This paper deals with a new approach for solving fuzzy differential equations based on genetic programming. This method produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Furthermore, the numerical results reveal the potential of the proposed appr...

Differential evolution (DE) algorithms have been extensively and frequently applied to solve optimizationproblems. Theoretical analyses of their properties are important to understand the underlying mechanismsand to develop more efficient algorithms. In this paper, firstly, we introduce an absorbing Markovsequence to model a DE algorithm. Secondly, we propose and prove two theorems that provide...

In this paper, we present a new method for the design of multi-band microstrip filters. The proposed design method is based on Differential Evolution (DE) with strategy adaptation. This selfadaptive DE (SaDE) uses previous experience in both trial vector generation strategies and control parameter tuning. We apply this algorithm to two design cases of dual and tri-band filters for WiFi and WiMa...

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as Multi-objective Optimization Problems (MOPs)) has attracted much attention recently. Being population based approaches, EAs offer a means to find a group of pareto-optimal solutions in a single run. Differential Evolution (DE) is an EA that was developed to handle optimization problems over continuous ...

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map a...

This paper is the text of a talk given by the second author at the Chern Conference. Intended for a general audience, it is based on joint work in progress with Mark Green. The purposes of the talk were (i) to discuss Abel’s differential equations (DE’s) for algebraic curves in both classical and modern form, (ii) to explain in a special case the extension of Abel’s DE’s to general algebraic va...

In this paper, an adaptive membrane evolutionary algorithm (AMEA) is proposed, which combines a dynamic membrane structure and a differential evolution with the adaptive mutation factor. In the AMEA, the feasibility proportion method is used to dynamically adjust the size of the elementary membrane in the optimization process. The results of the experimental indicate that the proposed algorithm...

We use very deep (Rlim=27) UnGRI imaging to study the evolution of the faint end of the UV-selected galaxy luminosity function from z∼4 to z∼2. We find that the luminosity function evolves with time and that this evolution is differential with luminosity: the number of sub-L galaxies increases from z∼4 to z∼3 by at least a factor of 2.3, while the bright end of the LF remains unchanged. Potenti...