Big Crunch Research Articles

A Comparative Study of Nature-Inspired Metaheuristic Algorithms in Search of Near-to-optimal Golomb Rulers for the FWM Crosstalk Elimination in WDM Systems

ABSTRACTNowadays, nature-inspired metaheuristic algorithms are the most powerful optimizing algorithms for solving NP-complete problems. This paper proposes five recent approaches to find near-optimal Golomb ruler (OGR) sequences based on nature-inspired algorithms in a reasonable time. The optimal Golomb ruler sequences found their application in channel-allocation method that allows suppression of the crosstalk due to four-wave mixing (FWM) in optical wavelength division multiplexing (WDM) systems. The simulation results conclude that the proposed nature-inspired metaheuristic optimization algorithms are superior to the existing conventional computing algorithms, i.e., Extended Quadratic Congruence (EQC) and Search algorithm (SA) and nature-inspired algorithms, i.e., Genetic algorithms (GAs), Biogeography-based optimization (BBO) and simple Big bang–Big crunch (BB-BC) optimization algorithm to find near-OGRs in terms of ruler length, total optical channel bandwidth and computation time.

Entropy Estimation for ADC Sampling-Based True Random Number Generators

True random number generators (TRNGs) are widely used in cryptographic systems, and their security is the base of many cryptographic algorithms and protocols. At present, entropy estimation based on a stochastic model is a well-recommended approach to evaluate the security of a specific TRNG structure. Besides, the generation speed is also an important property for TRNGs. For this purpose, an analog-to-digital converter (ADC) can be employed to sample the noisy signal to achieve high bit rate. However, no research focuses on the entropy estimation on the basis of the stochastic model toward ADC sampling. In this paper, we propose an entropy estimation for the ADC sampling-based TRNG through extending an existing model. In particular, we present an equivalent model to estimate the entropy of any single bit in the converted sample obtained by the ADC sampling. Furthermore, we propose a method of the entropy estimation for the multi-bit ADC output, which provides the lower bound of the entropy. By conducting simulations and hardware experiments on this type of TRNG, we confirm the correctness of the proposed entropy estimation theory. The prototype chip is fabricated in the SMIC 65-nm process, and the consumed power is 34 mW. The random bit sequences compatible with the AIS 31 standard are generated at a speed of 132.3 Mb/s. The sequences are able to pass the rigorous statistical test suites, including NIST SP 800-22, Diehard, and TestU01 (containing the Big Crush test), after simple post-processing at a bit rate of around 33 Mb/s.

A Modified Big Bang–Big Crunch Algorithm for Structural Topology Optimization

The purpose of this study is to develop a topology optimization scheme based on big bang–big crunch (BB–BC) algorithm, inspired from the evolution of the universe called big bang and big crunch theory. In order to apply the BB–BC algorithm to topology optimization for static and dynamic stiffness problems, the parameters of the algorithm were transformed to those of topology optimization scheme. In addition, some parameters such as big bang (BB) range, BB search, population and non-exchange limit were newly introduced to topology optimization scheme. Also, a parametric study for the parameters involved in the topology optimization scheme was performed to reduce the number of parameters, and find the appropriate ranges for topology optimization. Some examples were provided to examine the effectiveness of the developed topology optimization scheme for both static and dynamic stiffness problems throughout comparing with other metaheuristic topology optimization algorithms and the BESO (bi-directional evolutionary structural optimization) method. It was verified that the suggested algorithm shows superior to the compared typical metaheuristic topology optimization algorithms in the viewpoints of stability, robustness, accuracy and the convergence rate.

Non-minimally coupled nonlinear spinor field in Bianchi type-I cosmology

Within the scope of Bianchi type-$I$ cosmological model we have studied the role of spinor field in the evolution of the Universe. In doing so we have considered the case with non-minimal coupling. It was found that the non-diagonal components of the energy-momentum tensor of the spinor field, hence the restrictions on the space-time geometry remain the same as in case of minimal coupling. Since in this case the diagonal components of the energy-momentum tensor differ, the evolution of the corresponding universe also differs. For example, while a linear spinor field with non-minimal coupling or nonlinear spinor field with minimal coupling give rise to open universe, a nonlinear spinor field with non-minimal coupling with the same parameters can generate close universe that at the beginning expands, and after attaining some maximum value begin to contract and finally ends in a Big Crunch.

HGAB3C: A new hybrid global optimization algorithm

This paper proposes a new optimization algorithm, namely HGAB3C, and presents its performance on the CEC-2014 test suite. In HGAB3C, simple genetic algorithms (GAs) and big bang-big crunch (BB-BC) are hybridized. The algorithm carries out global searches using a simple GA. In every generation the BB-BC algorithm is used to carry out local searches. The addition of local search has improved the capability of simple GAs significantly. The performance of the proposed algorithm is compared with 17 other optimization algorithms on all 30 functions of the CEC-2014 benchmark suite. It is observed that HGAB3C outperforms all other algorithms on 4 benchmark functions. For the 3 other functions, its performance equaled the best of the competing algorithms, which makes HGAB3C's performance best in a total of 7 benchmark functions. Out of the 18 competing algorithms, the proposed algorithm ranked second for the unmatched best mean error measure. For the best performance measure (number of functions giving unmatched best and equaled best mean error), the proposed algorithm was the third best. As far as the speed of convergence is concerned, the algorithm gave an unmatched best performance for the shifted Schwefel function (function 10 of CEC-2014 test bench). It obtained a mean error value of 0.00E+00, outperforming the previous best of 1.23E-03, converging to the target result in an average of 346.44 generations, which no other algorithm could achieve.

Facebook’s Libra: Big Bang or Big Crunch? A Technical Perspective and Challenges for Cryptocurrencies

Libra cryptocurrency is a new invention; as with any disruptive invention, Libra blockchain presents some risks. Facebook’s formal announcement of Libra had the “big bang” effect in the cryptocurrency markets; equally, the industry will witness “big crunch” if Libra sputters out resulting from a failure to receive all appropriate approvals from central banks, regulators, and law makers who are eager to run headlong into backlash to Libra in order to punish Facebook with a troubled past of privacy abuse and exploitation of users’ data. Libra’s unique features are distinctly different from Bitcoin and over 2,400 altcoins. Although Facebook claims Libra as a permissioned decentralized blockchain, but this is far cry from truth because Libra is a non-mineable cryptocurrency without the need of providing mathematical solutions to double spending problem. Under Bitcoin’s permissionless decentralized blockchain without a trusted third party, every new bitcoin is minted through a mining process which starts with a block, and then a ledger comprising timestamped transactions in a chronological order is distributed to all nodes (miners) in the Bitcoin network who check and validate transactions based on consensus before they are added to the end of each coin in its block. As a start, Libra blockchain will be governed by the Libra Association as a de facto central authority, which will initially comprise 28 private founding-members, each of which will act as a validator to ensure Libra’s stability. Libra is cost efficient in electricity usage and more consistent than other cryptocurrencies; Libra’s superior functionality, higher security, and vast scale due to its user base of nearly 3 billion will eventually make Libra become a viable alternative reserve crypto-currency to the dollar. Libra’s proof-of-stake algorithm supported by a new programming language “Move” plus the use of LibraBFT consensus make Libra 1/3 more secure than Bitcoin, Libra can function correctly even if 1/3 of its network fails or hacked. Libra’s PoS leads to higher transaction throughput, lower latency, and lower energy cost.

ANN System Identification for Rapid Battery Charger using Parallel 3 Parent Genetic Algorithm

Model identification is one of the main concerns in the field of system modeling. The complete modeling of an ANN system using input output data consists of two processes: architecture selection in which number of hidden layers and the number of neurons in each hidden layer is to be decided. This is then followed by training of system by the given training data. The problem here is formulated as search and minimization problem. This paper presents the identification of ANN system for rapid Nickel Cadmium (Ni-Cd) batteries charger by applying a new version of Genetic algorithm called as parallel 3 parent genetic algorithm (P3PGA). It is a multi population based 3 parent genetic algorithm (3PGA) .The proposed approach was implemented using MATLAB R2018A and was observed to be computationally more efficient with minimum MSE. With increase in number of iterations, system performance gets improved. We further compared results of the proposed algorithm with the results of other recent soft computing based algorithms as well classical learning based algorithms namely, big bang big crunch (BB-BC), parallel big bang big crunch (PBB-BC), Levenberg-Marquardt algorithm (LM), error back propagation (EBP), Resilent prop (RPROP), particle swarm optimization (PSO), ant colony optimization (ACO) and artificial bee colony (ABC) for ANN model identification. The proposed algorithm outperformed all of the other 8 algorithms.

Model Order Reduction of Commensurate Fractional-Order Systems Using Big Bang – Big Crunch Algorithm

ABSTRACT In this paper, a soft computing based scheme is proposed for the model order reduction of single input-single output commensurate fractional-order (FO) systems. The fractional-order system is first converted into an integer order (IO) system. The reduced order model of the corresponding integer order system is then determined via big bang – big crunch (BBBC) optimization algorithm. Finally, the reduced IO transfer function is transferred back to its FO form through an inverse substitution. The proposed approach is substantiated by two numerical examples of different orders. The effectiveness of the technique is demonstrated by the comparison of two performance indices, i.e. integral square error (ISE) and error and the response characteristics in time and frequency domain with the existing techniques from the literature. It is revealed that the response of the proposed BBBC based reduced order model is much closer to that of the original higher-order system.

Cellular Automata Based Model for E-Healthcare Data Analysis

E-healthcare is warm area of research and a number of algorithms have been applied to classify healthcare data. In the healthcare field, a large amount of clinical data is generated through MRI, CT scans, and other diagnostic tools. Healthcare analytics are used to analyze the clinical data of patient records, disease diagnosis, cost, hospital management, etc. Analytical techniques and data visualization are used to get the real time information. Further, this information can be used for decision making. Also, this information is useful for the better treatment of patients. In this work, an improved big bang-big crunch (BB-BC) based clustering algorithm is applied to analyze healthcare data. Cluster analysis is an important task in the field of data analysis and can be used to understand the organization of data. In this work, two healthcare datasets, CMC and cancer, are used and the proposed algorithm obtains better results when compared to MEBB-BC, BB-BC, GA, PSO and K-means algorithms. The performance of the improved BB-BC algorithm is also examined against benchmark clustering datasets. The simulation results showed that proposed algorithm improves the clustering results significantly when compared to other algorithms.

Joining General Relativity to Particles Physics through Complex Numbers and Autism

Autistics and the plane of complex numbers suggest that if the accelerating expansion of our universe and the anti-universe succeeded a coasting expansion 8.8 billion years after the Big Bang, an accelerating contraction will start in 3.8 billion years. Mirroring the expansion phase, a coasting contraction of the two universes in cosmic space will come up in 12.6 billion years. The end of the fourth section of 8.8 billion years will host two Big Crunches, two White Holes, and a new Big Bounce. The reason for that paradox solves the “cosmological constant problem” and joins general relativity to particle physics. The z-plane and autism can also help us cross science with the arts and religion; retain the search for truth, beauty, and goodness by our descendants; and reach the message of progress buried in the Ark of the Covenant, the Great Pyramid, and Giza’s Sphinx: A selfish brain hides a selfless heart.

Development of optimum cold-formed steel beams for serviceability and ultimate limit states using Big Bang-Big Crunch optimisation

Cold-formed steel (CFS) elements are increasingly used as main structural members in modern construction practice. While flexibility of CFS cross-sectional shape allows achieving higher load carrying capacities by using more efficient shapes, obtaining optimum design solutions can be a challenging task due to end-use constraints and complex behaviour of CFS elements controlled by local, global and distortional buckling modes. This study aims to develop a practical methodology for optimum design of CFS beam sections with maximum flexural strength and minimum deflection under ultimate and serviceability load conditions, respectively, in accordance with Eurocode 3 by taking into account manufacturing and end-use design constrains. Population-based Big Bang–Big Crunch Optimisation method is employed to obtain optimum design solutions for twelve different CFS cross-sectional prototypes. To verify the flexural strength and stiffness of the optimum beam sections, detailed nonlinear finite element (FE) models are developed using ABAQUS by considering both material nonlinearity and initial geometrical imperfections. It is shown that the optimised sections based on serviceability limit state (SLS) and ultimate limit state (ULS) can provide, respectively, up to 44% higher effective stiffness and 58% higher bending moment capacity compared to a standard lipped channel beam section with the same plate width and thickness. Using plain channel and folded-flange sections generally leads to the best design solutions for SLS and ULS conditions, respectively. Finally, the results of detailed FE models are used to evaluate the adequacy of EC3 proposed procedures to estimate CFS beam capacity and deflection at ULS and SLS, respectively.

Primordial Universe with radiation and Bose–Einstein condensate

In this work we derive a scenario {in which} the early universe consists of {radiation fluid} and Bose-Einstein condensate. The possibility of gravitational self-interaction due to an attractive Bose-Einstein condensate is analyzed. The classical behavior of the scale factor of the universe is determined by a parameter associated with the Bose-Einstein fluid with bouncing or Big Crunch solutions. After we proceed to compute the finite-norm wave packet solutions to the Wheeler-DeWitt equation. The behavior of the scale factor is studied by applying the many-worlds interpretation of quantum mechanics. The quantum cosmological model is free from the singularities.

Hybrid parliamentary optimization and big bang-big crunch algorithm for globaloptimization

Researchers have developed different metaheuristic algorithms to solve various optimization problems. The efficiency of a metaheuristic algorithm depends on the balance between exploration and exploitation. This paper presents the hybrid parliamentary optimization and big bang-big crunch (HPO-BBBC) algorithm, which is a combination of the parliamentary optimization algorithm (POA) and the big bang-big crunch (BB-BC) optimization algorithm. The intragroup competition phase of the POA is a process that searches for potential points in the search space, thereby providing an exploration mechanism. By contrast, the BB-BC algorithm has an effective exploitation mechanism. In the proposed method, steps of the BB-BC algorithm are added to the intragroup competition phase of the POA in order to improve the exploitation capabilities of the POA. Thus, the proposed method achieves a good balance between exploration and exploitation. The performance of the HPO-BBBC algorithm was tested using well-known mathematical test functions and compared with that of the POA, the BB-BC algorithm, and some other metaheuristics, namely the genetic algorithm, multiverse optimizer, crow search algorithm, dragonfly algorithm, and moth-flame optimization algorithm. The HPO-BBBC algorithm was found to achieve better optimization performance and a higher convergence speed than the above-mentioned algorithms on most benchmark problems.

Hydrothermal Economic Dispatch Using Hybrid Big Bang-Big Crunch (HBB-BC) Algorithm

In power generation, it is expected to generate required amount of power based on the load system with minimum cost which is generally called as economic dispatch (ED). Therefore, providing an approach which can be used to solve ED problem in electric systems for effective operation is important. In this paper, hybrid big bang-big crunch (HBB-BC) algorithm was proposed to solve hydrothermal ED problem. Basically, HBB-BC is an algorithm which combined between BB-BC and PSO that use the PSO to improve ability of BB-BC algorithm. To examine the performance of HBB-BC algorithm for hydrothermal ED, IEEE 26 bus was utilized as test system with 6 generators (3 thermal and 3 hydro generator units). Next, simulation output was compared with improved PSO, and modified improved PSO algorithm. From results, HBB-BC algorithm shown the best result under tested case. It confirmed by obtained total operating cost for HBB-BC algorithm was the lowest (11,344.593 $/h) compared to IPSO (11,451.001 $/h) and MIPSO algorithms (11,387.000 $/h).

Interacting relativistic quantum dynamics of two particles on spacetimes with a Big Bang singularity

Relativistic quantum theories are usually thought of as being quantum field theories, but this is not the only possibility. Here, we consider relativistic quantum theories with a fixed number of particles that interact neither through potentials nor through exchange of bosons. Instead, the interaction can occur directly along light cones, in a way similar to the Wheeler-Feynman formulation of classical electrodynamics. For two particles, the wave function is here of the form ψ(x1, x2), where x1 and x2 are spacetime points. Specifically, we consider a natural class of covariant equations governing the time evolution of ψ involving integration over light cones or even more general spacetime regions. It is not obvious, however, whether these equations possess a unique solution for every initial datum. We prove for Friedmann-Lemaître-Robertson-Walker spacetimes that in the case of purely retarded interactions, there does, in fact, exist a unique solution for every datum on the initial hypersurface. The proof is based on carrying over similar results for a Minkowski half-space (i.e., the future of a spacelike hyperplane) to curved spacetime. Furthermore, we show that also in the case of time-symmetric interactions and for spacetimes with both a Big Bang and a Big Crunch, solutions do exist. However, initial data are then not appropriate anymore; the solution space gets parametrized in a different way.

Gauss–Bonnet gravity in D = 4 without Gauss–Bonnet coupling to matter: Cosmological implications

We propose a new model of D = 4 Gauss–Bonnet gravity. To avoid the usual property of the integral over the standard D = 4 Gauss–Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D = 4 Gauss–Bonnet action term nontrivial without the need to couple it to matter fields unlike the case of ordinary D = 4 Gauss–Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss–Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cosmological implications. (i) It yields specific solutions for the Hubble parameter and the Friedmann scale factor as functions of time, which are completely independent of the matter dynamics, i.e. there is no back reaction by matter on the cosmological metric. (ii) For M[Formula: see text]0, it predicts a “coasting”-like evolution immediately after the Big Bang, and it yields a late universe with dynamically produced dark energy density given through M. (iii) For the special value M = 0, we obtain exactly a linear “coasting” cosmology. (iv) For M[Formula: see text]0, we have in addition to the Big Bang also a Big Crunch with “coasting”-like evolution around both. (v) It allows for an explicit analytic solution of the pertinent Friedmann and [Formula: see text] scalar field equations of motion, while dynamically fixing uniquely the functional dependence on [Formula: see text] of the scalar potential.

Wave Asymptotics at a Cosmological Time-Singularity: Classical and Quantum Scalar Fields

We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of the linear Klein-Gordon equation, and similar results for the semilinear equation with a subcritical exponent. We prove that the number of cosmological particle creation is finite under general assumptions on the initial Big Bang and the final Big Crunch or Big Brake.

Optimization of Water-Supply and Hydropower Reservoir Operation Using the Charged System Search Algorithm

The Charged System Search (CSS) metaheuristic algorithm is introduced to the field of water resources management and applied to derive water-supply and hydro-power operating policies for a large-scale real-world reservoir system. The optimum algorithm parameters for each reservoir operation problems are also obtained via a tuning procedure. The CSS algorithm is a metaheuristic optimization method inspired by the governing laws of electrostatics in physics and motion from the Newtonian mechanics. In this study, the CSS algorithm’s performance has been tested with benchmark problems, consisting of highly non-linear constrained and/or unconstrained real-valued mathematical models, such as the Ackley’s function and Fletcher–Powell function. The CSS algorithm is then used to optimally solve the water-supply and hydropower operation of “Dez” reservoir in southern Iran over three different operation periods of 60, 240, and 480 months, and the results are presented and compared with those obtained by other available optimization approaches including Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and Constrained Big Bang–Big Crunch (CBB–BC) algorithm, as well as those obtained by gradient-based Non-Linear Programming (NLP) approach. The results demonstrate the robustness and superiority of the CSS algorithm in solving long term reservoir operation problems, compared to alternative methods. The CSS algorithm is used for the first time in the field of water resources management, and proves to be a robust, accurate, and fast convergent method in handling complex problems in this filed. The application of this approach in other water management problems such as multi-reservoir operation and conjunctive surface/ground water resources management remains to be studied.

Enhancing FRT performance and smoothing output power of DFIG wind farm equipped by SFCL and SMES in a fuzzy framework

Wind farms equipped by Doubly-Fed Induction Generators (DFIG) should have two capabilities so that system operators can efficiently utilizes them. These capabilities include Fault-Ride-Through (FRT) and smoothing the output active power fluctuations, especially when these generators provide significant electrical power. The Superconducting Fault Current Limiter (SFCL) and also the Superconducting Magnetic Energy Storage (SMES) are supplementary devices which are used to enhance these capabilities and reduce electrical power swings. In the present work, improvement of FRT capability and smoothing the output power of wind farms are formulated as a multi-objective problem in a fuzzy framework. The variables of optimization are the Proportional-Integral (PI) gains of DFIG and SMES controllers and also SMES and SFCL parameters. Minimization of the initial energy stored in the SMES unit, the energy losses of SFCL, deviations of the DC-link voltage of DFIG, deviations of output active power of DFIG, deviations of output voltage of DFIG, and DFIG speed deviations are six objective functions of the problem. These objective functions are scaled by a fuzzy operator, then the scaled objective functions are aggregated by the “max-geometric mean” operator to obtain the multi-objective function. For optimizing this multi-objective function, the Hybrid Big Bang Big Crunch (HBB-BC) as a meta-heuristic optimization algorithm is used. The proposed algorithm is implemented on a case study to numerically evaluate its efficiency. Simulation results show that the proposed algorithm is more effective to enhance FRT capability and smooth output power of wind farm in comparison with the other algorithms.

A mixed-method for order reduction of linear time invariant systems using big bang-big crunch and eigen spectrum algorithm

In this article, a novel mixed approach is presented for order reduction of complex higher order linear time invariant systems by merging the attributes of big bang-big crunch (BB-BC) optimisation and eigen spectrum algorithm. The cosmological theory based BB-BC optimisation has the advantage of numerical simplicity with relatively fewer control parameters which makes this algorithm easier to implement. BB-BC optimisation technique is based on the generation of random points in first step and contraction of these to a typical point in following step by the centre of mass or minimal cost approach. Eigen spectrum is based on the preservation of centroid and stiffness of the original system into reduced model which guarantees the stability of resulting reduced order model for a stable original model. In the proposed approach, denominator polynomial of the reduced order model (ROM) is determined by the Eigen spectrum approach whereas the minimisation of fitness function, i.e., integral square error (ISE) by the BB-BC algorithm approach is adopted for the computation of numerator polynomial coefficients. The effectiveness of the proposed approach over well-known methods is validated with the help of numerical examples by the comparison of transient parameters and performance indices.