Search results for: linear vibration

Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Pooja Sharma

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In the present paper the effects of radiation is studied on unsteady flow of viscous incompressible electrically conducting fluid past a vertical porous plate embedded in the porous medium in the presence of constant heat flux. A uniform Transverse Magnetic field is considered and induced magnetic field is supposed as negligible. The non-linear governing equations are solved numerically. Numerical results of the velocity and temperature fields are shown through graphs. The results illustrates that the appropriator combination of regulated values of thermo-physical parameters is expedient for controlling the flow system.

Keywords: heat transfer, radiation, MHD flow, porous medium

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Authors: Chi Zhang, Jun Jiang

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Constitutive equations are very important in finite element (FE) modeling, and the accuracy of the material constants in the equations have significant effects on the accuracy of the FE models. A wide range of constitutive equations are available; however, fitting the material constants in the constitutive equations could be complex and time-consuming due to the strong non-linearity and relationship between the constants. This work will focus on the development of a set of unified MATLAB programs for fitting the material constants in the constitutive equations efficiently. Users will only need to supply experimental data in the required format and run the program without modifying functions or precisely guessing the initial values, or finding the parameters in previous works and will be able to fit the material constants efficiently.

Keywords: constitutive equations, FE modelling, MATLAB program, non-linear curve fitting

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Authors: Woraprat Chaomuang, Sirikorn Sringern, Pawanrat Chamnanwongsritorn, Kridsada Luangthongkham

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In this study, we have applied a digital scale to demonstrate the electricity concept of changing the capacity (C), due to the weight of an object, as a function of the distance between the conductor plates and the pressing down. By calibrating on standard scales with the Visual Basic program and the Arduino Uno microcontroller board, we can obtain the weight of the object from the frequency (ƒ) that is measured from the electronic circuit (Astable Multivibrator). Our results support the concept, showing a linear correlation between the frequency and weight with an equation y = –0.0112x + 379.78 and the R2 value of 0.95. In addition, the effects of silicone rods shrinkage, permittivity and temperature were also examined and have found to affect various graph patterns observed.

Keywords: Arduino Uno board, frequency, microcontroller board, parallel plate conductor

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Authors: Hong Dinh Duong, Jong Il Rhee

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In this study, a ratiometric inorganic phosphate sensor was fabricated by a double layer of the rhodamine 6G-doped nanofibers and the CdSe/ZnS QDs-captured polymer. In which, CdSe/ZnS QDs with emission wavelengths of 595nm were synthesized and ligands on their surface were exchanged with mercaptopropionic acid (MPA). The synthesized MPA-QDs were combined with the mixture of sol-gel of 3-glycidoxypropyl trimethoxysilane (GPTMS), 3-aminopropyltrimethoxysilane (APTMS) and polyurethane (PU) to build a layer for sensing inorganic phosphate. Another sensing layer was of nanofibers doped R6G which were produced from poly(styrene-co-acrylonitrile) by electrospining. The ratio of fluorescence intensities between rhodamin 6G (R6G) and CdSe/ZnS QDs exposed at different phosphate concentrations was used for calculating a linear phosphate concentration range of 0-10mM.

Keywords: nanofiber, QDs, ratiometric phosphate sensor, rhodamine 6G, sol-gel

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Riona Dighe

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This research attempts to identify an alternative approach to the measurement of Gross National Happiness (GNH). It uses artificial intelligence (AI), incorporating natural language processing (NLP) and sentiment analysis to measure GNH. We use ‘off the shelf’ NLP models responsible for the sentiment analysis of a sentence as a building block for this research. We constructed an algorithm using NLP models to derive a sentiment analysis score against sentences. This was then tested against a sample of 20 respondents to derive a sentiment analysis score. The scores generated resembled human responses. By utilising the MLP classifier, decision tree, linear model, and K-nearest neighbors, we were able to obtain a test accuracy of 89.97%, 54.63%, 52.13%, and 47.9%, respectively. This gave us the confidence to use the NLP models against sentences in websites to measure the GNH of a country.

Keywords: artificial intelligence, NLP, sentiment analysis, gross national happiness

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Authors: Zainab Al-Maamari, Yassir Dinar

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The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

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Authors: Walied Hanora

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This paper presents the problem of robust state feedback H∞ for discrete time nonlinear system represented by Takagi-Sugeno fuzzy systems. Based on fuzzy lyapunov function, the condition ,which is represented in the form of Liner Matrix Inequalities (LMI), guarantees the H∞ performance of the T-S fuzzy system with uncertainties. By comparison with recent literature, this approach will be more relaxed condition. Finally, an example is given to illustrate the proposed result.

Keywords: fuzzy lyapunov function, H∞ control , linear matrix inequalities, state feedback, T-S fuzzy systems

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Authors: Olomon Wu, Hung Lu, Nick Wilkins, Daniel Kerr, Zekeriya Aliyazicioglu, H. K. Hwang

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Multiple Input Multiple Output (MIMO) radar has received increasing attention in recent years. MIMO radar has many advantages over conventional phased array radar such as target detection, resolution enhancement, and interference suppression. In this paper, the results are presented from a simulation study of MIMO Uniformly-Spaced Linear Array (ULA) antennas. The performance is investigated under varied parameters, including varied array size, Pseudo Random (PN) sequence length, number of snapshots, and Signal to Noise Ratio (SNR). The results of MIMO are compared to a traditional array antenna.

Keywords: MIMO radar, phased array antenna, target detection, radar signal processing

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Evangelos G. Ilias, Panagiotis G. Ilias, Vasileios T. Popotas

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The United Kingdom has one of the oldest railway networks in the world dating back to 1825 when the world’s first passenger railway was opened. The network has some 40,000 bridges of various construction types using a wide range of materials including masonry, steel, cast iron, wrought iron, concrete and timber. It is commonly accepted that the successful operation of the network is vital for the economy of the United Kingdom, consequently the cost effective maintenance of the existing infrastructure is a high priority to maintain the operability of the network, prevent deterioration and to extend the life of the assets. Every bridge on the railway network is required to be assessed every eighteen years and a structured approach to assessments is adopted with three main types of progressively more detailed assessments used. These assessment types include Level 0 (standardized spreadsheet assessment tools), Level 1 (analytical hand calculations) and Level 2 (generally finite element analyses). There is a degree of conservatism in the first two types of assessment dictated to some extent by the relevant standards which can lead to some structures not achieving the required load rating. In these situations, a Level 2 Assessment is often carried out using finite element analysis to uncover ‘latent strength’ and improve the load rating. If successful, the more sophisticated analysis can save on costly strengthening or replacement works and avoid disruption to the operational railway. This paper presents the ‘strengthening by assessment’ achieved by Level 2 analyses. The use of more accurate analysis assumptions and the implementation of non-linear modelling and functions (material, geometric and support) to better understand buckling modes and the structural behaviour of historic construction details that are not specifically covered by assessment codes are outlined. Metallic bridges which are susceptible to loss of section size through corrosion have largest scope for improvement by the Level 2 Assessment methodology. Three case studies are presented, demonstrating the effectiveness of the sophisticated Level 2 Assessment methodology using finite element analysis against the conservative approaches employed for Level 0 and Level 1 Assessments. One rail overbridge and two rail underbridges that did not achieve the required load rating by means of a Level 1 Assessment due to the inadequate restraint provided by U-Frame action are examined and the increase in assessed capacity given by the Level 2 Assessment is outlined.

Keywords: assessment, bridges, buckling, finite element analysis, non-linear modelling, strengthening

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Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

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This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components, as well as the introduction of the bars skew, in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars is neglected.

Keywords: modeling, MWFA, skew effect, squirrel cage induction motor, spectral domain

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Authors: Dawoon Choi, Jian Li, Yunhyun Cho

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Axial Flux Permanent Magnet (AFPM) machines have been widely used in various applications due to their important merits, such as compact structure, high efficiency and high torque density. This paper presents one of the most important characteristics in the design process of the AFPM device, which is a recent issue. To design AFPM machine, the predicting electromagnetic forces between the permanent magnets and stator is important. Because of the magnitude of electromagnetic force affects many characteristics such as machine size, noise, vibration, and quality of output power. Theoretically, this force is canceled by the equilibrium of force when it is in the middle of the gap, but it is inevitable to deviate due to manufacturing problems in actual machine. Such as large scale wind generator, because of the huge attractive force between rotor and stator disks, this is more serious in getting large power applications such as large. This paper represents the characteristics of Double-Stator Inner –Rotor AFPM machines when it has rotor eccentricity. And, unbalanced air-gap and inclined air-gap condition which is caused by rotor offset and tilt in a double-stator single inner-rotor AFPM machine are each studied in electromagnetic and mechanical aspects. The output voltage and cogging torque under un-normal air-gap condition of AF machines are firstly calculated using a combined analytical and numerical methods, followed by a structure analysis to study the effect to mechanical stress, deformation and bending forces on bearings. Results and conclusions given in this paper are instructive for the successful development of AFPM machines.

Keywords: axial flux permanent magnet machine, inclined air gap, unbalanced air gap, rotor eccentricity

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Authors: M. Y. Lee, D. H. Shin, S. H. Park, W.C. Ham, S.K. Ko, C. G. Song

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Photoacoustic Tomography (PAT) is a promising medical imaging modality that combines optical imaging contrast with the spatial resolution of ultrasound imaging. It can also distinguish the changes in biological features. But, real-time PAT system should be confirmed due to photoacoustic effect for tissue. Thus, we have developed a real-time PAT system using a custom-developed data acquisition board and ultrasound linear probe. To evaluate performance of our system, phantom test was performed. As a result of those experiments, the system showed satisfactory performance and its usefulness has been confirmed. We monitored the degradation of inflammation which induced on the rat’s kidney using real-time PAT.

Keywords: photoacoustic tomography, inflammation detection, rat, kidney, contrast agent, ultrasound

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Rohit Kumar Shrivastava, Amalia Thomas, Nathalie Vriend, Stefan Luding

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A mechanical wave or vibration propagating through granular media exhibits a specific signature in time. A coherent pulse or wavefront arrives first with multiply scattered waves (coda) arriving later. The coherent pulse is micro-structure independent i.e. it depends only on the bulk properties of the disordered granular sample, the sound wave velocity of the granular sample and hence bulk and shear moduli. The coherent wavefront attenuates (decreases in amplitude) and broadens with distance from its source. The pulse attenuation and broadening effects are affected by disorder (polydispersity; contrast in size of the granules) and have often been attributed to dispersion and scattering. To study the effect of disorder and initial amplitude (non-linearity) of the pulse imparted to the system on the coherent wavefront, numerical simulations have been carried out on one-dimensional sets of particles (granular chains). The interaction force between the particles is given by a Hertzian contact model. The sizes of particles have been selected randomly from a Gaussian distribution, where the standard deviation of this distribution is the relevant parameter that quantifies the effect of disorder on the coherent wavefront. Since, the coherent wavefront is system configuration independent, ensemble averaging has been used for improving the signal quality of the coherent pulse and removing the multiply scattered waves. The results concerning the width of the coherent wavefront have been formulated in terms of scaling laws. An experimental set-up of photoelastic particles constituting a granular chain is proposed to validate the numerical results.

Keywords: discrete elements, Hertzian contact, polydispersity, weakly nonlinear, wave propagation

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Authors: Rabia Ashfaq, Saeed Iqbal, Atiq ur Rehman, Irfanullah Khan

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An extensive series of radiopharmaceuticals have been explored in order to discover a better brain tumour diagnostic agent. Tc99m labelling with cysteine and its derivatives in liposomes shows effective tagging of about 70% to 80 %. Due to microscopic size it successfully crossed the brain barrier in 2 minutes which gradually decreases in 5 to 15 minutes. HMPAO labelled with Tc99m is another important radiopharmaceutical used to study brain perfusion but it comes with a flaw that it’s only functional during epilepsy. 1, 1 ECD is purely used in Tc99m ECD formulation; because it not only tends to cross the blood brain barrier but it can be metabolized which can be easily entrapped in human brain. Radio labelling of Cysteine with Tc99m at room temperature was performed which yielded no good results. Hence cysteine derivatives with salicylaldehyde were prepared that produced about 75 % yield for ligand. In order to perform it’s radio labelling a suitable solvent DMSO was selected and physical parameters were performed. Elemental analyser produced remarkably similar results for ligand as reported in literature. IR spectra of Ligand in DMSO concluded in the absence of SH stretch and presence of N-H vibration. Thermal analysis of the ligand further suggested its decomposition pattern with no distinct curve for a melting point. Radio labelling of ligand was performed which produced excellent results giving up to 88% labelling at pH 5.0. Clinical trials using Rabbit were performed after validating the products reproducibility. The radiopharmaceutical prepared was injected into the rabbit. Dynamic as well as static study was performed under the SPECT. It showed considerable uptake in the kidneys and liver considering it suitable for the Hypatobilliary study.

Keywords: marcapto compounds, 99mTc - radiolabeling, salicylaldicysteine, thiozolidine

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Authors: Nadia Sghaier

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In this paper, we aim to identify the determinants of the life and non-life insurance premiums of different lines for the case of the Tunisian insurance market over a recent period from 1997 to 2019. The empirical analysis is conducted using the linear cointegration techniques in the panel data framework, which allow both long and short-run relationships. The obtained results show evidence of long-run relationship between premiums, losses, and financial variables (stock market indices and interest rate). Furthermore, we find that the short-run effect of explanatory variables differs across lines. This finding has important implications for insurance tarification and regulation.

Keywords: insurance premiums, lines, Tunisian insurance market, cointegration approach in panel data

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Authors: Buti Suryabrahmam, V. A. Raghunathan

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We study the effect of short chain alcohols on mechanical properties of saturated lipid bilayers in the fluid phase. The Bending rigidity of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membrane was measured at 28 °C by employing Vesicle Fluctuation Analysis technique. The concentration and chain length (n) of alcohol in the buffer solution were varied from 0 to 1.5 M and from 2 to 8 respectively. We observed a non-linear reduction in the bending rigidity from ~17×10⁻²⁰ J to ~10×10⁻²⁰ J, for all chain lengths of alcohols used in our experiment. We observed approximately three orders of the concentration difference between ethanol and octanol, to show the similar reduction in the bending values. We attribute this phenomenon to thinning of the bilayer due to the adsorption of alcohols at the bilayer-water interface.

Keywords: alcohols, bending rigidity, DMPC, lipid bilayers

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Authors: Ilqar Ramazanli

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The matrix completion problem has been studied broadly under many underlying conditions. The problem has been explored under adaptive or non-adaptive, exact or estimation, single-phase or multi-phase, and many other categories. In most of these cases, the observation cost of each entry is uniform and has the same cost across the columns. However, in many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

Keywords: matroid optimization, matrix completion, linear algebra, algorithms

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: M. Yaqub Khan, Usman Shabbir

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History of plasma reveals that continuous struggle of experimentalists and theorists are not fruitful for confinement up to now. It needs a change to bring the research through entropy. Approximately, all the quantities like number density, temperature, electrostatic potential, etc. are connected to entropy. Therefore, it is better to change the way of research. In ion temperature gradient mode with the help of Braginskii model, Boltzmannian electrons, effect of velocity shear is studied inculcating entropy in the magnetoplasma. New dispersion relation is derived for ion temperature gradient mode, and dependence on entropy gradient drift is seen. It is also seen velocity shear enhances the instability but in anomalous transport, its role is not seen significantly but entropy. This work will be helpful to the next step of tokamak and space plasmas.

Keywords: entropy, velocity shear, ion temperature gradient mode, drift

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Authors: Mirco Tarozzi, Giacomo Pignagnoli, Andrea Benedetti

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Structural systems are often subjected to degradation processes due to different kind of phenomena like unexpected loadings, ageing of the materials and fatigue cycles. This is true especially for bridges, in which their safety evaluation is crucial for the purpose of a design of planning maintenance. This paper discusses the experimental evaluation of the stiffness reduction from frequency changes due to uniform damage scenario. For this purpose, a 1:4 scaled bridge has been built in the laboratory of the University of Bologna. It is made of concrete and its cross section is composed by a slab linked to four beams. This concrete deck is 6 m long and 3 m wide, and its natural frequencies have been identified dynamically by exciting it with an impact hammer, a dropping weight, or by walking on it randomly. After that, a set of loading cycles has been applied to this bridge in order to produce a uniformly distributed crack pattern. During the loading phase, either cracking moment and yielding moment has been reached. In order to define the relationship between frequency variation and loss in stiffness, the identification of the natural frequencies of the bridge has been performed, before and after the occurrence of the damage, corresponding to each load step. The behavior of breathing cracks and its effect on the natural frequencies has been taken into account in the analytical calculations. By using a sort of exponential function given from the study of lot of experimental tests in the literature, it has been possible to predict the stiffness reduction through the frequency variation measurements. During the load test also crack opening and middle span vertical displacement has been monitored.

Keywords: concrete bridge, damage detection, dynamic test, frequency shifts, operational modal analysis

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Authors: José E. Q. Souza, Marcio Fontana, Antonio C. C. Lima

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This paper presents analysis and characterization of a piezoelectric micro-generator for energy harvesting application. A low-cost experimental prototype was designed to operate as piezoelectric micro-generator in the laboratory. An input acceleration of 9.8m/s2 using a sine signal (peak-to-peak voltage: 1V, offset voltage: 0V) at frequencies ranging from 10Hz to 160Hz generated a maximum average power of 432.4μW (linear mass position = 25mm) and an average power of 543.3μW (angular mass position = 35°). These promising results show that the prototype can be considered for low consumption load application as an energy harvesting micro-generator.

Keywords: piezoelectric, micro-generator, energy harvesting, cantilever beam

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Authors: M. Khalid, G. N. Singh

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In this paper, we have considered the problem of estimation for population mean, on current (second) occasion in the presence of random non response in two-occasion successive sampling under two phase set-up. Modified exponential type estimators have been proposed, and their properties are studied under the assumptions that numbers of sampling units follow a distribution due to random non response situations. The performances of the proposed estimators are compared with linear combinations of two estimators, (a) sample mean estimator for fresh sample and (b) ratio estimator for matched sample under the complete response situations. Results are demonstrated through empirical studies which present the effectiveness of the proposed estimators. Suitable recommendations have been made to the survey practitioners.

Keywords: successive sampling, random non-response, auxiliary variable, bias, mean square error

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Authors: A. Danbaba

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Samurai Sudoku consists of five Sudoku square designs each having nine treatments in each row (column or sub-block) only once such the five Sudoku designs overlaps. Two or more Samurai designs can be joint together to give an extended Samurai design. In addition, two Samurai designs, each containing five Sudoku square designs, are mutually orthogonal (Graeco). If we superimpose two Samurai designs and obtained a pair of Latin and Greek letters in each row (column or sub-block) of the five Sudoku designs only once, then we have Graeco Samurai design. In this paper, simple method of constructing Samurai designs and mutually orthogonal Samurai design are proposed. In addition, linear models and methods of data analysis for the designs are proposed.

Keywords: samurai design, graeco samurai design, sudoku design, row or column swap

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Authors: H. R. Kamali, A. Sadegheih, M. A. Vahdat-Zad, H. Khademi-Zare

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In this paper, a single product, multi-echelon, multi-period closed loop supply chain is surveyed, including a variety of costs, time conditions, and capacities, to plan and determine the values and time of the components procurement, production, distribution, recycling and disposal specially for high-tech products that undergo a decreasing production cost and sale price over time. For this purpose, the mathematic model of the problem that is a kind of mixed integer linear programming is presented, and it is finally proved that the problem belongs to the category of NP-hard problems.

Keywords: closed loop supply chain, continuous price decrease, NP-hard, planning

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Authors: Francesca Schiavello

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This work aims to create a hybrid algorithm, combining Quantum Approximate Optimization Algorithm (QAOA) with an Evolutionary Algorithm (EA) in the place of traditional gradient based optimization processes. QAOA’s were first introduced in 2014, where, at the time, their algorithm performed better than the traditional best known classical algorithm for Max-cut graphs. Whilst classical algorithms have improved since then and have returned to being faster and more efficient, this was a huge milestone for quantum computing, and their work is often used as a benchmarking tool and a foundational tool to explore variants of QAOA’s. This, alongside with other famous algorithms like Grover’s or Shor’s, highlights to the world the potential that quantum computing holds. It also presents the reality of a real quantum advantage where, if the hardware continues to improve, this could constitute a revolutionary era. Given that the hardware is not there yet, many scientists are working on the software side of things in the hopes of future progress. Some of the major limitations holding back quantum computing are the quality of qubits and the noisy interference they generate in creating solutions, the barren plateaus that effectively hinder the optimization search in the latent space, and the availability of number of qubits limiting the scale of the problem that can be solved. These three issues are intertwined and are part of the motivation for using EAs in this work. Firstly, EAs are not based on gradient or linear optimization methods for the search in the latent space, and because of their freedom from gradients, they should suffer less from barren plateaus. Secondly, given that this algorithm performs a search in the solution space through a population of solutions, it can also be parallelized to speed up the search and optimization problem. The evaluation of the cost function, like in many other algorithms, is notoriously slow, and the ability to parallelize it can drastically improve the competitiveness of QAOA’s with respect to purely classical algorithms. Thirdly, because of the nature and structure of EA’s, solutions can be carried forward in time, making them more robust to noise and uncertainty. Preliminary results show that the EA algorithm attached to QAOA can perform on par with the traditional QAOA with a Cobyla optimizer, which is a linear based method, and in some instances, it can even create a better Max-Cut. Whilst the final objective of the work is to create an algorithm that can consistently beat the original QAOA, or its variants, due to either speedups or quality of the solution, this initial result is promising and show the potential of EAs in this field. Further tests need to be performed on an array of different graphs with the parallelization aspect of the work commencing in October 2023 and tests on real hardware scheduled for early 2024.

Keywords: evolutionary algorithm, max cut, parallel simulation, quantum optimization

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