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 alternative approach for the design of linear phase digital high pass FIR filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA). FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, PSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency characteristic. In this paper, for the given problem, the realization of the optimal FIR high pass filters of different orders has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithm such as genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Linear phase FIR high pass filter design using PSO-CFIWA with least square approach

Attainment of global optimal solution and reduction of computational time and resources have always been a trade off issue in formulation of nature inspired algorithms, this trade off challenge has brought in a deluge of new algorithms proposing their efficacy over one another. Particle swarm optimization (PSO) algorithm and its variants are quite popular in optimizing antenna designs particularly due to their algorithmic simplicity and fast convergence rates. However, as a matter of the ever present trade off, fast convergence often leads to sub optimal solutions. In some recent researches it has been shown that a class of boundary handling algorithms of PSO, known as position regulated boundary conditions (PRBCs), can minimize the trade off between fast convergence and accomplishment of global optimal solution, here, the performance of these boundary algorithms are compared with that of other established ones over three different optimization targets of antenna design namely, "Multi target optimization in linear antenna arrays", "Inset feed position optimization of rectangular patch antennas" and "Edge feed position optimization of rectangular patch antennas". Results show that the use of PRBCs in PSO leads to impressive improvement in the optimization efficiency in terms of lesser computational time and attainment of global optimal solution.

Role of Boundary Dynamics in Improving Efficiency of Particle Swarm Optimization on Antenna Problems

This paper presents an efficient approach for the optimal designs of two analog circuits, namely complementary metal oxide semiconductor two-stage comparator with p-channel metal oxide semiconductor input driver and n-channel input and folded-cascode operational amplifier using a recently proposed meta-heuristic-based optimization algorithm named as colliding bodies optimization CBO. It is a multi-agent algorithm that does not depend upon any internal control parameter, making the algorithm extremely simple. The main objective of this paper is to optimize the metal oxide semiconductor MOS transistors' sizes using CBO in order to reduce the areas occupied by the circuits and to get better performance parameters of the circuits. Simulation Program with Integrated Circuit Emphasis simulation has been carried out by using the optimal values of MOS transistors' sizes and other design parameters to validate that CBO-based design is satisfying the desired specifications. Simulation results demonstrate that the design specifications are closely met and the required functionalities are achieved. The simulation results also confirm that the CBO-based approach is superior to the other algorithms in terms of MOS area and performance parameters like gain, power dissipation, etc., for the examples considered. Copyright © 2016 John Wiley & Sons, Ltd.

Soft computing-based approach for optimal design of on-chip comparator and folded-cascode op-amp using colliding bodies optimization

In this paper, a hybrid meta-heuristic search algorithm is proposed with the combination of harmony search (HS) algorithm and differential evolution (DE) algorithm, which is named as HS-DE. HS is an optimization method mimicking the music improvisation process where musicians invent their instruments' pitches searching for a perfect state of harmony. DE is a stochastic and population-based heuristic approach having the capability to solve global optimization problems. The main idea is to hybrid together the fine tuning capability of DE with the ability of exploration in HS to get better near-global solution by utilizing both algorithms' strengths. Here, HS-DE is used for optimal symmetric switching characterization of CMOS inverter. The performance of HS-DE is compared with conventional particle swarm optimization reported in the recent literature. HS-DE-based design results are also compared with the PSPICE results. Extensive simulation results justify superior optimization capability of HS-DE over the afore-mentioned optimization technique for the examples considered and can be efficiently used for optimal CMOS inverter design.

Optimal design of high speed symmetric switching CMOS inverter using hybrid harmony search with differential evolution

In this paper, optimal design of single-ring and multi-ring circular array, hexagonal array, and elliptical array of isotropic antenna has been carried out using Simplex Particle Swarm Opti...

Durbadal Mandal

Papers

Linear phase FIR high pass filter design using PSO-CFIWA with least square approach

Role of Boundary Dynamics in Improving Efficiency of Particle Swarm Optimization on Antenna Problems

Soft computing-based approach for optimal design of on-chip comparator and folded-cascode op-amp using colliding bodies optimization

Optimal design of high speed symmetric switching CMOS inverter using hybrid harmony search with differential evolution

Optimal Design of Single and Multi-ring Planar Array Antenna Using Simplex-PSO