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

An efficient electronic beam steering method in timed antenna array is proposed in this paper by controlling only the high-speed switches connected with the radiating elements of the array. The timed antenna arrays have an extra dimension—‘time’ to control the array radiation pattern compared to traditional antenna arrays. The simple on–off sequence of these arrays inherently generates undesired harmonic patterns along with the desired pattern. These unwanted and spatially individual patterns generated at lower-order harmonic frequencies are exploited in this paper with appropriate on–off sequence to generate multiple steered patterns toward preselected directions. The sidelobes of all the desired patterns are reduced, and the unwanted harmonics are suppressed. To achieve the desired objectives, unique pulse-shifted on–off sequences are derived with a modified differential evolution algorithm by implementing an efficient wavelet-based mutation operation. A linear arrangement of timed array with ten isotropic elements is considered to exhibit the potentialities of the proposed approach.

Electronic Beam Steering in Timed Antenna Array by Controlling the Harmonic Patterns with Optimally Derived Pulse-Shifted Switching Sequence

Optimal design of complementary metal-oxide-semiconductor analogue circuits: An evolutionary approach

Circular Array is one of the most widely used antenna array designs. Its applications include radio direction finding, air and space navigation, underground propagation, radar, sonar, and many other applications. A broadside uniform circular array radiates (receives) not only in the broadside direction, but, in the other directions as well. Such an array has a significant power loss due to along resting plane scanning property. The power radiation or reception pattern of a circular array is dependent on the linear distance between two consecutive elements, the radius, and the number of elements. This paper aims to reduce the along resting plane scanning by adjusting the uniform inter-element distance and the radius of the array. It has been shown analytically that, with proper choice of number of elements, and radius, the on-resting plane scanning of the array can be minimized significantly.

Synthesis of broadside uniform circular antenna array with low on-surface scanning

Circular antenna array has gained immense popularity in the field of communications. It has been proved to be a better alternative over other types of antenna array configurations due to its all-azimuth scan capability, and a beam pattern which can be kept invariant. This paper is basically concerned with the thinning of a large multiple concentric circular ring arrays of uniformly excited isotropic antennas based on Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA) method. In this paper a 9 ringed Concentric Circular Antenna Array (CCAA) with central element feeding is considered. The computational results show that the number of antenna array elements can be brought down from 279 to 135 with the simultaneous reduction in Side Lobe Level (SLL) of −20.56 dB with a fixed half power beamwidth.

Thinned concentric circular array antenna synthesis using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach

In this paper, particle swarm optimization (PSO) method, which represents a recent approach for optimization problems in electromagnetic, is applied for array pattern synthesis of hexagonal array (HA) and concentric hexagonal array (CHA) of uniformly excited isotropic antennas which can generate directive beam with minimum relative side lobe level (SLL). Two examples has been presented and solved. In first example, the PSO is used to determine an optimal set of ‘ON-OFF’ elements in a 12-element thinned HA and 24-element thinned CHA, and in second example, PSO is used to determine an optimal set of amplitude distributions in a 12-element HA and a 24-element CHA that provide a radiation pattern with maximum SLL reduction. Optimization is done without significant change in the value of first null beam width (FNBW). Simulation results show that, in first example, the number of effective antenna elements can be brought down from 12 to 6 totals with simultaneous reduction in SLL by −23.85 dB for HA and from 24 to 11 totals with simultaneous reduction in SLL by −20.71 dB for CHA. In second example, SLL is reduced to less than −31 and −27 dB for HA and CHA, respectively, by optimizing inter-element spacing and inter-ring spacing along with amplitude using PSO.

Durbadal Mandal

Papers

Electronic Beam Steering in Timed Antenna Array by Controlling the Harmonic Patterns with Optimally Derived Pulse-Shifted Switching Sequence

Optimal design of complementary metal-oxide-semiconductor analogue circuits: An evolutionary approach

Synthesis of broadside uniform circular antenna array with low on-surface scanning

Thinned concentric circular array antenna synthesis using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach

Application of Particle Swarm Optimization Technique in Hexagonal and Concentric Hexagonal Antenna Array for Side Lobe Level Reduction