Rudolf Neydorf

Monochrome Multitone Image Approximation on Lowered Dimension Palette with Sub-optimization Method Based on Genetic Algorithm

The problem of sub-optimum approximation of monochrome multitone images (MMI) by a palette with reduced amount of tones, called support palette (SP), is solved. The SP palette tones are defined with the images analysis, which arise in related scientific topics as: technical sight, recognition of images, etc. In this work the research objective was to assess the opportunity of using efficiently such analysis, by applying the genetic algorithms (GA) for sub-optimum approximation of MMI, considering the original big size tones palette [1]. The proposed approximation consists in replacing the original MMI pixels with the approximated pixels from a smaller size tone palette. This procedure is of importance in the synthetic vision approach, where image recognition procedures are expected to define the main contours within the image. The developed method reduces the amount of tones used to display an image, whose approximation approach is presented in this paper. In order to solve it, two alternative problems are considered: (1) minimization of losses in such image transformation, and (2) minimization of the SP size (for example, to simplify the image recognition process). The approximated MMI quality is defined as the mean square deviation of pixels brightness (original to approximated). The chromosome in GA is SP, where tones are represented as genes. Such approximations are resulting from the mutational variation of the MMI palette tones, within gene alleles, which are formed by applying the original palette tones. The palette is iteratively changing from generation to generation, where the reduction of the stop risks is done on the local extremum. This fact increases the available search opportunities, as provided by the multi-point crossing-over algorithm, whose parameters are able to mutate during such an evolution process. In addition, to demonstrate the result of this work, an appropriate software has been developed, having an easy-to-use user interface, enabling to show the highly efficient processing of the investigated algorithm. The presented solutions are validated with photo examples of several technical objects, on which the sub-optimum method has been applied.

Robot Path Planning Based on Ant Colony Optimization Algorithm for Environments with Obstacles

In modern industrial processes, robotic equipment is widely used, and one of the most pressing problems is to have to have navigation available for mobile robots. In this paper, the ant algorithm for laying and optimizing the robots paths in 2-dimensional environments with obstacles, is described and shown on construction site examples. The most important requirement is to be able to plan the shortest or permissible robot navigation route in such a complex environment with obstacles. It is well known that one of the most effective solutions to resolve such optimization problems of route seals is provided by the ant colony optimization (ACO) algorithm. The exploratory nature of the ant colony behaviour requires a classical partition of the search space, which is incomparably smaller, when compared to the obstacles fragments, as considered within this paper. The ant’s agents use the traditional logic of selecting the transition from fragment to fragment: the memory of the most popular routes based on pheromone are investigated, and formulated within the task elements, adopting appropriate tactics and situational awareness, and based on the random decisions. In addition, the new elements of the decision-making tactics are formulated for each task. For example, “feeling” of targeted routes by laying points is added to the algorithm. The natural analogue of this mechanism is similar to sensing the odors by the mustaches of real ants. The special software tool “Path Planning Optimization with Obstacle Avoidances by Ant Algorithm” is designed as the research test bed. A comprehensive study of the proposed algorithm, which shows superior performance, is done by utilizing the developed software. The examples, of the construction site with different complexity, are provided to explain the finding of the suboptimal routes for the specially designed test tracks, with defined obstacles in the simulated construction site landscape. The analysis of the results confirms the relevance and effectiveness of the developed software, which is based on the ant algorithm for the robot path planning, and validated for the environments containing complex obstacles.

Monochrome multitone image approximation with low-dimensional palette

The report is devoted to the problem of suboptimal approximation of monochrome multitone image. The proposed approximation consists in replacing the original image tone palette with a reduced size tone palette. The suboptimum approximation is based on the evolutionarily genetic algorithm. The algorithm provides the suboptimal selection of tones for the new palette and its covering range. The weight-dividing strategy of the original monochrome multitone images frequency diagram of brightness is used to define the initial tones of the new palette and its covering range. These numerical vectors, considered as chromosomes, define the approximated image created by 2 respective chromosomes. The standard genetic operators of mutation is crossed over with the selection strategy, which provides an effective approximation optimization according to the criteria of the least square deviation between pixels of their original tones, when related to the new palette tones. The developed algorithm can be applied to the wide class of problems. Examples are the pattern recognition tasks, image defects detection, and image transformation, for printing equipment. The report illustrates the image approximation of the “on board electronic circuit” with the sub-optimization of the specific algorithm probabilistic parameters.

“Cut-Glue” Approximation Method for Strongly Nonlinear and Multidimensional Object Dependencies Modeling

The main difficulties in modeling a variety of technical systems are experienced when creating appropriate mathematical objects to simulate their behavior. It is well known that such inter-objects dependences are defined with their variable with strong nonlinear and multidimensional characteristics. The mathematical models (MM) dependences are approximated with advance numerical methods, such as polynomial decomposition, spline functions, etc., which are today still very time-consuming and laborious to be correctly created and applied, also considering their precision. In this paper, the authors have created and investigated the high-precision analytical approximation method to model the nonlinear MM dependences, which are defined only by appropriate analytical functions. These approaches have been already studied in details, where the Cut-Glue approximation method defines 1-dimensional dependences, and to 2-dimensional dependences were approximated with analytical functions of 2 arguments. The important advantage of the Cut-Glue method is that it well approximates the differentiability of the proposed MM dependencies, as its enables to investigate analytically the related modeling functions and thus, use them efficiently in applying MM in dynamical systems simulations. In this work, the Cut-Glue method has been further developed: (1) to prove its applicability by creating nonlinear models of any dimension, (2) to analyze its performance at all the stages, in which the “Cut-Glue” approximation is applied, and (3) to implement this formal algorithm, which allows numerical verification and validation of its applicability. The considered optimization criteria for both respective issues, accuracy and complexity, have been applied to the investigated MM-s. The proposed method is formalized by the optimal splitting of its experimental dependence into separate parts, which are then numerically defined and implemented within the proposed software, developed in this work. In this paper, the different possibilities of applying the optimal multidimensional “Cut-Glue” approximation method are illustrated by examples. The achieved results represent a strong base to significantly expand the proposed method applicability, and further on, they indicate potential opportunities to improve the existing solutions. Especially, when solving a variety of problems, which requires mathematical modeling of any type of technical objects, to simulate overall systems dynamics.

“Cut-Glue” Approximation Based on Particle Swarm Sub-optimization for Strongly Nonlinear Parametric Dependencies of Mathematical Models

The difficulties in the experimental and computer modeling of the static and dynamic transport media are associated with a significant non-linearity of the present model dependencies. This is due to the mechanical friction effects, backlash, aerodynamic effects and other physical phenomena. The construction of the mathematical models (MM) for such objects is most often associated with the mathematical treatment of the experimental data. The point-like dependencies of the output variables linked to the input are essentially non-linear, piecewise and sometimes discontinuous. These dependencies, when approximated with polynomial or spline functions, are difficult to control, and thus associated with large errors. The radically new solution to this problem is proposed in paper [1]. This method is called the «cut-glue» approximation (CGA) method. It is based on partitioning the simulated dependence within specified areas; approximating each fragment with the polynomial dependencies; multiplicative “cutting” for each dependence is the fragments along border area; the additive “gluing” of these fragments is grouped into a single function, as the approximated dependence model. The analytical characteristics of this approximating “gluing” function is the main feature and advantage, properties of functions allow to analyze analytically the model and its application for simulating the dynamic models of the transport media. For a broad CGA method introduction in the experimental modeling research practice, it is necessary to develop, justify and explore the local methodologies implementation of these stages. One of the CGA stage is the “glue” process, when the additive fragments are “glued” into a single function. The auxiliary multiplicative allocation function (MAF) is used for that. The MAF structure includes the edge steepness parameter—e. In this paper, the algorithm is developed based on the modification of the particle swarm optimization (PSO) method, which is used in this research, together with the sub-optimization e parameter. The hybrid PSO method smoothly includes the basic prototype of the fundamental equations defining the mechanic laws, gravitation and the stochastic “blurring” movement parameters. The developed special software tool, as a research test bed, for conducting the numerical experiments is illustrated in this paper.

“Cut-Glue” Approximation Based on Pseudo-genetic Algorithm for Strongly Nonlinear Parametric Dependencies of Mathematical Models

In the present work we consider one of the basic methods of Cut-Glue approximation—the approximation method for fragments with essentially nonlinear dependencies. As an instrument of approximation, a hybrid application of the classical regression analysis is used and specially developed for the evolutionarily modified genetic algorithm. The proposed approach allows finding the optimal dependence of the specified fragment.

Universal generator of irregular multidimensional multiextremal functions

The paper describes the development of a universal test functions generator to validate and setup the algorithms for investigating multiextremal systems characteristics. The main difference between the proposed functions and the set of known multiextremal test functions is their irregularity related to the extremes coordinate location and their respective quantitative values, since all known test functions are based on the analytical functions. The functionality of the developed “Lambda Function” software is described in details to validate such approach, supporting the test functions controlled generation, their editing and studying the multi-dimensional, multi-extremal test functions characteristics. Its fundamental novelty is that these functions are based on the multiplicative functions, developed by R. Neudorf, which extreme and multidimensionality characteristics enable to completely exclude the influence of their structure patterns when the results are computed. The “Lambda Function” software provides a wide range of possibilities to develop and investigate the test functions being created. Such results can be applied in variety of research domains, and the developed software can be easily integrated with third-party software, based on its extensive modular design.

A high-speed hybrid algorithm of monochrome multitone images approximation

The paper considers the problem of increasing the speed of monochrome multitone image (MMI) approximation, which consists in replacement of original palette with palette that has less number of tones. Often, for solving such a problem, the heuristic optimization-search algorithms are used. Their drawback is that, they cannot guarantee to find the solution for the given optimization criteria, which motivates to find the approximating palette of the potential extreme. The solution of this problem is to define the deterministic algorithm, that guarantees finding the extreme, through the integration with the heuristic algorithm. Such hybridization takes in consideration the main advantage of these 2 approaches: (1) speed of the heuristic algorithm and (2) accuracy of the deterministic one. The hybrid algorithm applies the heuristic approach to decrease the search area and the deterministic approach guarantees to find extremes within this area. This approach defines the time, as the optimization criteria for the algorithm processing speed. Thus, the proposed hybridization enables to find the bi-optimal solution for the defined MMI approximation problem that provides both, the optimal quality of approximation within the available time frame.