Radomil Matousek

Promising GAHC and HC12 algorithms in global optimization tasks

This paper deals with a new stochastic heuristic searching algorithm inspired by the fundamental biological principles of survival. It presents a very promising version of a commonly known genetic algorithm denoted as GAHC and an algorithm denoted as HC12. Global optimization properties of these algorithms are illustrated with several nonlinear optimization problems. These problems are also solved by sophisticated solvers in general algebraic modelling system to increase objectivity and to compare different methods. Presented optimization algorithms are implemented in our own optimization toolbox GATE in Matlab environment.

GAHC: Improved Genetic Algorithm

This paper introduces a novel improved evolutionary algorithm, which combines genetic algorithms and hill climbing. Genetic Algorithms (GA) belong to a class of well established optimization meta-heuristics and their behavior are studied and analyzed in great detail. Various modifications were proposed by different researchers, for example modifications to the mutation operator. These modifications usually change the overall behavior of the algorithm. This paper presents a binary GA with a modified mutation operator, which is based on the well-known Hill Climbing Algorithm (HCA). The resulting algorithm, referred to as GAHC, also uses an elite tournament selection operator. This selection operator preserves the best individual from the GA population during the selection process while maintaining the positive characteristics of the standard tournament selection. This paper discusses the GAHC algorithm and compares its performance with standard GA.

Genetic Algorithm and Advanced Tournament Selection Concept

Genetic Algorithms (GA) are a common probabilistic optimization method based on the model of natural evolution. One important operator in these algorithms is the selection. Some works has been done to classify the different selection schemes as roulette wheel selection, tournament selection etc. An enhanced version of tournament selection named elite tournament selection is introduced in this paper. This novel selection method solves probably the only one disadvantage of the standard tournament selection, which is that it does not guarantee reproduction of the best solution. In the part of this paper probability equations for the tournament and elite tournament selection are defined. On this base we derive further conclusions. The binomial distribution and convolution are used for mathematical description. Theoretical calculations are verified by means of real experiments.

Transplant Evolution for Optimization of General Controllers

This paper describes a new method of evolution that is named Transplant Evolution (TE). None of the individuals of the transplant evolution contains genotype. Each individual of the transplant evolution contains only phenotype. Reproduction methods as crossover and mutation work and store only the phenotype. The hierarchical structure of grammar-differential evolution that is used for finding optimal structures and parameters of general controllers is described.

A Note about Robust Stabilization of Chaotic Hénon System Using Grammatical Evolution

The paper deals with robust stabilization of a well-known deterministic discrete chaotic system denoted as Henon map. By means of proper utilization of metaheuristic optimization tool, the Grammatical Evolution (GE) can synthesise a new robust control law. As a model of deterministic chaotic system the two-dimensional Henon map with original definition was used. The Henon map is an iterated discrete-time system which exhibits chaotic behaviour in two-dimension. Stabilization for the period-2 orbits of the two-dimensional Henon map is presented. The chaotic system stabilization is based on a time-delay auto-synchronization with its own synthesized control law. This synthesized chaotic controller utilizes own design of advanced GE algorithm with two-level optimization procedures and a proper objective function. The original objective function design considers a low sensitivity dependence on initial conditions and also proper time for stabilisation of the control process. All computing experiments are performed using Matlab/Simulink environment where the double precision floating point arithmetic was used.

Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution

The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors.

GA with fuzzy inference system

Applications of genetic algorithms (GA) for optimisation problems are widely known as well as their advantages and disadvantages compared with classical numerical methods. In practical tests, GA appears a robust method with a broad range of applications. The determination of GA parameters could be complicated. Therefore for some real-life applications, several empirical observations of an experienced expert are needed to define these parameters. This fact degrades the applicability of a GA for most of the real-world problems and users. Therefore, this article discusses some possibilities with setting GA parameters. The setting method of GA parameters is based on the fuzzy control of values of GA parameters. The feedback for the fuzzy control of GA parameters is realized by virtue of the behavior of some GA characteristics. The goal of this article is to present the conception of the solution and some new ideas.

Nilpotent approximation of a trident snake robot controlling distribution

We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with respect to the given filtration. Note that all constructions are local in the neighbourhood of a particular point. We compare the motions corresponding to the Lie bracket of the original controlling vector fields and their nilpotent approximation.

Trident Snake Control Based on Conformal Geometric Algebra

Local controllability of a trident snake robot is solved by means of 5D conformal geometric algebra. The non–holonomic kinematic equations are assembled, their property to be a Pfaff system is discussed and the solution is found. The functionality is demonstrated on a virtual model in CLUCalc programme.

Combined Heuristic Approach to Resource-Constrained Project Scheduling Problem

This chapter deals with the resource-constrained project scheduling problem that belongs to NP-hard optimisation problems. There are many different heuristic strategies how to shift activities in time when resource requirements exceed their available amounts. We propose a transformation of the problem to a sequence of simpler instances of (multi)knapsack problems that do not use traditionally predefined activity priorities and enable to maximise limited resources in all time intervals given by start or end of an activity and therefore to reduce the total time.