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

This paper presents an optimal design of a CMOS Low Noise Amplifier (LNA) implemented in the inductive source degeneration topology using Particle Swarm Optimization (PSO) technique. The optimized design has a substantially low noise figure with better forward gain. The proposed LNA is made to work at 2.4 GHz and is implemented in 0.18μm CMOS technology. It has a forward gain of 32 dB and a noise figure of 0.52 dB at 2.4 GHz.

Optimization of Low Noise Amplifier using Particle Swarm Optimization

The comparative optimizing efficiency of particle swarm optimization (PSO) and simplex particle swarm optimization (Simplex-PSO) method is explored in this work. A CMOS operational amplifier (Op-Amp) with low voltage has been optimized using this method. The concept of PSO is based on communal manner of bird flocking. PSO suffers from stagnation problem and premature convergence. Nelder–Mead simplex method (NMSM) is hybridized with PSO to produce simplex-PSO. Simplex-PSO is very fast and efficient optimization technique. Simplex-PSO gives high accuracy in terms of computational complexity. The main idea is to reduce the overall circuit’s area of low-voltage CMOS op-amp. PSO and simplex-PSO based optimized results are verified by SPICE. SPICE-based results demonstrate that the design and essential specifications are approximately reached. Simplex-PSO shows the better optimizing efficiency than PSO for the designed circuit.

Design of Low-Voltage CMOS Op-Amp Using Evolutionary Optimization Techniques

In this paper, the optimal thinning of two-ring Concentric Hexagonal Array (CHA) of uniformly excited isotropic antennas which can generate directive beam with minimum relative Side Lobe Level (SLL) is described. The Improved Particle Swarm Optimization (IPSO) method, which represents a new approach for optimization problems in electromagnetic, is used in the optimization process. To determine an optimal set of ‘ON-OFF’ elements that provide a radiation pattern with maximum SLL reduction, the IPSO algorithm is used. The simulation results show that the number of antenna array elements can be brought down more than 50% of total isotropic elements with simultaneous reduction in Side Lobe Level (SLL) with an approximately fixed first null beam width (FNBW). Particle Swarm Optimization (PSO), as well is also adopted to compare the results of above IPSO.

Application of improved Particle Swarm Optimization technique for thinning of concentric hexagonal array antenna

This article introduces an optimal design of finite impulse response-type Riesz fractional-order digital differentiator (FODD) of orders p = 0.3, 0.5, and 0.75. A very little study on Riesz-based differentiator has been reported so far. Moreover, none of the published Riesz FODD-based literature has studied the optimal design of Riesz FODD, which is explored in this article. In the reported literature, the Riesz FODD is realized by adopting conventional mathematical approaches, which are not efficient for the Riesz FODD-type design problem where the nature of the search landscape is multidimensional, multimodal, non-uniform, and nonlinear. To solve this problem, the design parameters of the proposed Riesz FODDs are estimated by using three independent metaheuristic optimization algorithms called salp swarm algorithm (SSA), gases Brownian motion optimization (GBMO), and gravitational search algorithm (GSA). In SSA, the adaptive variation of the iteration-dependent parameters helps the search agents not only to avoid the suboptimal solutions, but also ensures the faster convergence to reach the near-global optimal solution compared to GSA- and GBMO-based design approaches. The maximum phase error (MPE) and maximum absolute magnitude error (MAME) of the proposed SSA-based Riesz FODD are as low as 3.7119E−014 degree and − 9.6824 dB, respectively, for p = 0.3; 3.1523E−014 degree and − 15.6443 dB, respectively, for p = 0.5; and 3.5780E−014 degree and − 18.7525 dB, respectively, for p = 0.75. In terms of MPE and MAME, the proposed SSA-based Riesz FODD significantly outperforms the GSA- and GBMO-based Riesz FODD designs. The proposed SSA-based Riesz FODD of order p = 0.5 is also implemented on the TMS320C6713 digital signal processor, and its precise zero-phase performance is tested on real electrocardiogram (ECG) signal. Moreover, the proposed Riesz FODD is utilized in the ECG QRS complex identification system to demonstrate its real-time application.

Optimal design of zero-phase digital Riesz FIR fractional-order differentiator

The advent of dynamic CMOS logic, more precisely domino logic, made them widely used for the implementation of low power VLSI circuits. However, the main drawback of this logic is the non implementation of inverted logic. To implement the inverted logic, it is required to duplicate the logic circuit up to that part with inverted inputs. This obviously results the increase in area, delay as well as the power dissipation of the circuit. On the other hand, it is very simple to realize the circuit with both the inverted and non-inverted logic using static CMOS implementation. In this paper, this problem is addressed with the realization of the circuit which requires the implementation of inverted logic using mixed static and domino logic. To show the efficiency of the proposed model, a simple example like implementation of high fan-in NAND gate cascaded with AND gate is considered. With the comparison of all the three logics with a fixed fan-in of 7, 8 and 9 for both the gates, on an average 69.7% improvement is achieved in Power Delay Product (PDP), 11.4% improvement in area in terms of transistors using mixed logic implementation over static logic implementation and 68.64% improvement in PDP and 28.4% improvement in area over dynamic CMOS implementation when designed in 180nm technology.

Durbadal Mandal

Papers

Optimization of Low Noise Amplifier using Particle Swarm Optimization

Design of Low-Voltage CMOS Op-Amp Using Evolutionary Optimization Techniques

Application of improved Particle Swarm Optimization technique for thinning of concentric hexagonal array antenna

Optimal design of zero-phase digital Riesz FIR fractional-order differentiator

Low power VLSI circuit implementation using mixed static CMOS and domino logic with delay elements