Efficient Solution Procedure Research Articles

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. From a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

Improved softened truss model for prestressed concrete composite box girders with corrugated steel webs under pure torsion

This paper aimed at developing a theoretical model for prestressed composite box girders with corrugated steel webs (CSW) under pure torsion, based on the combined action softened truss model (CA-STM). The equilibrium equations and materials' constitutive laws were modified, considering the relationship between the initial stress and strain generated by prestressing. According to the yield state of the CSW, proper shear flow conditions were also introduced to describe the deformation coordination relationship between the CSW and concrete slabs. The effect of the width of cantilever slabs on the torsional performance of composite box girders was investigated. An optimized algorithm was employed to solve the CA-STM, resulting in a more efficient and stable solution procedure. The validity of the model was confirmed through the available experimental data. Results showed that the prediction accuracy of the improved CA-STM for depicting entire torsional behavior is great, when considering the reasonable shear strain relationship and modified initial torque calculation formula.

A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme

This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a systematic and efficient manner. Furthermore, a significant advantage of this procedure is its consistency, achieved by excluding arbitrary coefficients from the formulations employed. The effectiveness of the proposed procedure is demonstrated through several numerical examples. In the majority of the examples, it is observed that the stress prediction error is reduced by more than half after applying the proposed procedure.

An efficient entropy-based stopping rule for mitigating risk factors in supply nets

Potential supply-net risk factors include capacity issues, currency volatility, design changes, frequent changes in tax regulations, unsafe information systems, and port shutdowns. Such risk factors make it challenging for decision makers to design efficient risk-management procedures and minimize the operational costs associated with mitigating these risks. Since complete information about all risks is generally not available, we utilize an axiomatic approach, based on the notion of entropy, to develop an efficient solution procedure. The strategy involves developing a stopping rule that enables the decision maker to decide online whether or not to continue investing in the acquisition of information about risk factors. The problem is formulated as a non-linear integer optimization model. We develop sufficient conditions for the entropy function such that a unique global solution is obtained.A case study that addresses risks associated with the transportation of aquatic products in refrigerated containers demonstrates the superior performance of the stopping rule relative to a standard risk-assessment procedure. In addition, numerous computerized experiments are carried out, under different problem settings, to compare the stopping rule with an anticipative optimum. The cost incurred when using the stopping rule is found to be no more than 0.4% higher than the cost of the anticipative optimum (the lower bound for the objective). These findings clearly demonstrate the efficiency of the proposed stopping rule for a wide range of problem sizes.

SAGE: Stealthy Attack Generation in cyber-physical systems

Cyber-physical systems (CPSs) have been increasingly attacked by hackers. CPSs are especially vulnerable to attackers that have full knowledge of the system's configuration. Therefore, novel anomaly detection algorithms in the presence of a knowledgeable adversary need to be developed. However, this research is still in its infancy, due to limited attack data availability and test beds. By proposing a holistic attack modeling framework, we aim to show the vulnerability of existing detection algorithms and provide a basis for novel sensor-based cyber-attack detection. Stealthy Attack GEneration (SAGE) for CPSs serves as a tool for cyber-risk assessment of existing systems and detection algorithms for practitioners and researchers alike. Stealthy attacks are characterized by malicious injections into the CPS through input, output, or both, which produce bounded changes in the detection residue. By using the SAGE framework, we generate stealthy attacks to achieve three objectives: (i) Maximize damage, (ii) Avoid detection, and (iii) Minimize the attack cost. Additionally, an attacker needs to adhere to the physical principles in a CPS (objective (iv)). The goal of SAGE is to model worst-case attacks, where we assume limited information asymmetries between attackers and defenders (e.g., insider knowledge of the attacker). Those worst-case attacks are the hardest to detect, but common in practice and allow understanding of the maximum conceivable damage. We propose an efficient solution procedure for the novel SAGE optimization problem. The SAGE framework is illustrated in three case studies. Those case studies serve as modeling guidelines for the development of novel attack detection algorithms and comprehensive cyber-physical risk assessment of CPSs. The results show that SAGE attacks can cause severe damage to a CPS, while only changing the input control signals minimally. This avoids detection and keeps the cost of an attack low. This highlights the need for more advanced detection algorithms and novel research in cyber-physical security.

New resource-constrained project scheduling instances for testing (meta-)heuristic scheduling algorithms

The resource-constrained project scheduling problem (RCPSP) is a well-known scheduling problem that has attracted attention since several decades. Despite the rapid progress of exact and (meta-)heuristic procedures, the problem can still not be solved to optimality for many problem instances of relatively small size. Due to the known complexity, many researchers have proposed fast and efficient meta-heuristic solution procedures that can solve the problem to near optimality. Despite the excellent results obtained in the last decades, little is known why some heuristics perform better than others. However, if researchers better understood why some meta-heuristic procedures generate good solutions for some project instances while still falling short for others, this could lead to insights to improve these meta-heuristics, ultimately leading to stronger algorithms and better overall solution quality.In this study, a new hardness indicator is proposed to measure the difficulty of providing near-optimal solutions for meta-heuristic procedures. The new indicator is based on a new concept that uses the σ distance metric to describe the solution space of the problem instance, and relies on current knowledge for lower and upper bound calculations for problem instances from five known datasets in the literature.This new indicator, which will be called the σD indicator, will be used not only to measure the hardness of existing project datasets, but also to generate a new benchmark dataset that can be used for future research purposes. The new dataset contains project instances with different values for the σD indicator, and it will be shown that the value of the σ distance metric actually describes the difficulty of the project instances through two fast and efficient meta-heuristic procedures from the literature.

Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations

In this paper, a new orthogonal basis for the space of cubic splines has been introduced. A linear combination of cubic orthogonal splines is considered to approximate the functions in which the coefficients are calculated with numerically stable formulae. Applications to the numerical solutions of some parabolic partial differential equations are given, in which the approximations are obtained using the first and second integral of orthogonal splines which leads to an efficient solution procedure. The convergence analysis in the approximate scheme is investigated. A comparison of the obtained numerical solutions with some other papers indicates that the presented method is reliable and yields result with good accuracy. The main parts of our study are as follows:•We propose a robust approach based on the orthogonal cubic splines procedure in conjunction with the operational matrix.•The convergence in the approximate scheme is analyzed.•Numerical examples show that the proposed method is very accurate.

A fully-implicit hybridized discontinuous Galerkin spectral element method for two phase flow in petroleum reservoirs

A hybridized discontinuous Galerkin method with high order spectral element discretization is presented for modeling multiphase immiscible 2D fluid flow in petroleum reservoir simulations. The time dependent nonlinear governing equations for reservoir simulation are presented, and a fully coupled implicit time stepping procedure is implemented using a high order W-Rosenbrock algorithm. For incompressible fluids considered in the present study, the governing PDE's include an elliptic PDE for the pressure field and a parabolic convective diffusion equation for the saturation (water volume fraction) in a two phase oil-water system. The PDE systems are coupled through the highly nonlinear relative permeability and capillary pressure functions relating the fluid velocities of individual species to the individual species pressures and saturations. With HDG/spectral element (HDGSEM) spatial discretization of the coupled governing equations, the system constitutes an index 1 differential algebraic equation. It is shown that the W-Rosenbrock algorithm in combination with the HDGSEM method yields an efficient and effective solution procedure which demonstrates robust, high order temporal accuracy.Numerous physical tests cases are presented demonstrating that the versatility of this approach is sufficient to address the challenges in modeling heterogeneous permeability fields and geologic features of arbitrary shape with discontinuous permeability functions. It is also capable of resolving the sharp time dependent displacement fronts in oil-water systems encountered in secondary oil recovery. It is demonstrated that the high order polynomial basis functions (up to 12th order) used in the HDGSEM algorithm have the ability to resolve complex geometry and achieve accurate results utilizing a simple Cartesian mesh for non-conforming geological features. Eliminating the need to re-grid and conform the mesh to the boundaries of different geological features greatly simplifies the workflow for petroleum engineers.

A game-theoretic approach for pollution control initiatives

There are numerous regional, national, and international efforts to establish mechanisms to curb pollution and emissions. In this paper, we mainly focus on emissions trading systems. Using a static Cournot oligopoly game, we investigate a multi-product multi-pollutant market in which several supply chains compete in a non-cooperative manner in their product markets. This study characterizes conditions under which an efficient solution procedure converges to the unique Nash equilibrium of the oligopoly. Meanwhile, its partners establish a cooperative triopoly game within each supply chain in a nonsuperadditive characteristic function form. Drawing on the cooperative game theory literature, we provide a closed-form solution for a rational distribution of joint rewards between the supply chain’s partners.

A semi-Lagrangian relaxation heuristic algorithm for the simple plant location problem with order

The Simple Plant Location Problem with Order (SPLPO) is a variant of the Simple Plant Location Problem (SPLP) where the customers have preferences over the facilities that will serve them. In particular, customers define their preferences by ranking each of the potential facilities from the most preferred to the least preferred. Even though the SPLP has been widely studied in the literature, the SPLPO, which is a harder model to deal with, has been studied much less and the size of instances that can be solved is very limited. In this article, we study a Lagrangian relaxation of the SPLPO model and we show that some properties previously studied and exploited to develop efficient SPLP solution procedures can be extended for their use in solving the SPLPO. We propose a heuristic method that takes a Lagrangian relaxation solution as the starting point of a semi-Lagrangian relaxation algorithm. Finally, we include some computational studies to illustrate the good performance of this method, which quite often ends with the optimal solution.

Multi-objective non-linear solid transportation problem with fixed charge, budget constraints under uncertain environments

ABSTRACT Transportation-based models are widely used to solve real-life problems such as supply chain problems, inventory level problems, business models, management problems, etc. The parameters of these problems have been conventionally measured as deterministic. However, these parameters have vagueness due to the uncertainty in the data sets. Such uncertainty of the parameters is generally measured using randomness (probability theory) or fuzziness (fuzzy theory), with certain assumptions and limitations. Closed intervals interpretation is another concept to deal with the uncertainties of real-world issues in recent decades, avoiding the limitations in probability theory and fuzzy set theory. This study formulates a fixed-charged multi-objective non-linear solid transportation with parameters such as availability of items, conveyance capacity, transportation cost, requirement, and budget for destinations in the form of closed intervals, where objectives are minimization of total transportation cost and action of time under the restriction over budget. An efficient solution procedure is developed with the help of interval analysis based on the parametric perception of intervals. Initially, the objective functions are converted into a crisp function using multiple integrations, and as a result, the problem is converted into a deterministic multi-objective non-linear programming problem. In addition, a real-world numerical problem is considered for testing the developed solution process for greater comprehension and clarity.

A Chance-Constrained Two-Echelon Vehicle Routing Problem with Stochastic Demands

Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit within the second-echelon vehicle capacity with a high probability. We propose two efficient solution procedures based on column generation. Key to the efficiency of these procedures is the underlying labeling algorithm to generate new columns. We propose a novel labeling algorithm based on simultaneous construction of second-echelon routes and a labeling algorithm that builds second-echelon routes sequentially. To further enhance the performance of the solution procedure, we use statistical inference tests to ensure that the chance constraints are met. We reduce the number of customer combinations for which the chance constraint needs to be verified by imposing feasibility bounds on the stochastic customer demands. With these bounds, the runtimes of the labeling algorithms are reduced significantly. The novel labeling algorithm, statistical inference, and feasibility bounds can also be applied to dependent, correlated, and data-driven (scenario-based) demand distributions. Finally, we show the value of the stochastic formulation in terms of improved solution cost and guaranteed feasibility of second-echelon routes. Funding: This work was funded by the Dutch Research Council (NWO) DAREFUL project [Grant 629.002.211] and was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1162 .

A complemented multiaxial creep constitutive model for materials with different properties in tension and compression

A complemented multiaxial creep constitutive model is proposed in this paper. The model is able to describe the different creep behaviors in tension and compression under a complex multiaxial stress state. To improve the convergence and adaptability for large-scale structures in engineering, a complemented constitutive model is established by complementing the shear part of the creep constitutive matrixes in principal space through a limitation process. The finite element method and forward Euler method are used to establish the numerical calculation framework. Efficient solution procedures are also proposed and implemented. Room temperature creep experiments of titanium alloy Ti–6Al–3Nb–2Zr–1Mo are performed. It is found that titanium alloy has different creep properties in tension and compression. The numerical results show that the proposed creep constitutive model and numerical calculation framework are in good agreement with the experimental results. The response of each specific creep strain component under a complex stress multiaxial state can be accurately calculated, and the different properties of the creep response in tension and compression in different directions are reflected.

Hydrodynamic force on a ship floating on the water surface near a semi-infinite ice sheet

The hydrodynamic problem of wave interaction with a ship floating on the water surface near a semi-infinite ice sheet is considered based on the linearized velocity potential theory for fluid flow and the thin elastic plate model for ice sheet deflection. The properties of an ice sheet are assumed to be uniform, and zero bending moment and shear force conditions are enforced at the ice edge. The Green function is first derived, which satisfies both boundary conditions on the ice sheet and free surface, as well as all other conditions apart from that on the ship surface. Through the Green function, the differential equation for the velocity potential is converted into a boundary integral equation over the ship surface only. An extended surface, which is the waterplane of the ship, is introduced into the integral equation to remove the effect of irregular wave frequencies. The asymptotic formula of the Green function is derived and its behaviors are discussed, through which an approximate and efficient solution procedure for the coupled ship/wave/ice sheet interactions is developed. Extensive numerical results through the added mass, damping coefficient and wave exciting force are provided for an icebreaker of modern design. It is found that the approximate method can provide accurate results even when the ship is near the ice edge, through which some insight into the complex ship/ice sheet interaction is investigated. Extensive results are provided for the ship at different positions, for different ice sheet thicknesses and incident wave angles, and their physical implications are discussed.

Technical Note—A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems

Analyzing Capacitated Two-Echelon Systems with Permutation-Dependent Separability Capacitated multiechelon systems are common in practice due to the escalating costs of labor and advanced manufacturing technology. However, identifying the optimal replenishment policies for such systems is a largely open area of research due to the intrinsic complexity, especially when there is an upstream bottleneck. In “A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems”, Shen, Yu, and Huh propose a new approach, that is, permutation-dependent separability, to tackle a capacitated two-echelon system in which the capacity of upstream stage can be the bottleneck. They show that the value function for the capacitated two-echelon system in each period is permutation-dependent separable, and that for each echelon, a permutation-dependent echelon base stock policy is optimal. The authors also develop efficient solution procedures on how to obtain the optimal policy.

A differential evolution algorithm for the customer order scheduling problem with sequence-dependent setup times

Although the customer order scheduling problem to minimize the total completion time has received a lot of attention from researchers, the literature has not considered so far the case where there are sequence-dependent setups between jobs belonging to different orders, a case that may occurs in real-life scenarios. For this NP-hard problem we develop a novel efficient approximate solution procedure. More specifically, we develop an innovative discrete differential evolution algorithm where differential mutations are performed directly in the permutation space and that uses a novel, parameter-free, restart procedure. The so-obtained solutions are improved by two proposed local search mechanisms that employ problem-specific, heuristic dominance relations. We carry out an extensive computational experience with randomly generated test instances to compare our proposal with existing algorithms from related problems. In these experiments, the proposed algorithm obtains the best results in terms of their average relative percentage deviation and success rate. Furthermore, an analysis of variance test, followed by a Tukey’s test, confirms the excellent performance of the algorithm proposed.

A risk-averse two-stage stochastic programming model for a joint multi-item capacitated line balancing and lot-sizing problem

In this paper, a comprehensive production planning problem under uncertain demand is investigated. The problem intertwines two NP-hard optimization problems: an assembly line balancing problem and a capacitated lot-sizing problem. The problem is modelled as a two-stage stochastic program assuming a risk-averse decision maker. Efficient solution procedures are proposed for tackling the problem. A case study related to mask production is presented. Several insights are provided stemming from the COVID-19 pandemic. Finally, the results of a series of computational tests are reported.

Natural frequency responses of hybrid polymer/carbon fiber/FG-GNP nanocomposites paraboloidal and hyperboloidal shells based on multiscale approaches

This paper is devoted to obtain the vibrational behavior of doubly curved shells with paraboloidal and hyperboloidal geometries using an efficient semi-analytical solution method. To obtain the governing differential equations of the shells, the First-order Shear Deformation Theory (FSDT) is used. In addition, the shell structure is composed of a new hybrid three phases nanocomposite material. The material includes three parts: (1) polymer matrix, (2) carbon macroscale fiber, and (3) Graphene NanoPlatelets (GNP) nanoscale filler. Three different multiscale approaches including (1) bridging model, (2) Mori-Tanaka scheme, and (3) generalized self-consistent model are employed for homogenization of hybrid matrix and macroscale carbon fibers. The governing equation of motions are obtained using Hamilton's principles and Green-Gauss theory. Afterwards, an efficient semi-analytical solution procedure entitled Generalized Differential Quadrature Method (GDQM) is used for solving the governing differential equations of the structure. Finally, the frequency parameter of the structure is achieved for different states of boundary conditions and geometric properties. Moreover, the results are verified with the responses of other references obtained for a paraboloidal (Cap) shell structure. It is worth mentioning that the effect of homogenization approach, boundary conditions, volume fraction of carbon fibers and distribution pattern of GNP within the polymer matrix are studied numerically. It is concluded that the solution method is accurate, efficient and capable to obtain the natural frequency of doubly curved shells.

Some properties of orthogonal linear splines and their applications to inverse problems

In this paper, an orthogonal basis for the space of linear splines based on linear B-splines is introduced. Some properties and modifications of this basis are investigated, then operational matrices of integration in collocation points are obtained using stable formula. Theoretical considerations are discussed. Applications to the numerical solutions for some linear and nonlinear inverse problems are given, in which the approximations are obtained using the first and second integrals of orthogonal linear splines that lead to an efficient solution procedure. For solving linear problems, the proposed method is combined with the Tikhonov regularization. Also, the trust-region-dogleg method is used for nonlinear equations. Numerical results validate the effectiveness of the orthogonal linear spline basis for linear and nonlinear inverse problems.