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.

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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

This paper presents an efficient approach to design digital Fractional-Order Integrators (FOIs) exhibiting an accurate magnitude response by employing a metaheuristic algorithm called Improved Particle Swarm Optimisation (IPSO). The proposed infinite impulse response (IIR) filter type IPSO-based digital FOIs have been judged against the Real-coded Genetic Algorithm, Particle Swarm Optimisation (PSO), and Differential Evolution -based digital FOIs with respect to various performance metrics. The superior performance of the IPSO-based designs is also emphasised using different statistical indices. Parametric and non-parametric statistical hypothesis tests demonstrate the reliable performance of IPSO-based designs. MATLAB simulation results confirm the accurate magnitude response of the proposed digital FOIs as compared with the published literature.

Optimal design of IIR digital FOI using IPSO

A single expression of directivity for arbitrary planar antenna array is derived in closed form. Element Pattern in the array is taken as sinμθcosυθ, {μ > -1, θ > - 1/2;}. Other parameters of this expression are location, excitation amplitude and phase of each element. The expression is derived from the definition of Directivity. As this work does not assume any special lattice of array and aperture distribution, performance of this expression is not limited by these parameters. Simplicity and compactness of this expression saves the runtime, memory requirement and any extra software costs. More, as each element pattern is periodic with Θ and if the Fourier series coefficients of the element pattern are known, the same expression is useful to calculate the radiated power even for real elements. Examples of directivity show exact match between directivity results obtained by the derived analytical expression and numerical method. Simpson's 1 / 3 rd rule is the numerical method utilized for numerical estimation of directivity.

A generalized expression of directivity for planar antenna arrays

Through detailed quantum calculations, the presence of classical discrete breathers and, subsequently, a two-phonon bound state (TPBS) or quantum breather (QB) state have already been shown in nonlinear photonic materials such as ferroelectrics. The latter was done in a periodic boundary condition in terms of the variations of TPBS parameters against impurity that is related to nonlinearity. Metamaterials are also nonlinear optical materials for applications as a split-ring-resonator (SRR) in antenna arrays. By using a Klein–Gordon approach, first multi-solitons and classical breathers are shown. For QBs, by using a periodic boundary condition, the variation of the TPBS parameters with coupling within the SRR elements is observed. Finally, in a non-periodic boundary condition approach, the temporal evolution of the number of quanta is shown eventually in order to derive the critical time of redistribution of quanta that is proportional to the QB's lifetime in femtoseconds, which also shows variation with coupling in the SRR system.

Role of coupling of discrete breathers in split-ring-resonator-based metamaterials

A low power 9T SRAM architecture for both active and passive (sleep) modes has been suggested in the present paper. The design contains voltage source which is connected to the output nodes of the cell. At the time of switching these sources minimizes the required swing voltage. This minimization of swing voltage reduces the dynamic (active) power utilization. To reduce the subthreshold current in passive mode a sleep transistor attached to the ground path. This sleep transistor produces the stack effect and minimizes the static power consumption. 45nm CMOS libraries are used for simulation.

Durbadal Mandal

Papers

Optimal design of IIR digital FOI using IPSO

A generalized expression of directivity for planar antenna arrays

Role of coupling of discrete breathers in split-ring-resonator-based metamaterials

A Low Power 9T SRAM Cell Design for both Active and Passive Mode

Distribution of soil carbon fractions under different bamboo species in northwest Himalayan foothills, India