There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Tables of integrals

Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms.

/pdf/a-comprehensive-survey-on-particle-swarm-optimization-1d380v5xx1.pdf

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

In nature, the eastern North American monarch population is known for its southward migration during the late summer/autumn from the northern USA and southern Canada to Mexico, covering thousands of miles. By simplifying and idealizing the migration of monarch butterflies, a new kind of nature-inspired metaheuristic algorithm, called monarch butterfly optimization (MBO), a first of its kind, is proposed in this paper. In MBO, all the monarch butterfly individuals are located in two distinct lands, viz. southern Canada and the northern USA (Land 1) and Mexico (Land 2). Accordingly, the positions of the monarch butterflies are updated in two ways. Firstly, the offsprings are generated (position updating) by migration operator, which can be adjusted by the migration ratio. It is followed by tuning the positions for other butterflies by means of butterfly adjusting operator. In order to keep the population unchanged and minimize fitness evaluations, the sum of the newly generated butterflies in these two ways remains equal to the original population. In order to demonstrate the superior performance of the MBO algorithm, a comparative study with five other metaheuristic algorithms through thirty-eight benchmark problems is carried out. The results clearly exhibit the capability of the MBO method toward finding the enhanced function values on most of the benchmark problems with respect to the other five algorithms. Note that the source codes of the proposed MBO algorithm are publicly available at GitHub (
 https://github.com/ggw0122/Monarch-Butterfly-Optimization
 , C++/MATLAB) and MATLAB Central (
 http://www.mathworks.com/matlabcentral/fileexchange/50828-monarch-butterfly-optimization
 , MATLAB).

Monarch butterfly optimization

Pattern synthesis of timed antenna array with the exploitation and suppression of harmonic radiation

This paper presents an efficient method to improve the far-field radiation pattern of concentric circular antenna array (CCAA) design using two stochastic optimization algorithms known as social sp...

Side Lobe Suppression of Concentric Circular Antenna Array Using Social Spider Algorithm

Research on the construction of teaching platform of drama film and television literature based on IoT

EEG/ERP signal enhancement through an optimally tuned adaptive filter based on marine predators algorithm

A precise control in the stopband attenuation characteristics can be achieved by using the fractional-step filters instead of the traditional integer-order filters. In this paper, nine nature-inspired optimization algorithms, such as five advanced variants of differential evolution (DE), three advanced variants of particle swarm optimization (PSO), and an efficient evolutionary strategy method (CMA-ES-RIS) are employed to design the fractional-step low pass Butterworth filter (FLBF). The proposed ( 1 + α ) and ( 2 + α ) order models, where α ∈ ( 0 ,  ​ 1 ) , are optimally approximated as an integer-order transfer function by using the magnitude-frequency information of the ideal FLBF. Comparisons regarding the solution quality and robustness reveal an improved accuracy for the DE variants and CMA-ES-RIS over all the PSO variants. Results from the pair-wise Wilcoxon rank-sum test demonstrate the superiority of enhanced fitness-adaptive differential evolution (EFADE) algorithm as the most efficient optimization tool for solving this problem. Comparisons with the state-of-the-art approaches also confirm the superior modelling accuracy of the proposed FLBFs. The canonical structure circuit realization of the FLBFs using current feedback operational amplifiers is presented. Simulations carried out in OrCAD PSPICE platform suggest proximity in the magnitude responses between the proposed and the theoretical models. The optimal design of stable, minimum-phase ( 2 + α ) order FLBFs is also presented for the first time without employing the cascading concept involving the integer-order Butterworth polynomials.

Durbadal Mandal

Papers

Pattern synthesis of timed antenna array with the exploitation and suppression of harmonic radiation

Side Lobe Suppression of Concentric Circular Antenna Array Using Social Spider Algorithm

Research on the construction of teaching platform of drama film and television literature based on IoT

EEG/ERP signal enhancement through an optimally tuned adaptive filter based on marine predators algorithm

Comparative study of nature-inspired algorithms to design (1+α) and (2+α)-order filters using a frequency-domain approach