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 work considers the problem of optimizing sidelobe (SLL) and directivity (D) for concentric regular hexagonal antenna arrays (CRHAA). The relation between and SLL and D is generally considered to be convex. An objective vector comprising of functions of SLL and D is proposed. The aim is to compare the convergences of the obtained SLL - D fronts of two bi-objective vectors: i) {SLL,D}, and ii) the proposed bi-objective vector. For simplicity in pattern computation, the elements are considered to be ideal, without loss of generality. A popular multiobjective optimization algorithm, named MOEA/D is utilized to obtain the pareto optimal fronts for the considered objective vectors. Results reveal that, proposed objective vector outperforms the {SLL,D} objective vector.

Multiobjective space-only synthesis of concentric regular hexagonal antenna arrays

In this paper, optimal designs of three-ring Concentric Circular Antenna Arrays (CCAA) without and with central element feeding are reported. For each optimal design, optimal current excitation weights and optimal radii are determined having the objective of maximum Sidelobe Level (SLL) reduction. The optimization technique adopted is Bacteria Foraging Optimization (BFO). The extensive computational results show that the CCAA having central element feeding yield much more reduction in SLL as compared to the same not having central element feeding. Moreover, the particular CCAA containing 4, 6 and 8 number of elements in three successive rings along with central element feeding yields grand minimum SLL (-36.14 dB).

Bacteria Foraging Optimization based synthesis of Concentric Circular Antenna Array

In this paper, various swarm based algorithms like real coded genetic algorithm (RGA), conventional particle swarm optimization (PSO), a proposed novel particle swarm optimization (NPSO) have been applied for the optimal design of hyper beamforming of linear antenna array. Hyper beam is derived from sum and difference beam patterns each raised to the power of the hyper beam exponent parameter for the array. NPSO uses new definition for the velocity vector. The simulation results show NPSO outperforms RGA and PSO in the optimal hyper beamforming by achieving much greater reduction in sidelobe level (SLL) and much more improved first null beam width (FNBW) keeping the same value of hyper beam exponent. The optimized hyper beam is achieved by optimization of current excitation weights and uniform inter-element spacing. The approach is illustrated through 10-, 14-, and 20-element linear antenna arrays.

/pdf/novel-particle-swarm-optimization-based-hyper-beamforming-of-8myy3l1iiq.pdf

Novel particle swarm optimization based hyper beamforming of linear antenna arrays

Linear Antenna Arrays are the simplest and most popular type of antenna arrays. In this paper, symmetric linear array structures, with and without centre element are assumed. Simulated results reveal, non-uniform location profile and non-uniform excitation distribution can provide low and decreasing sidelobe and narrow first null beamwidth. Low tapering of excitation moreover restricts the directivity to that of a uniform linear broadside array with inter-element spacing as λ/2. Optimal radiation pattern is compared to initial radiation pattern and with that of the uniform array of same length. Improvement has been found for both cases. Optimal non-uniform location and excitation profile is worked out by using Novel Particle Swarm Optimization (NPSO).

Low current tapered non-uniform linear array synthesis with decreasing sidelobe using NPSO

This paper proposes an accurate and efficient strategy for identification of Hammerstein model based nonlinear systems using Craziness based Particle Swarm Optimization (CRPSO) algorithm. The closeness of estimation of the proposed CRPSO based identification scheme has been justified with the optimal value of MSE and the corresponding comparative study with the other techniques reported in earlier literature. The statistical information of the MSE has also been provided to justify consistency of the CRPSO algorithm for identification of Hammerstein model. The estimated parameters along with their corresponding deviations and convergences are shown to justify the accuracy of the proposed identification scheme. Accurate identification of the linear block also ensures the stability of the overall system in the presence of noise.

Durbadal Mandal

Papers

Multiobjective space-only synthesis of concentric regular hexagonal antenna arrays

Bacteria Foraging Optimization based synthesis of Concentric Circular Antenna Array

Novel particle swarm optimization based hyper beamforming of linear antenna arrays

Low current tapered non-uniform linear array synthesis with decreasing sidelobe using NPSO

Hammerstein model based system identification using craziness based particle swarm optimization algorithm