Hybrid Solution Technique Research Articles

Hybrid of monolithic and staggered solution techniques for the computational analysis of fracture, assessed on fibrous network mechanics

The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of interacting one-dimensional elements, such as truss-bars and beams. Failure may then be modeled as strong discontinuities in the displacement field that are directly embedded within the structural finite elements. As for other strain-softening materials, the tangent stiffness matrix can be non-positive definite, which diminishes the robustness of the solution of the coupled (monolithic) two-field problem. Its uncoupling, and thus the use of a staggered solution method where the field variables are solved alternatingly, avoids such difficulties and results in a stable, but sub-optimally converging solution method. In the present work, we evaluate the staggered against the monolithic solution approach and assess their computational performance in the analysis of fiber network failure. We then propose a hybrid solution technique that optimizes the performance and robustness of the computational analysis. It represents a matrix regularization technique that retains a positive definite element stiffness matrix while approaching the tangent stiffness matrix of the monolithic problem. Given the problems investigated in this work, the hybrid solution approach is up to 30 times faster than the staggered approach, where its superiority is most pronounced at large loading increments. The approach is general and may also accelerate the computational analysis of other failure problems.

Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products

This study introduces a fuzzy bi-level Decision Support System (DSS) to optimize a sustainable multi-level multi-product Supply Chain (SC) and co-modal transportation network for perishable products distribution. To this end, two integrated multi-objective Mixed Integer Linear Programming (MILP) models are proposed to formulate the problem. On-time delivery is taken into account as the main factor that determines model performance due to perishability of products. Optimizing the design of SC network using the first level of the proposed DSS, the transportation network configuration is provided optimally in the second level considering different modes and options. In order to contribute to the literature, mainly by addressing uncertainty and perishability, a hybrid solution technique based on possibilistic linear programming and Fuzzy Weighted Goal Programming (FWGP) approach is developed to accommodate our suggested bi-level model. This technique can deal with problem uncertainty while also ensuring the sustainability of the overall system. Lp-metric method is implemented along with three well-known quality indicators to assess the performance of the proposed solution method and quality of obtained solutions. Finally, three illustrative numerical examples are provided using the CPLEX solver to showcase the applicability of the proposed methodology and discuss the complexity of the model. Results demonstrate the efficiency of the proposed methodology in finding optimal solutions compared to Lp-metric method, such that it is able to treat a problem with more than 2.2 million variables and 1.3 million constraints in 1093.08 s.

Hybrid Classical-Quantum Optimization Techniques for Solving Mixed-Integer Programming Problems in Production Scheduling

Quantum computing (QC) holds great promise to open up a new era of computing and has been receiving significant attention recently. To overcome the performance limitations of near-term QC, utilizing the current quantum computers to complement classical techniques for solving real-world problems is of utmost importance. In this paper, we develop QC-based solution strategies that exploit quantum annealing and classical optimization techniques for solving large-scale scheduling problems in manufacturing systems. The applications of the proposed algorithms are illustrated through two case studies in production scheduling. First, we present a hybrid QC-based solution approach for the job-shop scheduling problem. Second, we propose a hybrid QC-based parametric method for the multi-purpose batch scheduling problem with a fractional objective. The proposed hybrid algorithms can tackle optimization problems formulated as mixed-integer linear and mixed-integer fractional programs, respectively, and provide feasibility guarantees. Performance comparison between state-of-the-art exact and heuristic solvers and the proposed QC-based hybrid solution techniques is presented for both job-shop and batch scheduling problems. Unlike conventional classical solution techniques, the proposed hybrid frameworks harness quantum annealing to supplement established deterministic optimization algorithms and demonstrate performance efficiency over standard off-the-shelf optimization solvers.

Charge‐Current Output in Plasma‐Immersed Hydrogen Atom with Noncentral Interaction

AbstractA theoretical investigation on the charge‐currents and induced magnetizations of hydrogen atoms with noncentral interaction, immersed in a plasma environment, under the influence of spherical encompassing is performed. The Hartmann potential for noncentral interaction is considered, but it is modified due to the plasma‐embedded hydrogen atom. The interactions in plasma are delineated by keeping in view the more general exponential cosine screened Coulomb (MGECSC) potential which reproduces more general and detailed outcomes. The shielding effect of the plasma environment is regarded by modifying the Hartmann potential through the MGECSC potential. Thus, the hydrogen atom is considered to be under the influence of the plasma modified Hartmann (PMH) potential. While the numerical tridiagonal matrix method (TMM) is employed due to the difficulty of analytical solution to the radial wave equation in nonrelativistic scheme including PMH potential, a hybrid solution technique is preferred by using asymptotic iteration method (AIM) to solve the angular wave equation. This study provides a detailed analysis of the plasma shielding, spherical confinement, and noncentral effect on the production and control of charge‐currents and induced magnetizations. In this analysis, the altenativeness to each other of the plasma environment, spherical encompassing, and noncentral effect is also evaluated, and suggestions are made for related application studies.

Evaluating the Usable-Security of Healthcare Software Through Unified Technique of Fuzzy Logic, ANP and TOPSIS

The current research efforts in the security domain are essentially inspired by the intention to ensure both healthcare software's security and usability. Practitioners are continuously working on techniques that can optimise security while affording the ease of use. Inspite of the numerous efforts by the developers and security experts in this context, the level of usability-security is not the same as it should be. Furthermore, it is important to do more work on the most effective strategies for evaluating and increasing the usable-security of healthcare technology. Quantitative usability and security assessment is an important part of increasing the standards of software security especially with regard to software used in healthcare. This study's objective, in particular, is to evaluate the usability-security of healthcare software. Thereafter, based on the empirical analysis of comprehensive data, the study recommends the strategies that would facilitate in designing healthcare software with optimum security while preserving its' usability. Decision makers often find it difficult to integrate highly secure software with maximum usability while developing the software. Hence, this research endeavour enlists the assimilation of usability and safety with their contributory attributes. Moreover, this study proposes the use of a novel technique of combining the Analytic Network Method (ANP), Fuzzy Sets (FS), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to test usability together with security. The researchers employed the suggested methodology on six applications of the hospital management systems in Mecca, Saudi Arabia, to ascertain the utility of the FS-AHP-TOPSIS hybrid solution technique. Usability results along with security assessment corroborated that the most accurate and effective method for evaluating the usable-security of healthcare applications will be this innovative hybrid approach. Most relevantly, these findings will be useful in the security management without impacting the usability for the end users.

On Neighborhood Structures and Repair Techniques for Blocking Job Shop Scheduling Problems

The job shop scheduling problem with blocking constraints and total tardiness minimization represents a challenging combinatorial optimization problem of high relevance in production planning and logistics. Since general-purpose solution approaches struggle with finding even feasible solutions, a permutation-based heuristic method is proposed here, and the applicability of basic scheduling-tailored mechanisms is discussed. The problem is tackled by a local search framework, which relies on interchange- and shift-based operators. Redundancy and feasibility issues require advanced transformation and repairing schemes. An analysis of the embedded neighborhoods shows beneficial modes of implementation on the one hand and structural difficulties caused by the blocking constraints on the other hand. The applied simulated annealing algorithm generates good solutions for a wide set of benchmark instances. The computational results especially highlight the capability of the permutation-based method in constructing feasible schedules of valuable quality for instances of critical size and support future research on hybrid solution techniques.

A hybrid integer grey programming for an integrated problem of project selection and scheduling with interval data

Projects are inherently subject to uncertainty since in most cases, the information at hand is either approximate or partial. Grey numbers can handle the uncertainty in projects without requiring a predefined membership or probability function. The current paper proposes a hybrid solution technique for the integrated problem of project selection and scheduling with interval grey data. The presented method combines the concept of grey programming with branch and bound algorithm to achieve Pareto interval solutions. The algorithm is then applied to a grey bi-objective project selection and scheduling model. Additional experiments are carried out regarding the effects of grey weights and objective weights on the goal values. Moreover, the proposed algorithm is compared with fuzzy goal programming method. The results indicate that the developed approach has more precision than fuzzy programming and can achieve acceptable alternate solutions for small to medium scale problems.

An Integrated Decision Making Model for Manufacturing Cell Formation and Supplier Selection

Optimization of the complete manufacturing and supply process has become a critical ingredient for gaining a competitive advantage. This article provides a unified mathematical framework for modeling manufacturing cell configuration and raw material supplier selection in a two-level supply chain network. The commonly used manufacturing design parameters along with supplier selection and a subcontracting approach are incorporated into our mathematical model. To the authors’ knowledge, there is no single model which integrates all of these attributes simultaneously. A sensitivity analysis is also performed to study the effects of this integration. An efficient meta-heuristic based on Genetic Algorithm (GA) search procedure is employed to effectively solve the model in medium and large scales. We improve the GA search mechanism by proper combination of linear programming optimization technique and GA in a cooperative framework. Computational results show that our hybrid solution technique can find satisfactory solutions in a timely manner.

Hybrid solution techniques for structural acoustics

Ira Dyer’s structural acoustics research at MIT emphasized developing an understanding of wave interaction mechanisms and the role of structural complexity in dictating energy transport, dissipation, and radiation to the surrounding media. His work stressed a combination of experimentation and analytic-numeric methods to delineate the essential wave propagation mechanisms governing the response of the structure and the radiated field. Here we present an extension of research Ira led to study acoustic scattering from internally loaded shell structures. Hybrid analysis techniques employing wave transmission methods to represent plate and shell structures, and analytic or finite element methods to represent attached structures provide a means to discern the partitioning between wave types comprising the response. The method directly represents all allowable wave types and quantifies their displacement functions and dispersion behavior enabling detailed evaluation of energy transport mechanisms. Interaction loads produced at attached structures are computed using shell structure Green’s function matrices, impedance matrix descriptions of the attachments, and unloaded shell response vectors. The method is illustrated for marine pile driving and aerospace liftoff applications. Broadband impulse response maps are shown to illustrate the temporal evolution of the field over the structure and complement frequency domain evaluations providing further physical insight.

A symplectic analytical wave propagation model for damping and steady state forced vibration of orthotropic composite plate structure

• A symplectic analytical wave model is proposed for damping of orthotropic composites. • The vibration of composites is solved by a hybrid wave and finite element model. • The relationship between the wave damping and the modal damping is revealed. An analytical wave propagation model is proposed in this paper for damping and steady state forced vibration of orthotropic composite plate structure by using the symplectic method. By solving an eigen-problem derived in the symplectic dual system of free bending vibration of orthotropic rectangular thin plates, the wave shape of plate is obtained in symplectic analytical form for any combination of simple boundary conditions along the plate edges. And then the specific damping capacity of wave mode is obtained symplectic analytically by using the strain energy theory. The steady state forced vibration of built-up plates structure is calculated by combining the wave propagation model and the finite element method. The vibration of the uniform plate domain of the built-up plates structure is described using symplectic analytical waves and the connector with discontinuous geometry or material is modeled using finite elements. In the numerical examples, the specific damping capacity of orthotropic rectangular thin plate with three different combinations of boundary condition is first calculated and analyzed. Comparisons of the present method results with respect to the results from the finite element method and from the Rayleigh–Ritz method validate the effectiveness of the present method. The relationship between the specific damping capacity of wave mode and that of modal mode is expounded. At last, the damped steady state forced vibration of a two plates system with a connector is calculated using the hybrid solution technique. The availability of the symplectic analytical wave propagation model is further validated by comparing the forced response from the present method with the results obtained using the finite element method.

A comprehensive mathematical model for dynamic cellular manufacturing system design and Linear Programming embedded hybrid solution techniques

Considering the ever changing market conditions, it is essential to design responsive and flexible manufacturing systems. This study addresses the multi-period Dynamic Cellular Manufacturing System (DCMS) design problem and introduces a new mathematical model. The objective function of the mathematical model considers inter-cell and intra-cell material handling, machine purchasing, layout reconfiguration, variable and constant machine costs. Machine duplication, machine capacities, operation sequences, alternative processing routes of the products, varying demands of products and lot splitting are among the most important issues addressed by the mathematical model. It makes decisions on many system related issues, including cell formation, inter- and intra-cell layout, product routing and product flow between machines. Due to the complexity of the problem, we suggest two heuristic solution approaches that combine Simulated Annealing (SA) with Linear Programming and Genetic Algorithm (GA) with Linear Programming. The developed approaches were tested using a data set from the literature. In addition, randomly generated test problems were also used to investigate the performance of the hybrid heuristic approaches. A problem specific lower bound mathematical model was also proposed to observe the solution quality of the developed approaches. The suggested approaches outperformed the previous study in terms of both computational time and the solution quality by reducing the overall system cost.

Fast and accurate earthquake location within complex medium using a hybrid globallocal inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares (RMS) error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Fréchet derivatives to simultaneously update all possible initial source parameters around most local minima (including the global minimum) in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to find the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.

Probability Density Function (PDF) Simulation of Turbulent Reactive Gas‐Solid Flow in a Riser

AbstractA hybrid Lagrangian‐Eulerian methodology is developed for the numerical simulation of turbulent reactive gas‐solid flow. The SO2‐NOx Adsorption Process (SNAP) in a riser reactor with dilute gas‐solid flow is taken as a test case. A three‐dimensional time‐dependent simulation is performed. By using the transported composition PDF method [1], modeling of the mean chemical source term and mass transfer terms in the gas‐solid flow model equations is no longer needed. A notional particle‐based Monte‐Carlo algorithm is used to solve the transported composition PDF equations. A Finite‐Volume technique is used to calculate the hydrodynamic fields from the Reynolds Averaged Navier Stokes (RANS) equations combined with the k‐ϵ turbulence model for the gas phase and the Kinetic Theory of Granular Flow (KTGF) for the solid phase [2]. The newly developed hybrid solution technique is tested with the SNAP chemistry that has a total of 13 scalars (i.e., 5 gas phase components and 8 solid phase species) for which the composition fields of the reactive species are calculated. A good agreement between simulated and experimental gas‐outlet composition of a demonstration unit is obtained.

Inverse Characterization of NAPL Source Zones

This work presents a possible tool for inverse characterization of NAPL (nonaqueous phase liquid) source zones in terms of contaminant mass flux. A hybrid solution technique was applied that considers contaminant transport through a vertical flux plane. The hybrid solution technique takes advantage of the robust solution capabilities of simulated annealing (SA) and the uncertainty estimation capabilities of minimum relative entropy (MRE). The coupled technique (SA-MRE) provides probability density functions and confidence intervals that would not be available from an independent SA algorithm, and they are obtained more efficiently than if provided by an independent MRE algorithm. The SA-MRE method was used to characterize a NAPL source zone that was emplaced in a three-dimensional aquifer model. When dissolution experiments were complete, the aquifer model was excavated, and the distribution of NAPL zones was recorded using digital images of excavation grids. The excavation images were compiled into a three-dimensional representation of the source zone for comparison with and validation of modeling results.

Dynamic interaction between the soil and an anchored sheet pile during seismic excitation

AbstractA subdomain approach for dynamic soil–structure interaction is proposed for the linear elastic seismic analysis of an anchored sheet pile, retaining a horizontally layered soil on rigid bedrock. A hybrid solution technique is used, employing a finite element formulation for the generalized sheet pile, a thin layer formulation for the soil and a direct stiffness formulation for the tieback; the displacement vectors of the sheet pile and the soil are decomposed, using the eigenmodes of the sheet pile and the propagating or decaying modes in the soil. The discretization can be limited to the interface(s), where pointwise continuity of the displacements is enforced, whereas a weak variational formulation is used for the stress equilibrium. The solution technique is illustrated by means of a numerical example, where the harmonic response of a flexible anchored sheet pile is considered and compared to the case where no tieback is present. Copyright © 2002 John Wiley & Sons, Ltd.

Transient analytic and numerical results for the fluid–solid interaction of prolate spheroidal shells.

A transient solution is presented that models the fluid–solid interaction of a thin elastic prolate spheroidal shell loaded end-on by a nonconservative acoustic shock wave. Solutions to the Lagrangian equations of motion are provided for the normal and tangential shell displacement fields, as well as for the incident, scattered, and radiated fluid pressure fields. The temporally and spatially dependent shell displacement and fluid pressure fields are expressed modally in terms of an orthonormal basis that is selected specifically to satisfy the kinematic boundary conditions at the fluid–solid interface identically. Further, the modal representations for the shell displacements resolve the boundary conditions imposed by the problem configuration; and the modal representations for the fluid field satisfy causality. The solutions are developed in terms of prolate spheroidal angular and radial wave functions. For both analytic and computational reasons, the shell displacement and fluid pressure fields are ultimately expressed in terms of Legendre polynomials and modified spherical Bessel functions of the first and third kinds. The resulting solutions are exact within the limit of series solutions. A novel analytic/numerical hybrid solution technique is introduced for solving the inhomogeneous coupled PDE’s; the spectral method is a Galerkin variation. The explicit analytic solutions converge to the exact solution of the actual coupled differential equations over the entire temporal and spatial domains both in the structure and in the fluid. Series truncation is postponed until the final expressions and their mathematical structure are known, thereby ensuring that all relevant physics has been correctly modeled having taken full advantage of inherent symmetries. Numerical results for the free vibrations and for the transient fluid–solid interactions of a fluid-loaded prolate spheroidal shell are presented. Specifically, the axisymmetric in-vacuo nondimensionalized frequencies are tabulated for three characteristic cases corresponding to low, intermediate, and high aspect ratio geometries. The fluid loading is shown to shift the frequencies, as well as introduce additional structural frequencies. Plots of the shell displacements, velocities, accelerations, strains, and strain rates are presented for the submerged shock-loaded low aspect ratio case. Insights into the qualitative and quantitative effects of the fluid on the structural response are revealed. DOE-macsyma was used extensively to develop and verify the solutions to this problem. [This work was performed under the auspices of DOE by LLNL under Contract No. W-7405-Eng-48.]

Wave interaction with rubble toe protection

A model is formulated to predict wave-induced flows and pressures in rubble toes fronting a seawall or caisson. The model is based on the linearized Forchheimer equation of fluid motion in the coarse, granular medium. The toe may be a multilayered rubble mound with arbitrary material properties and cross-section. The waves are taken to be simple periodic and normally incident to the structure. The boundary value problem is solved using a hybrid solution technique which employs the boundary element method within the rubble toe and near field matched with an analytical far field solution. Results indicate that the reflection coefficient is inversely related to the size and dissipation of the rubble toe and that long waves are more highly reflected. The presence of the rubble toe may result in wave pressures on the seawall greater than if no toe was present. This yields a corresponding increase in the wave-induced forces and mud line moments. The force may be increased by as much as 20%. The theory was verified by large-scale experiments. The comparison between theoretical and experimental results of the reflection coefficient and the dynamic pressure inside the rubble toe are in reasonable agreement.

A finite element‐finite difference solution of three‐dimensional viscous‐inviscid interaction

AbstractBased on the concept of viscous‐inviscid interaction, a hybrid solution technique in studying external flow past three‐dimensional bodies is developed. The finite element method is employed to solve the inviscid part of the flow and the finite difference technique is utilized in solving the viscous part of the flow. This hybrid technique is applied to study the flow past a swept bump on a circular cylinder. The 8‐noded trilinear brick elements are used for the finite element formulation of the problem where the flow is considered potential. In the viscous part, however, three‐dimensional boundary‐layer equations simplified with small cross‐flow assumption and expressed in the surface co‐ordinates are solved utilizing the finite difference method. Numerical studies are made for both the laminar and the turbulent flow cases using the boundary‐layer edge velocity distribution obtained through inviscid solution. The results are compared with the available experimental data. The boundary‐layer edge velocity distribution is in good agreement with the experimental data; the prediction of the separation point for the laminar case is the same. For the turbulent flow case, the velocity profiles in the flow direction when compared to the measurements are overall in reasonably good agreement, and the discrepancies are due to small cross‐flow assumption. However, the agreement concerning the wall shear stress component in the flow direction is more satisfactory.

Convergence properties of Newton's method for the solution of the semiconductor transport equations and hybrid solution techniques for multidimensional simulation of VLSI devices

In this paper the Kantorovich theorem has been modified to evaluate the simple sufficient conditions for the quadratic convergence of Newton's method. By the modified Kantorovich theorem, convergence properties of Poisson's equation and more generally total transport equations have been investigated. It is shown that sufficient condition of quadratic convergence of Newton's method can be satisfied when the maximum magnitude norm of the correction vectors becomes less than 0.5 kT/q for the Poisson's equation, while for the total carrier transport equations this criterion becomes 0.25 kT/q. Under the light of these convergence criteria, a hybrid solution algorithm is defined which employs both the coupled and decoupled solution techniques. This method and a variable mesh concept are combined to achieve dramatic reduction in CPU time for the simulation of VLSI devices. It is demonstrated that overall CPU time is reduced by a factor of two to eight by employing these techniques.