Cecília Reis

Some Applications of Fractional Calculus in Engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Interactive Evolutionary Computation in music

This paper presents a simple approach for implementing Interactive Evolutionary Computation (IEC) - a paradigm in which humans directly intervene in fitness evaluation - in the field of musical melody generation. Music is an art and, as all kinds of art, it involves creativity. However, creativity is still a human capability. A Genetic Algorithm (GA) based application has been developed and tested. The initial population was generated according to Zipfs Law. Simple melodies, obtained in a few iterations, can be quickly transformed into complete and interesting songs.

Computational Intelligence in Circuit Synthesis

This paper is devoted to the synthesis of combinational logic circuits through computational intelligence or, more precisely, using evolutionary computation techniques. Are studied two evolution- ary algorithms, the Genetic and the Memetic Algo- rithm (GAs, MAs) and one swarm intelligence algo- rithm, 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 indi- vidual optimization as part of its search strategy, be- ing the individual optimization in the form of a local search. The PSO is a population-based search algo- rithm that starts with a population of random solu- tions called particles. This paper presents the results for digital circuits design using the three above algo- rithms. The results show the statistical characteristics of this algorithms with respect to the number of gen- erations required to achieve the solutions. The article analyzes also a new fitness function that includes an er- ror discontinuity measure, which demonstrated to im- prove significantly the performance of the algorithm.

Application of Fractional Calculus in Engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Evolutionary computation in the design of logic circuits

This paper presents two evolutionary schemes and a swarm intelligence algorithm for the design of combinational logic circuits. A genetic and a memetic schemes as the evolutionary algorithms. The particle swarm optimization as the swarm algorithm. The fitness function used in these three algorithms is sequential, that is, divided in two parts. The first part of the fitness function f1 evaluates the circuit functionality, while the second part f2 deals with the circuit complexity. The experiments consist in applying the algorithms in the design of two arithmetic circuits: the one-bit full adder and the one-bit full subtracter. We also present a scalability analysis using the parity checker family of circuits.

Fractional dynamic fitness functions for GA-based circuit design

This paper proposes and analyses the performance of a Genetic Algorithm (GA) using two new concepts, namely a static fitness function including a discontinuity measure and a fractional-order dynamic fitness function. The GA is adopted for the synthesis of combinational logic circuits. In both cases, experiments reveal superior results in terms of speed and convergence to achieve a solution.

Computational Intelligence and Decision Making

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Music and Evolutionary Computation

This paper presents a brief history of the western music: from its genesis to serialism and the Darmstadt school. Also some mathematical aspects of music are then presented and confronted with music as a form of art. The question is, are these two distinct aspects compatible? Can computers be of real help in automatic composition? The more appealing algorithmic approach is evolutionary computation as it offers creativity potential. Therefore, the Evolutionary Algorithms are then introduced and some results of GAs and GPs application to music generation are analysed.

Application of Computational Intelligence to Engineering

Computational Intelligence (CI) includes four main areas: Evolutionary Computation (genetic algorithms and genetic programming), Swarm Intelligence, Fuzzy Systems and Neural Networks. This article shows how CI techniques overpass the strict limits of Artificial Intelligence field and can help solving real problems from distinct engineering areas: Mechanical, Computer Science and Electrical Engineering.

Fitness Function Evaluation Through Fractional Algorithms

This paper proposes a Genetic Algorithm (GA) for the design of combinational logic circuits. The fitness function evaluation is calculated using Fractional Calculus. This approach extends the classical fitness function by including a fractional-order dynamical evaluation. The experiments reveal superior results when comparing with the classical method.