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 integer order transfer function approximation of the fractional order impedance model of the B &K type 4185 commercial human ear simulator. The third order rational approximation of the fractional order capacitor is obtained by employing Flower Pollination Algorithm. The impedance characteristic of the approximated model is then investigated by synthesizing the fractional order capacitor in Foster-I structure. Comparison with the reported literature demonstrates the improved accuracy of the proposed model.

Optimal Integer Order Approximation of Fractional Order Human Ear Simulator

In this paper, optimal designs of three-ring concentric circular array antennas (CCAA) without and with central element feeding are reported. For each design set, optimal current excitations and radii are determined with the objective of maximum Sidelobe Level (SLL) reduction. The optimization technique adopted is Novel Particle Swarm Optimization (NPSO). To enhance the optimization performance of NPSO further in exploring the solution space more effectively for a better solution, the wavelet theory is again applied in terms of mutation. This wavelet mutation based NPSO is named as NPSOWM. The extensive computational results show that the CCAA having central element feeding yield much more reductions 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 (-43.48 dB) as determined by NPSOWM. Conventional Particle Swarm Optimization (PSO), its Wavelet Mutation based improved version (PSOWM) and NPSO as well are adopted to compare the results of the above technique, NPSOWM. The NPSOWM consistently shows the best solution quality.

Wavelet Mutation Based Novel PSO for Optimal Design of Concentric Circular Array Antennas

A bio-inspired optimisation technique to design recursive digital fractional order differentiator (DFOD) is presented in this paper. The proposed Bat Algorithm (BA) based optimised DFOD can operate over a full band, i.e., over the entire Nyquist frequency range. Design performance and efficiency of BA is extensively compared with an advanced variant of particle swarm optimisation algorithm. Comparisons with the published designs validate the superior modelling accuracy of the proposed model.

Optimal Design of Recursive Fullband Digital Fractional Order Differentiator

Effect of Structural Refinement and Modification on the Mechanical Properties of Al-7Si Alloy

Performance Comparison of Two Recently Proposed Adaptive Differential Evolution Algorithms on Space Only Low Sidelobe Synthesis Problem of Concentric Regular Hexagonal Antenna Arrays

Durbadal Mandal

Papers

Optimal Integer Order Approximation of Fractional Order Human Ear Simulator

Wavelet Mutation Based Novel PSO for Optimal Design of Concentric Circular Array Antennas

Optimal Design of Recursive Fullband Digital Fractional Order Differentiator

Effect of Structural Refinement and Modification on the Mechanical Properties of Al-7Si Alloy

Performance Comparison of Two Recently Proposed Adaptive Differential Evolution Algorithms on Space Only Low Sidelobe Synthesis Problem of Concentric Regular Hexagonal Antenna Arrays