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Extensive research on heuristic algorithms has proved their potential in solving complex optimization problems. However, it is not easy to choose the best heuristic technique for solving a particular problem. Fitness landscape analysis is used for understanding the problem characteristics based on which the best-suited algorithm for the problem can be chosen. Compared to the literature on discrete search spaces, only a few significant works have been undertaken on landscape analysis in continuous search spaces. Random walk (RW) algorithm has been used for generating sample points in the search space, and fitness landscape is created based on the relative fitness of the neighboring sample points. This paper proposes a chaos-based random walk algorithm, called as the chaotic random walk (CRW), applied in continuous search space to generate the landscape structure for a problem. The chaotic map is used to generate the chaotic pseudorandom numbers for determining variable scaled step size and direction of the proposed RW algorithm. Histogram analysis demonstrates better coverage of search space by the CRW algorithm compared to the simple and progressive random walk algorithms. In addition, we test the efficiency of the proposed method by quantifying the ruggedness and deception of a problem using entropy and fitness distance correlation measures. Experiments are conducted on the IEEE Congers on Evolutionary Computing 2013 benchmark functions in continuous search space having different levels of complexity. Extensive experiments indicate the capability for generating landscape structure on the continuous search space and efficiency of the proposed method to investigate the structural features of fitness landscapes.

Accurate optic disc (OD) segmentation is an important step in obtaining cup-to-disc ratio-based glaucoma screening using fundus imaging. It is a challenging task because of the subtle OD boundary, blood vessel occlusion and intensity inhomogeneity. In this Letter, the authors propose an improved version of the random walk algorithm for OD segmentation to tackle such challenges. The algorithm incorporates the mean curvature and Gabor texture energy features to define the new composite weight function to compute the edge weights. Unlike the deformable model-based OD segmentation techniques, the proposed algorithm remains unaffected by curve initialisation and local energy minima problem. The effectiveness of the proposed method is verified with DRIVE, DIARETDB1, DRISHTI-GS and MESSIDOR database images using the performance measures such as mean absolute distance, overlapping ratio, dice coefficient, sensitivity, specificity and precision. The obtained OD segmentation results and quantitative performance measures show robustness and superiority of the proposed algorithm in handling the complex challenges in OD segmentation.

Characterizing the petrophysical properties holds significant importance in shale oil reservoirs. Two-dimensional (2-D) nuclear magnetic resonance (NMR), a nondestructive and noninvasive technique, has numerous applications in petrophysical characterization. However, the complex occurrence states of the fluids and the highly non-uniform distributions of minerals and organic matter pose challenges in the NMR-based petrophysical characterization. A novel T1-T2 relaxation theory is introduced for the first time in this study. The transverse and longitudinal relaxivities of pore fluids are determined based on numerical investigation and experimental analysis. Additionally, an improved random walk algorithm is proposed to, on the basis of digital shale core, simulate the effects of the hydrogen index (HI) for the organic matter, echo spacing (TE), pyrite content, clay mineral type, and clay content on T1-T2 spectra at different NMR frequencies. Furthermore, the frequency conversion cross-plots for various petrophysical parameters influenced by the above factors are established. This study provides new insights into NMR-based petrophysical characterization and the frequency conversion of petrophysical parameters measured by laboratory NMR instruments and NMR logging in shale oil reservoirs. It is of great significance for the efficient exploration and environmentally friendly production of shale oil.

In this paper, iterative stochastic simulation algorithms for the Lamé equation describing the displacements of an isotropic elastic body are constructed. Three different stochastic methods are proposed: the first one is based on a global algorithm of random walk on spheres to compute the solution and its derivatives for an anisotropic diffusion equation. It does not use grids and does not require large amounts of RAM. The second method is based on a randomized algorithm for solving large systems of linear equations and requires the introduction of a grid. The third method is also grid-based and uses a random walk algorithm. All three methods implement an iterative process, at each step of which anisotropic diffusion equations are solved. The paper provides a comparative analysis of the proposed methods and discusses the limits of applicability of each of them.

For the petrophysics model of tight sandstones, the elastic modulus of their sandstone and mudstone components are often substituted with those of quartz and clay, which affects model accuracy. To solve this problem, we innovate an adaptive approach for model the rock physics characteristics of tight sandstone. First, based on the relationship between P- and S-wave velocities from well logs and the elastic modulus of the rocks, the equivalent elastic modulus of tight sandstone under saturated conditions is calculated. Next, The Lee model and the Gassmann equation were jointly used to determine the equivalent elasticity modulus of tight sandstone matrix. The upper and lower limits of the equivalent elasticity modulus for mudstone and sandstone are established using the mudstone content curve, the least-squares method and the Voigt–Reuss–Hill (VRH) model. We used the random-walk algorithm to accurately calculate the equivalent elastic modulus of the sandstone and mudstone components. Finally, using the accurately obtained elastic modulus of sandstone and mudstone, the equivalent elastic modulus of the matrix is calculated. The Kuster–Toksöz model is subsequently applied to compute the dry-frame bulk modulus and shear modulus of the rock. Following this, the Brie model is used to calculate the elastic modulus of the mixed fluid, thereby completing the construction of the rock physics model for the study area. The results demonstrate that our improved petrophysics model can predict the S-wave velocity curve with ≤15% errors relative to the true curve. When sweet spot prediction was performed using reservoir-sensitive parameter (Vp/Vs) derived from the petrophysics template, the agreement between the predictions and well-log data was 80%. Thus, our petrophysics model method can be used to predict tight gas reservoirs effectively and will aid efforts to improve petroleum exploration works in the study area.

Heuristic algorithms are effective methods for solving complex optimization problems. The optimal algorithm selection for a specific optimization problem is a challenging task. Fitness landscape analysis (FLA) is used to understand the optimization problem's characteristics and help select the optimal algorithm. A random walk algorithm is an essential technique for FLA in continuous search space. However, most currently proposed random walk algorithms suffer from unbalanced sampling points. This article proposes a Lévy flight-based random walk (LRW) algorithm to address this problem. The Lévy flight is used to generate the proposed random walk algorithm's variable step size and direction. Some tests show that the proposed LRW algorithm performs better in the uniformity of sampling points. Besides, the authors analyze the fitness landscape of the CEC2017 benchmark functions using the proposed LRW algorithm. The experimental results indicate that the proposed LRW algorithm can better obtain the structural features of the landscape and has better stability than several other RW algorithms.

Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.

This paper aims at developing a numerical algorithm for the chloride diffusivity of concrete containing spheroidal aggregates. In the algorithm, spheroidal aggregates of various sizes are generated for a given sieve curve and placed into a cubic simulation element. The mesostructure of concrete is reconstructed by surrounding each aggregate with an interfacial transition zone (ITZ). To increase the computational efficiency, an equivalent aggregate model (EAM) is built and the equivalent ITZ thickness and chloride diffusivity are derived analytically. The chloride diffusivity of concrete is estimated with the random walk algorithm. Finally, the validity of the numerical algorithm is verified with the experimental results obtained in this paper and collected from the literature and the effect of aggregate aspect ratio on the chloride diffusivity is evaluated quantitatively. Keywords: chloride diffusivity; equivalent aggregate model; random walk algorithm; spheroidal aggregate.

Lung cancer is the leading cause of cancer death worldwide. A lung nodule is the most common symptom of lung cancer. The analysis of lung cancer relies heavily on the segmentation of nodules, which aids in optimal treatment planning. However, because there are several lung nodules, accurate segmentation remains challenging. We propose an RW-T hybrid approach capable of segmenting all types of nodules, primarily externally attached nodules (juxta-pleural and juxta-vascular), and estimate the effect of nodule segmentation techniques to assess the quantitative Computer Tomography (CT) imaging features in lung adenocarcinoma. On 301 lung CT images from 40 patients with lung adenocarcinoma cases from the LungCT- Diagnosis dataset publicly available in The Cancer Imaging Archive, we used a random-walk strategy and a thresholding method to implement nodule segmentation (TCIA). We extracted two quantitative CT features from the segmented nodule using morphological techniques: convexity and entropy scores. The proposed method’s resultant segmented nodules are compared to the single-click ensemble segmentation method and validated using ground-truth segmented nodules. Our proposed segmentation approach had a high level of agreement with ground truth delineations, with a dice-similarity coefficient of 0.7884, compared to single-click ensemble segmentation, with a dice-similarity metric of 0.6407.

Fly ash is a by-product of coal-fired thermal power plants and offers great potential for the use of resources. To effectively improve the durability of reinforced concrete structures in marine environment and achieve waste to treasure, fly ash is widely used as a pozzolanic material due to its long-hydration characteristics and effects of micro-aggregate, micro-filling and secondary hydration. In this study, both the experimental investigation and numerical simulation are carried out to study the chloride transport characteristics of fly ash cement paste. The variation in chloride diffusivity with fly ash content, water-to-binder ratio and curing age up to 360 days is studied via accelerated conductivity measurement, and it is found that the above three experimental variables have a significant impact on the chloride diffusivity. For the influence of the dosage of fly ash, the optimum dosage is 30%. By introducing specific rules for the particle distribution, the fresh fly ash cement paste is first made. Based on the volume change characteristics of fly ash and cement particles after hydration, the vector hydration model of fly ash cement paste is established by considering the water shortage effect caused by hydration layer interference. After the accuracy of this hydration model is verified by the results from third-party experiments, the random walk algorithm is proposed to calculate the diffusion coefficient of the reconstructed mineral admixture cement paste. By comprehensive comparison with the experimental results from the third-party and self-conducted experiments, the numerical model for predicting the chloride diffusivity of fly ash cement paste is verified.