Gholami and Brian J. Ross [8], January 2014. [PDF [24]] [abstract [25]] [close [26]]Passive solar building design considers the effect that sunlight has on energy usage. The goal is to reduce the need for artificial cooling and heating devices, thereby saving energy costs. A number of competing design objectives can arise. Window heat gain during winter requires large windows. These same windows, however, reduce energy efficiency during nights and summers. Other model requirements add further complications, which creates a challenging optimization problem. We use genetic programming for passive solar building design. The EnergyPlus system is used to evaluate energy consumption. It considers factors ranging from model construction (shape, windows, materials) to location particulars (latitude/longitude, weather, time of day/year). We use a split grammar to build 3D models, and multi-objective fitness to evaluate the multiple design objectives. Experimental results showed that balancing window heat gain and total energy use is challenging, although our multi-objective strategy could find interesting compromises. Many factors (roof shape, material selection) were consistently optimized by evolution. We also found that geographic aspects of the location play a critical role in the final building design.

*Feature Extraction Languages and Visual Pattern Recognition*

Mehran Maghoumi and Brian J. Ross [8], January 2014. [PDF [27]] [abstract [28]] [close [29]]Visual pattern recognition and classification is a challenging computer vision problem. Genetic programming has been applied towards automatic visual pattern recognition. An important factor in evolving effective classifiers is the suitability of the GP language for defining expressions for feature extraction and classification. This research presents a comparative study of a variety of GP languages suitable for classification. Four different languages are examined, which use different selections of image processing operators. One of the languages does block classification, which means that an entire region of pixels is classified simultaneously. The other languages are pixel classifiers, which determine classification for a single pixel. Pixel classifiers are more common in the GP-vision literature. We tested the languages on different instances of Brodatz textures, as well as aerial and camera images. Our results show that the most effective languages are pixel-based ones with spatial operators. However, as is to be expected, the nature of the image will naturally determine the effectiveness of the language used.

*Real-Time Automatic Object Classification and Tracking using Genetic Programming and NVidia® Cuda*^{TM}

Mehran Maghoumi, August 2014. [PDF [30]] [abstract [31]] [close [32]]Genetic Programming (GP) is a widely used methodology for solving various computa- tional problems. GP’s problem solving ability is usually hindered by its long execution time for large and complex problems. In this thesis, GP is applied toward real-time com- puter vision. In particular, object classification and tracking using a parallel GP system is discussed. First, a study of suitable GP languages for object classification is presented. To this end two main GP approaches for visual pattern classification were studied. These approaches include the block-classifiers and the pixel-classifiers. According to the experi- ments, the pixel-classifiers were generally more accurate and performed better. Next, using the results of these experiments, a suitable language was selected for the implementation of the real-time tracking system. The real-time system was implemented using NVIDIA CUDA. Synthetic video data was used in the experiments. The goal of the experiments was to evolve a unique classifier for each texture pattern that was present in the video. The experiments revealed that the system was capable of correctly classifying and tracking the textures in the video. Furthermore, the performance of the system was on-par with real-time requirements.

*Discrete dualities for n-potent MTL–algebras and 2-potent BL–algebras*

Ivo Düntsch [1], Ewa Orłowska, Clint van Alten, September 2014. [PDF [33]] [abstract [34]] [close [35]]Discrete dualities are developed for n-potent MTL–algebras and for 2-potent BL–algebras. That is, classes of frames, or relational systems, are defined that serve as dual counterparts to these classes of algebras. The frames defined here are extensions of the frames that were developed for MTL–algebras by Orlowska, Radzikowska (2009) and Orlowska, Rewitzky (2010) ; the additional frame conditions required are given here and also the proofs that discrete dualities hold with respect to such frames. The duality also provides an embedding from an n-potent MTL–algebra, or 2-potent BL–algebra, into the complex algebra of its canonical frame, which is a complete algebra in the lattice sense.

**2013**

*Discrete PSO for the Uncapacitated Single Allocation Hub Location Problem*

Alexander Bailey, Beatrice Ombuki-Berman [36], Stephen Asobiela, January 2013. [PDF [37]] [abstract [38]] [close [39]]Efficient network design and optimization of transportation and distribution systems has significant economic and service efficiency implications for both the public and private sectors. We propose a new solution based on a particle swarm optimization (PSO) for the uncapacitated single allocation hub location problem (USAHLP). Although various meta-heuristics have been proposed for this problem, to the authors. knowledge, this is the first attempt to use a PSO framework for this problem. An empirical study is done using well-known benchmark problems from the Civil Aeronautics Board and Australian Post data sets with node sizes of up to 200. The beauty of the proposed approach is its simplicity and effectiveness, where its solution quality is compared with that of other meta-heuristics. The proposed discrete PSO matches or out-performs the solution quality of the current best-known methods for the USAHLP.

*On the homogeneous countable Boolean contact algebra*

Ivo Düntsch [1] and Sangiang Li, March 2013. [PDF [40]] [abstract [41]] [close [42]]In a recent paper, we have shown that the class of Boolean contact algebras (BCAs) has the hereditary property, the joint embedding property and the amalgamation property. By Fraïssé.s theorem, this shows that there is a unique countable homogeneous BCA. This paper investigates this algebra and the relation algebra generated by its contact relation. We first show that the algebra can be partitioned into four sets f0g, f1g, K, and L, which are the only orbits of the group of base automorphisms of the algebra, and then show that the contact relation algebra of this algebra is finite, which is the first non.trivial extensional BCA we know which has this property.

*Generative Representations for Artificial Architecture and Passive Solar Performance*

Adrian Harrington and Brian J. Ross [43], March 2013. [PDF [44]] [abstract [45]] [close [46]]This paper explores how the use of generative representations improves the quality of solutions in evolutionary design problems. A genetic programming system is developed with individuals encoded as generative representations. Two research goals motivate this work. One goal is to examine Hornby.s features and measures of modularity, reuse and hierarchy in new and more complex evolutionary design problems. In particular, we consider a more difficult problem domain where the generated 3D models are no longer constrained by voxels. Experiments are carried out to generate 3D models which grow towards a set of target points. The results show that the generative representations with the three features of modularity, regularity and hierarchy performed best overall. Although the measures of these features were largely consistent to those of Hornby, a few differences were found.

Our second research goal is to use the best performing encoding on some 3D modeling problems that involve passive solar performance criteria. Here, the system is challenged with generating forms that optimize exposure to the Sun. This is complicated by the fact that a model.s structure can interfere with solar exposure to itself; for example, protrusions can block Sun exposure to other model elements. Furthermore, external environmental factors (geographic location, time of the day, time of the year, other buildings in the proximity) may also be relevant. Experimental results were successful, and the system was shown to scale well to the architectural problems studied.

*Automatic Inference of Hierarchical Graph Models Using Genetic Programming with an Application to Cortical Networks*

Alexander Bailey, Beatrice Ombuki-Berman [36], Mario Ventresca, March 2013. [PDF [47]] [abstract [48]] [close [49]]The pathways that relay sensory information within the brain form a network of connections, the precise organization of which is unknown. Communities of neurons can be discerned within this tangled structure, with inhomogeneously distributed connections existing between cortical areas. Classification and modelling of these networks has led to advancements in the identification of unhealthy or injured brains, however, the current models used are known to have major deficiencies. Specifically, the community structure of the cortex is not accounted for in existing algorithms, and it is unclear how to properly design a more representative graph model. It has recently been demonstrated that genetic programming may be useful for inferring accurate graph models, although no study to date has investigated the ability to replicate community structure. In this paper we propose the first GP system for the automatic inference of algorithms capable of generating, to a high accuracy, networks with community structure. We utilize a common cat cortex data set to highlight the efficacy of our approach. Our experiments clearly show that the inferred graph model generates a more representative network than those currently used in scientific literature.

*A Scalability Study of Multi-Objective Particle Swarm Optimizers*

Kyle Robert Harrison, Andries P. Engelbrecht, Beatrice Ombuki-Berman [36], March 2013. [PDF [50]] [abstract [51]] [close [52]]Particle swarm optimization (PSO) is a well-known optimization technique originally proposed for solving singleobjective, continuous optimization problems. However, PSO has been extended in various ways to handle multi-objective optimization problems (MOPs). The scalability of multi-objective PSO algorithms as the number of sub-objectives increases has not been well examined; most observations are for two to four objectives. It has been observed that the performance of multiobjective optimizers for a low number of sub-objectives can not be generalized to problems with higher numbers of sub-objectives. With this in mind, this paper presents a scalability study of three well-known multi-objective PSOs, namely vector evaluated PSO (VEPSO), optimized multi-objective PSO (oMOPSO), and speed-constrained multi-objective PSO (SMPSO) with up to eight sub-objectives. The study indicates that as the number of subobjectives increases, SMPSO scaled the best, oMOPSO scaled the worst, while VEPSO.s performance was dependent on the knowledge transfer strategy (KTS) employed, with parent centric recombination (PCX) based approaches scaling consistently better.

*PRE and variable precision models in rough set data analysis*

Ivo Düntsch [1] and Günther Gediga, April 2013. [PDF [53]] [abstract [22]] [close [23]]We present a parameter free and monotonic alternative to the parametric variable precision model of rough set data analysis. The proposed model is based on the well known PRE index lambda of Goodman and Kruskal. Using a weighted lambda model it is possible to define a two dimensional space based on (Rough) sensitivity and (Rough) specificity, for which the monotonicity of sensitivity in a chain of sets is a nice feature of the model. As specificity is often monotone as well, the results of a rough set analysis can be displayed like a receiver operation curve (ROC) in statistics. Another aspect deals with the precision of the prediction of categories -- normally measured by an index alpha in classical rough set data analysis. We offer a statistical theory for alpha and a modification of alpha which fits the needs of our proposed model. Furthermore, we show how expert knowledge can be integrated without losing the monotonic property of the index. Based on a weighted lambda, we present a polynomial algorithm to determine an approximately optimal set of predicting attributes. Finally, we exhibit a connection to Bayesian analysis. We present several simulation studies for the presented concepts. The current paper is an extended version of a paper presented at FedCSiS 2012.

*Genetic Programming for Non-Photorealistic Rendering*

Maryam Baniasadi, June 2013. [PDF [54]] [abstract [28]] [close [29]]This thesis focuses on developing an evolutionary art system using genetic programming. The main goal is to produce new forms of evolutionary art that alter existing images into new non-photorealistic (NPR) styles, by obtaining images that look like traditional media such as watercolor or pencil, as well as brand new effects. The approach permits GP to generate creative forms of NPR results. The GP language is extended with different techniques and methods inspired from NPR research such as colour mixing expressions, image processing filters and painting algorithm. Colour mixing is a major new contribution, as it enables many familiar and innovative NPR effects to arise. Another major innovation is that many GP functions process the canvas (rendered image), while is dynamically changing. Automatic fitness scoring uses aesthetic evaluation models and statistical analysis, and multi-objective fitness evaluation is used. Results showed a variety of NPR effects, as well as new, creative possibilities.

*Standard Errors of Indicies in Rough Set Data Analysis*

Günther Gediga and Ivo Düntsch [1], September 2013. [PDF [55]] [abstract [31]] [close [32]]The sample variation of indices for approximation of sets in the context of rough sets data analysis is considered. We consider the gamma and alpha indices and some other ones – lower and upper bound approximation of decision classes. We derive confidence bounds for these indices as well as a two group comparison procedure. Finally we present procedures to compare the approximation quality of two sets within one sample

*Relational Properties of Sequential Composition of Co-Algebras*

Michael Winter [56] and Peter Kempf, October 2013. [PDF [57]] [abstract [34]] [close [35]]In this paper we define a sequential composition for arbitrary co-algebras in a Dedekind category. We show some basic algebraic properties of this operation up to bisimulation. Furthermore, we consider certain recursive equations and provide an explicit solution, i.e., a solution not based on an iterative process.

*Passive Solar Building Design Using Genetic Programming*

Mohammad Mahdi Oraei Gholami, October 2013. [PDF [58]] [abstract [59]] [close [60]]Passive solar building design is the process of designing a building while considering sunlight exposure for receiving heat in winter and rejecting heat in summer. The main goal of a passive solar building design is to remove or reduce the need of mechanical and electrical systems for cooling and heating, and therefore saving energy costs and reducing environmental impact. This research will use evolutionary computation to design passive solar buildings. Evolutionary design is used in many research projects to build 3D models for structures automatically. In this research, we use a mixture of split grammar and string-rewriting for generating new 3D structures. To evaluate energy costs, the EnergyPlus system is used. This is a comprehensive building energy simulation system, which will be used alongside the genetic programming system. In addition, genetic programming will also consider other design and geometry characteristics of the building as search objectives, for example, window placement, building shape, size, and complexity. In passive solar designs, reducing energy that is needed for cooling and heating are two objectives of interest. Experiments show that smaller buildings with no windows and skylights are the most energy efficient models. Window heat gain is another objective used to encourage models to have windows. In addition, window and volume based objectives are tried. To examine the impact of environment on designs, experiments are run on five different geographic locations. Also, both single floor models and multi-floor models are examined in this research. According to the experiments, solutions from the experiments were consistent with respect to materials, sizes, and appearance, and satisfied problem constraints in all instances.

For reports released previous to 2013, please see the Archives [61]

*All papers are Copyright © of the respective authors.*