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

In this paper we propose a novel design of a low power static random access memory (SRAM) cell for high speed operations. The model adopts the voltage mode method for reducing the voltage swing during the write operation switching activity. Dynamic power dissipation increases when the operating frequency of the SRAM cell increases. In the proposed design we use two voltage sources connected with the Bit line and Bit bar line for reducing the voltage swing during the write “0” or write “1” operation. We use 90 nm CMOS technology with 1 volt of power supply. Simulation is done in Microwind 3.1 by using BSim4 model. Dynamic power for different frequencies is calculated. We compare it with conventional 6-T SRAM cell. The simulation results show that the power dissipation is almost constant even the frequency of the proposed SRAM model increases. This justifies the reduction of the dynamic power dissipation for high frequency CMOS VLSI design.

A low power CMOS voltage mode SRAM cell for high speed VLSI design

This paper presents an efficient approach to design wideband, accurate, stable, and minimum-phase fractional-order digital differentiators (FODDs) in terms of the infinite impulse response (IIR) filters using an evolutionary optimization technique called flower pollination algorithm (FPA). The efficiency comparisons of FPA with real-coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE)-based designs are conducted with respect to different magnitude and phase response error metrics, parametric and nonparametric statistical hypotheses tests, computational time, and fitness convergence. Exhaustive simulation results clearly demonstrate that FPA significantly outperforms RGA, PSO, and DE in attaining the best solution quality consistently. Extensive analysis is also conducted in order to determine the role of control parameters of FPA on the performance of the designed FODDs. The proposed FPA-based FODDs outperform all the designs published in the recent literature ...

Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

Steering the main beam of a time modulated antenna array (TMAA) with reduced side lobe level (SLL) is proposed in this paper. Linear antenna array of 16 and 18 isotropic elements are considered here with time modulation. Predefined switching scheme has been used to generate the desired radiation pattern at fundamental and multiple harmonic frequencies to achieve beam steering. A modified version of particle swarm optimization (PSO) with wavelet mutation is used to lower the overall side lobe level. Switching time sequences and inter element spacing between radiating elements are optimized to get the desired radiation pattern with minimal changes in first null beam width (FNBW).

Beam steering in a Time Switched Antenna Array with reduced Side Lobe Level using Evolutionary Optimization Technique

In this paper the authors propose the optimal radiation pattern synthesis of time modulated linear isotropic antenna array with improved directivity and maximum reduction of side lobe level (SLL) and minimum side band levels (SBL) at its harmonics based on evolutionary algorithms applied individually. Evolutionary algorithms are real coded genetic algorithm (RGA), particle swarm optimisation (PSO), novel particle swarm optimisation (NPSO), and the fourth dimension parameter as time. The same array radiates at various harmonic frequencies. The first two harmonic frequencies have been considered in this work. The objective function judiciously chosen enables comparative performance evaluation of the case studies. The numerical results show Case-4 outperforms Case-1, Case-2, and Case-3 with respect to better side lobe level and more improved directivity. Again, the performance of NPSOWM is the best among RGA, PSO, and NPSO for all the case studies. The numerical results also show power radiated by any harmon...

Improvement in various radiation characteristics of time modulated linear antenna arrays using evolutionary algorithms

In this paper time modulation technique is implied to linear antenna array. The evolutionary optimization algorithm like real coded genetic algorithm (RGA) and particle swarm optimization (PSO) is used to get the optimal radiation pattern by controlling the switching time sequence of each element of the array. The time modulation period is divided into numerous minimal time steps, where the ON-OFF status for each time step is optimized by evolutionary algorithms. The side lobe level of time modulated linear antenna arrays can be reduced significantly by optimal switching time sequence of each element. The approach is illustrated through 16 element time modulated linear antenna arrays. Various results are presented to show the advantages of this approach considering maximal side lobe level reduction.

Durbadal Mandal

Papers

A low power CMOS voltage mode SRAM cell for high speed VLSI design

Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

Beam steering in a Time Switched Antenna Array with reduced Side Lobe Level using Evolutionary Optimization Technique

Improvement in various radiation characteristics of time modulated linear antenna arrays using evolutionary algorithms

Synthesis of time modulated linear antenna arrays using particle swarm optimization