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 describes the practical implementation of time-modulated linear dipole antenna arrays (TMLDAAs) using EM simulator. Cat swarm optimization (CSO) algorithm is applied to improve the null performance of TMLDAAs by radio frequency switch. The nulls at the particular positions of the direction of arrival of a TMLDAA can be reduced effectively by the proper optimization of current excitation weights and an effective design of switch-on time intervals of each element. CSO gives the optimized value of the current excitation weights of the radiation pattern. The optimized results obtained by CSO algorithm using MATLAB simulation are practically implemented and are designed through computer simulation technology–microwave studio simulation software for half-wave dipole antenna arrays. The dipole antenna is designed to operate at a resonant frequency of 2 GHz. The antenna exhibits a frequency band from 1.8331 to 2.1285 GHz, which is applicable for wireless applications.

Null Placement in Time-Modulated Linear Antenna Arrays of Dipole Element

It has been descriptively shown in the past that the boundary conditions in particle swarm optimizers are an important algorithmic part which restricts the particles within the solution space, thereby increasing their scope of participation in solution finding process. Usually, velocities of the particles are regulated to bring them back to solution space; here, a different fundamental approach of regulating the position of particles is taken; particles which go out of solution place are relocated inside by maintaining symmetry about the boundary. A three concentric ring circular antenna array is taken as the optimization target for the reduction of side lobes in the radiation pattern. Results show better performance of this boundary condition over other established ones in terms of quicker convergence and obtaining better optimization solution.

PSO in Concentric Circular Arrays for Side Lobe Reduction with Symmetric Relocation Boundary Condition

This paper describes optimal thinning of an Elliptical Cylindrical Array (ECA) of uniformly excited isotropic antennas which can generate directive beam with minimum relative Side Lobe Level (SLL). The Particle Swarm Optimization (PSO) method, which represents a new approach for optimization problems in electromagnetic, is used in the optimization process. The PSO is used to determine the optimal set of ‘ON-OFF’ elements that provides a radiation pattern with maximum SLL reduction. Optimization is done without prefixing the value of First Null Beam Width (FNBW). The variation of SLL with element spacing of thinned array is also reported. Simulation results show that the number of array elements can be reduced by more than 50% of the total number of elements in the array with a simultaneous reduction in SLL to less than -27dB. Keywords—Thinned array, Particle Swarm Optimization, Elliptical Cylindrical Array, Side Lobe Label.

Thinned Elliptical Cylindrical Antenna Array Synthesis Using Particle Swarm Optimization

Wavelet Mutation based Novel Particle Swarm Optimization (NPSOWM) technique is applied for the comparison of the performances of Circular array (CA), Hexagonal Array (HA) and Elliptical Array (EA) of isotropic antenna elements which can produce array pattern with maximum reduced Side-Lobe Level (SLL). Novel Particle Swarm Optimization (NPSO) explores the solution space more effectively for a better solution when the wavelet theory is applied in terms of mutation. Syntheses of 24-element single ring planar antenna arrays are presented which illustrate the effectiveness of the NPSOWM algorithm to achieve the optimization goal. As Compared with conventional PSO and NPSO methods, NPSOWM outperforms with the goal of maximum SLL suppression with improvement of directivity and that too for elliptical array of eccentricity 0.4. Numerical results for synthesizing three different array geometries have demonstrated the superiority of EA over the CA and EA.

Wavelet Mutation based Novel Particle Swarm Optimization technique for comparison of the performance of single ring planar antenna arrays

Boundary conditions in particle swarm optimizers are an important algorithmic part which can constrain the particles within the solution space which increases their scope of participation in solution finding process. Usually, velocities of the particles are regulated to bring them back to solution space; Here the basic approach of regulating the position of particles is different than the conventional approaches, particles which go out of solution place are relocated inside by maintaining symmetry about the boundary. A twelve element linear antenna array is taken as the optimization target for the reduction of side lobes in the radiation pattern without increase in the mainlobe beamwidth. Results of the proposed boundary condition show better performance in terms of better global solution and quicker convergence compare to the other established boundary algorithms.

http://ieeexplore.ieee.org/iel7/7439604/7443873/07443954.pdf

Durbadal Mandal

Papers

Null Placement in Time-Modulated Linear Antenna Arrays of Dipole Element

PSO in Concentric Circular Arrays for Side Lobe Reduction with Symmetric Relocation Boundary Condition

Thinned Elliptical Cylindrical Antenna Array Synthesis Using Particle Swarm Optimization

Wavelet Mutation based Novel Particle Swarm Optimization technique for comparison of the performance of single ring planar antenna arrays

Sidelobe and beamwidth optimization of linear antenna arrays with symmetric relocation boundary condition of PSO