Fractional dynamic fitness functions for GA-based circuit design

This paper is devoted to the synthesis of combinational logic circuits through computational intelligence or, more precisely, using evolutionary computation techniques. Are studied two evolutionary algorithms, the Genetic and the Memetic Algorithm (GAs, MAs) and one swarm intelligence algorithm, the Particle Swarm Optimization (PSO). GAs are optimization and search techniques based on the principles of genetics and natural selection. MAs are evolutionary algorithms that include a stage of individual optimization as part of its search strategy, being the individual optimization in the form of a local search. The PSO is a population-based search algorithm that starts with a population of random solutions called particles. This paper presents the results for digital circuits design using the three above algorithms. The results show the statistical characteristics of this algorithms with respect to the number of generations required to achieve the solutions. The article analyzes also a new fitness function that includes an error discontinuity measure, which demonstrated to improve significantly the performance of the algorithm.

An approach to the design of multilevel, multi-output combinational logic circuits in which all path delay faults are detectable by robust tests is proposed. Inadequacies of previous approaches for synthesis for testability of path delay faults are discussed. A necessary and sufficient condition for the existence of a hazard-free robust test for a path is stated. Violation of this condition is adopted as the criterion for identifying the paths, in a given circuit, which are not testable by hazard-free robust tests. Transformation methods to render these paths testable are proposed. >

This paper presents a virtual reconfigurable architecture (VRA)-based evolvable hardware for automatic synthesis of combinational logic circuits. The VRA processor is implemented on a Xilinx FPGA and works through two-stage evolutions: (1) finding a functional circuit, and (2) minimizing the number of gates used. To optimize the algorithm performance in the evolutionary process, a self-adaptive mutation rate control scheme is introduced. The efficiency of the proposed methodology is tested with the evolution of a 3-bit multiplier. The obtained results demonstrate that our approach improves the evolutionary design of electronic circuits in terms of quality of the evolved circuit as well as the computational effort.

Development and Research of Algorithms for the Synthesis of Combinational Logic Circuits Based on the Evolutionary Approach

We attempt to find mutation / crossover rate pairs that facilitate the performance of a genetic algorithm (GA) on a simple dynamic fitness function. This research results in two products. The first is a dynamic fitness function that is founded in previous analysis done on both static and dynamic landscapes, and that avoids problematic issues with previously proposed dynamic landscapes for GAs. The second is a general relationship between the crossover and mutation rates that are most useful for a dynamic fitness function with a specific rate of change in Hamming distance, and that could possibly provide insight into the utility of the standard GA approach for the optimization of dynamic landscapes.

Energy-efficient virtual machine placement in data centres via an accelerated Genetic Algorithm with improved fitness computation

The paper proposes a fast online learning method for neural network structures by using genetic algorithm (GA) and dynamic back propagation algorithm (BP) jointly. GA is used in the coarse tuning process which adjusts interconnection weights of the neural network. The dynamic back propagation algorithm is subsequently applied to achieve fine adjusting of the network weights. The fitness function, based on the squared error between the teaching signal and the network output value, is redefined at every time step and the proposed GA based algorithm solves a nonstationary function optimization task. At every time step the solution with the best fitness function is used for current representation of the neural network weights and biases. It is shown through the simulations and real time temperature control of drying oven that this learning algorithm has faster convergence ability and better performance on reducing mapping error in the online learning neural network structures. This leads to an improvement of the transient response of neuro adaptive systems. The proposed method has the potential to be applied to many practical areas such as system modeling and control, signal processing and pattern recognition.

SUMMARY The seismic waveform inversion problem is usually cast into the framework of Bayesian statistics in which prior information on the model parameters is combined with the data and physics of the forward problem to estimate the a posteriori probability density (PPD) in model space. The PPD is a function of an objective or fitness function computed from the observed and synthetic data. In general, the PPD or the fitness function is multimodal and its shape is unknown. Global optimization methods such as simulated annealing (SA) and genetic algorithms (GA) do not require that the shape of the fitness function be known. In this paper, we investigate GA to rapidly sample the most significant portion or portions of the PPD, when very little prior information is available. First, we use a simple three operator (selection, crossover and mutation) GA acting on a randomly chosen finite population of haploid binary coded models. We use plane wave transformed synthetic seismic data and a normalized cross-correlation function [E(m)] in the frequency domain as a fitness function. A moderate value of crossover probability, a low value of mutation probability, a high value of update probability and a proper population size are required to reach very close to the global maximum of the fitness function. Next, with an attempt to accelerate convergence we show that the concepts from simulated annealing can be used in stretching of the fitness function, i.e., we use exp [E(m)/T] rather than E(m) as the fitness function, where T is a control parameter analogous to temperature in simulated annealing. By a schemata analysis, we show that at low temperatures, schemata with above average fitness values are reproduced in large numbers causing a much more rapid convergence of the algorithm. A high value of temperature T assigns nearly equal selection probability to most of the schemata and thus retains diversity among the members of the population. Thus a GA with a step function type cooling schedule (very high temperature in the beginning followed by rapid cooling to a very low temperature) improves the performance dramatically: high values of the fitness function are obtained rapidly using only half as many models as would be required by a conventional GA. Similar performance could also be achieved by first using a high mutation probability and then decreasing the mutation probability to a very low value, while retaining the same low temperature throughout. We also address the problem of ‘genetic drift’ which causes the finite GAs to converge to one peak or the other when the algorithm is applied to a highly multimodal fitness function with several peaks of nearly the same height. A parallel genetic algorithm based on the concept of ‘punctuated equilibria’ is implemented to circumvent the problem. We run several GAs each with a finite subpopulation in parallel and collect many good models from each one of these runs. These are then used to grasp the most significant portion(s) of the PPD in model space. We then compute the weighted mean model and use the derived good models to estimate uncertainty in the derived model parameters.

In design systems for digital VLSI (very large integrated circuits), the BDD is used for VLSI verification, as well as for technologically independent optimization, performed as the first stage in the synthesis of logic circuits in various technological bases. BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph corresponds to the complete or reduced Shannon expansion formula. Having constructed BDD representation for systems of Boolean functions, it is possible to perform additional logical optimization based on the proposed method of searching for algebraic representations of cofactors (subfunctions) of the same BDD level in the form of a disjunction or conjunction of other cofactors of this BDD level. The method allows to reduce the number of literals by replacing the Shannon expansion formulas with simpler formulas that are disjunctions or conjunctions of cofactors, and to reduce the number of literals in specifying a system of Boolean functions. The number of literals in algebraic multilevel representations of systems of fully defined Boolean functions is the main optimization criterion in the synthesis of combinational circuits from library logic gates.

The main concern of all economic companies is the resources equipping and allocating them in different economic sectors with the aim of maximizing profit and minimizing risk. Decentralization is one of the important factors that reduce investment risk. The investors plan to create investment by carefully planning and collecting sufficient information on the economic situation and analyzing the situation of various industries. As an economic enterprise, banks are looking for short- and long-term investments in a types of loans ,such as bailment of a capital , civil participation, reward, etc, which guarantees the return of their capital. In this paper, considering the condition of a bank as an economic enterprise, a model is presented which not only increases profit but also reduces risk. Two objective functions have been defined that the first objective is to minimize the risk and the second objective function is to maximize the of the bank profit, which is used by robust programming and Malvi Sim model. In this paper, we have investigated the Risky and non-Risky Partfolio and the optimal portfolio of bank assets from scenario based solution of the model and by using PSO and Genetic Optimization Algorithm. At all levels of confidence and optimal values of risk based on the estimation of SPP-CVAR method by Particle Swarm Algorithm (PSA) is less than genetic algorithm, which indicates better performance of Particle Swarm Algorithm (PSA) than Genetic Algorithm (GA). Also, the optimum wealth obtained from PSA solution is higher at all levels of confidence than the corresponding value of Genetic Algorithm (GA), and this is another reason to confirm the performance of PSO algorithm compared to the Genetic Algorithm (GA). The values of the first goal function, obtained from the PSO algorithm, for all confidence levels are lower than those of the genetic algorithm. The optimum wealth obtained from PSA is higher than genetic algorithm. At 0.9 level, the value of LR of kupiec statistics for the SPP-CVAR method was less than the Chi-square statistics (Critical value) which was assumed to be acceptable.

Genetic Algorithm (GA) classifier can automatically search a proper clustering number according to fitness evaluation instead of assignment by users. In this study, a GA classifier with various fitness functions is adopted to search the cluster centers and a suitable cluster number for digital images to overcome the disadvantages of the conventional unsupervised classifier. By employing a proper clustering index as fitness, a GA with length-variable chromosome can determine the most suitable number of clusters and the most proper cluster centers.

In the present paper, optimization of functions with uncertainty by means of Genetic Algorithms (GA) is discussed. For such problems, there have been proposed methods of sampling fitness function several times and taking average of them for evaluation of each individual. However, important applications having uncertain fitness functions are online adaptation of real systems and complicated computer simulation using random variables. In such applications, possible number of fitness evaluation is quite limited. Hence, methods achieving optimization with less number of fitness evaluation is needed. In the present paper, the authors propose a GA for optimization of continuous fitness functions with observation noise utilizing history of search so as to reduce number of fitness evaluation. In the proposed method, value of fitness function at a novel search point is estimated not only by the sampled fitness value at that point but also by utilizing the fitness values of individuals stored in the history of search. Computer experiments using quadric fitness functions show that the proposed method outperforms the conventional GA of sampling fitness values several times at each search point in noisy environment.

In this study, the Genetic Algorithm (GA) was used to search the 4 modes filter frequencies to be applied to the multiple Positive Position Feedback (PPF) controller. The PPF technique, which makes use of generalized displacement measurements to maximize damping in a specific mode effectively and accomplish vibration suppression was employed as control scheme. However it is necessary to tune the filter frequency of the controller to the structural resonance prior to compensator design. Another disadvantage in the multi mode PPF control is that the lower mode natural frequency is shifted to the low-ward as the effect of the higher mode control by PPF controller. To minimize the effect of frequency shift and search the optimal filter frequencies for the multiple modes PPF controller, the GA was applied. The generally used fitness function of the GA in low modes PPF control, the square sum of sensor voltage output hardly distinguishes the definite difference in higher modes. Instead of it, in this study, the GA with the fitness function as the power spectrum information was performed. As a result of GA algorithm with this fitness function, the optimal filter frequencies of higher modes were found successfully.

The chapter covers two main areas, these being an introduction to the technology and techniques associated with genetic algorithms and then the second part looks at how genetic algorithms can be used to search for good topological solutions to engineering design challenges. The start of the chapter places genetic algorithms in context compared to other evolutionary algorithms and also describes the reasons why genetic algorithms are potentially useful. This is then followed by a look at the concept of a search space. Section two looks at the canonical genetic algorithm as a basic introduction to the technology and includes an examination of the main techniques used to encode the genome, fitness functions, operators and selection. Section three looks at how genetic algorithms can be used for design and chooses the specific example of the conceptual design of commercial office buildings. Section four introduces the basic concepts of topological search and explains how having the right form of representation is vital before looking at example relating to structural components and the design of domes using a genetic algorithm linked to computational geometry techniques. The final section then looks at further methods using generative representations and generative geometries as possible solutions to the need to develop powerful forms of representation for handling topological search in genetic algorithms.

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.