Efficient Solution Method Research Articles

МАТЕМАТИЧНА МОДЕЛЬ ВЗАЄМОДІЇ СТАЦІОНАРНИХ SH-ХВИЛЬ З СИСТЕМОЮ КРИВОЛІНІЙНИХ ТРІЩИН У НАПІВПРОСТОРІ

A method for solving mathematical physics problems is proposed for semi-infinite media containing systems of curved crack-slits. Most of the studies known from the literature relate to the problems of diffraction of elastic waves on straight and circular cuts. However, in reality, the crack is usually not straight or circular. Studies have shown that the curvature of a crack significantly affects the value of the dynamic stress intensity coefficients. The value of this parameter also depends on the proximity of the defects to each other, since they always fall within the range of the reflected wave. The stress-strain state of media with complex properties can be effectively modeled by computing complexes in combination with software systems. Most studies are devoted to the development of the finite element method. However, the method of integral equations is very effective for solving anti-planar problems of diffraction theory. The advantage of this method is the reduction in the number of spatial variables, the high speed of convergence, and the possibility of using various efficient numerical solution methods. The method also has the ability to build efficient parallel computing schemes. A unified approach to solving the problem is developed on the basis of singular integral equations (SIEs). The corresponding dynamic boundary value problems for a clamped and force-free half-plane are investigated. The influence of the defect curvature, their interaction, and the proximity of the boundary on the magnitude and nature of the dynamic stress intensity coefficients is studied. Parallel algorithms allow to significantly reduce the computation time and analyse the characteristics of the wave field in more detail. The combination of the SIE method, which reduces the dimensionality of the problem by one, and provides significant savings in computing time due to the parallelization of computational procedures, leads to a significant increase in the efficiency of the proposed algorithm. The method can be used to assess the influence of various mechanical or geometric factors on the strength of bodies with defects.

Airline operational crew-aircraft planning considering revenue management: A robust optimization model under disruption

Airline planning involves various issues that, in a general, can be grouped as network planning, schedule design and fleet planning, aircraft planning, and crew scheduling decisions. This study mainly aims to optimize the Crew Scheduling (CS) decisions considering the operational constraints related to Aircraft Maintenance Routing (AMR) regulations. Since, after fuel, crew costs are vital for airlines, and aircraft maintenance constraints are important operationally, the integrated Crew Scheduling and Aircraft Maintenance Routing (CS-AMR) problem is an important issue for the airlines. The present research addresses this problem using the Revenue Management (RM) approach under some disruption scenarios in the initial schedule. The proposed approach enables airlines to make more efficient decisions during disruptions to prevent flight delay/cancellation costs and recaptures an acceptable part of the spilled demand caused by disruption through the fleet stand-by capacity. This approach considers a set of disruptions in the flight schedule under different probable scenarios and provides the optimal decisions. Accordingly, airlines have two decision-making stages: Here-and-Now (HN) decisions related to the initial schedule for crew, aircraft routing and stand-by capacity to face probable disruptions and Wait-and-See (WS) decisions that determine what the executive plan of each crew and aircraft should be under each scenario, and how to use different options for flight cancellation and substitution. To this end, a novel Two-Stage Robust Scenario-based Optimization (TSRSO) model is proposed that considers the HN and WS decisions simultaneously. A numerical example is solved, and its results verify the applicability and evaluate the performance of the proposed TSRSO model. Regarding the complexity of the proposed MILP model categorized as NP-hard problems, we develop a computationally efficient solution method to solve large-scale problem instances. A single-agent local search metaheuristic algorithm, Adaptive Large Neighborhood Search (ALNS), is applied to solve the CS-AMR problem efficiently. According to the result obtained by applying the proposed revenue management approach for the CS-AMR problem, airlines can drive a robust solution under disruption scenarios that not only minimizes the total delay/cancellation costs but also increases the profit by recapturing the spilled demand.

An extended Bueckner–Rice theory for arbitrary geometric perturbations of cracks

The aim of this paper is to define a new, simple and efficient method of solution of elasticity problems for 3D bodies containing cracks slightly perturbed out of their original plane or surface. This method extends that proposed by Rice (1985, 1989), from a re-formulation of Bueckner (1987)’s 3D weight function theory, for the treatment of coplanar crack perturbations. First, a general formula is derived for the variation of total energy of a cracked elastic body, resulting from some small but otherwise arbitrary geometric perturbation of the embedded crack(s). This formula, which involves integrals over both the front and the surface of the crack, is derived from an expression of deLorenzi (1982) and Destuynder et al. (1983) in the form of a volumic integral, originally limited to purely tangential crack perturbations but duly extended here to arbitrary perturbations having both tangential and normal components. It is then used to derive a general expression of the variation of displacement arising from a general perturbation of the crack(s), anywhere in the cracked body. The reasoning here basically follows the same lines as in the works of Rice (1985, 1989), but for the presence of an additional normal component of the crack perturbation. The possible use of the formalism developed to treat problems of out-of-plane, or out-of-surface perturbations of cracks is finally briefly evoked; the straightforwardness of the new method proposed is hoped to permit future applications to non-coplanar crack problems too complex to be accessible by more conventional methods.

Measurement and simulation of thermal-induced residual stresses within friction stir lapped Al/steel plate

Welding residual stress and distortion usually affect the assembly accuracy, product performance, and service life, with no exception for the Al/steel hybrid structure. The lapped joint of 5052 Al alloy and DP590 steel was made by friction stir welding (FSW) at various rotation speeds. A subsequentially coupled computational modeling approach based on the in-house software JWRIAN combining an efficient hybrid solution method was developed to predict the temperature field, the residual stress distribution and the warpage deformation. Based on the simulation, a higher welding temperature with subsequently a higher average cooling rate was created at a high rotation velocity, leading to the area extension of the longitudinal tensile stress and transverse compressive stress near the weld zone. The thermal expansion coefficient mismatch leads to the mirroring distribution of the near interfacial residual stress on both sides, particularly for transverse residual stress. With the increasing rotation speed, the longitudinal residual stress on the steel side near the interface was changed from compressive to the tensile state. The maximum warpage deformation in the Al plate border became larger at a higher rotation speed. The surface residual stress was measured by X-ray diffusion method and the internal residual stress was reconstructed by the contour method with the aid of elastic FE analysis. The comparisons of temperature history, residual stress and deformation indicated satisfactory agreements between simulation and experiment ones.

Travel demand matrix estimation for strategic road traffic assignment models with strict capacity constraints and residual queues

This paper presents an efficient solution method for the matrix estimation problem using a static capacity constrained traffic assignment (SCCTA) model with residual queues. The solution method allows for inclusion of route queuing delays and congestion patterns besides the traditional link flows and prior demand matrix whilst the tractability of the SCCTA model avoids the need for tedious tuning of application specific algorithmic parameters.The proposed solution method solves a series of simplified optimization problems, thereby avoiding costly additional assignment model runs. Link state constraints are used to prevent usage of approximations outside their valid range as well as to include observed congestion patterns. The proposed solution method is designed to be fast, scalable, robust, tractable and reliable because conditions under which a solution to the simplified optimization problem exist are known and because the problem is convex and has a smooth objective function.Four test case applications on the small Sioux Falls model are presented, each consisting of 100 runs with varied input for robustness. The applications demonstrate the added value of inclusion of observed congestion patterns and route queuing delays within the solution method. In addition, application on the large scale BBMB model demonstrates that the proposed solution method is indeed scalable to large scale applications and clearly outperforms the method mostly used in current practice.

Critical buckling loads of embedded perforated microbeams with arbitrary boundary conditions via an efficient solution method

Abstract In the present work, the small size effects on stability properties of perforated microbeams under various types of deformable boundary conditions are studied considering the Fourier sine series solution procedure and a mathematical procedure known as Stokes’ transformation for the first time. The main benefit of the present method is that, in addition to considering both the gradient elasticity and the size effects, the kinematic boundary conditions are modeled by two elastic springs as deformable boundary conditions. The deformable boundary conditions and corresponding stability equation are described using the classical principle which are then used to construct a linear system of equations. Afterward, an eigenvalue problem is adopted to obtain critical buckling loads. The correctness and accuracy of the present model are demonstrated by comparing results with those available from other works in the literature. Moreover, a numerical problem is solved and presented in detail to show the influences of the perforation properties, geometrical, and the variation of small-scale parameters and foundation parameters on the stability behavior of the microbeams. In addition, according to the best knowledge of the authors, there is no study in the literature that examines the buckling behavior of perforated microbeams on elastic foundation with the gradient elasticity theory.

Elite collaborative search algorithm and its application in power generation scheduling optimization of cascade reservoirs

The joint optimization scheduling model of cascade reservoirs has the characteristics of high dimensionality, dynamic, nonlinear, multivariate, and strong constraint. Around its solution problem, this paper carries out the research of the efficient model solution method based on the group intelligent optimization algorithm. Firstly, given the defect of the standard collaborative search algorithm that it is easy to falls into local optimization and weakening of global search ability in the later stage, three efficient improvement strategies are proposed through parameter randomization, elite reinforcement learning, and elite help learning. And based on this, an elite collaborative search algorithm (ECSA) coupled with the three improvement strategies is established, which enhances the ability of individuals to search globally and jump out of local optimality, and it has strong robustness and optimization ability. Secondly, taking six cascade power stations in the Yalong River Basin as an example, the power generation dispatching model of cascade reservoirs considering various constraints such as reservoir discharge flow and water level restriction are constructed, and six typical runoff scenarios are selected, and the joint power generation scheduling test is carried out by using five algorithms, i.e., ECSA, CSA, PSO, GWO, and WOA. Finally, through the comparison of the scheduling results, it is found that compared with the other algorithms, the solution obtained by the proposed ECSA in this paper can effectively improve the overall power generation of the basin and the efficiency of water resource utilization in river basins. Taking the normal year as an example, compared with the CSA、PSO、GWO，and WOA method, the average annual increase of power generation by the ECSA method is 32, 4778, 4153, and 2288 million kWh respectively.

Wellbore multiphase flow behaviors of gas kick in deep water horizontal drilling

During the deepwater drilling, the complicated gas-liquid-solid multiphase flow will occur if the formation gas enters and migrates in the wellbore. Through understanding of the wellbore flow behaviors is of great importance for the blowout prevention and well control. Considering the dynamic mass and heat transfer process in wellbore caused by alternating ambient temperature field, a multiphase flow model of multicomponent fluid in wellbore is deduced and developed, including the continuity equation, momentum conservation equation and energy conservation equation. Furthermore, the corresponding initial and boundary conditions are proposed for different working conditions in deepwater drilling, and an efficient numerical solution method is established, including dynamic mesh generation method and discrete solution method of partial differential equations. Applied in a deep-water kicking well, the proposed model is used to analyze the multiphase flow rules in the wellbore. The results show that in the process of annular fluid returning from the bottomhole, the pressure generally decreases linearly, while the temperature change is nonlinear. The temperature first rises and then falls at the formation section, and first falls and then rises at the seawater section. Furthermore, the pit gain increases approximately in a quadratic polynomial relationship, caused by the rise and expansion of gas in the wellbore, and the pressure drop and gas influx rate increase at the bottomhole. In the process of kick evolution, the standpipe pressure and bottomhole pressure gradually decrease, which can be an important sign for kick detection.

A combined tactical and operational framework for maintenance scheduling and routing in offshore wind farms

This article proposes a framework for the integration of tactical and operational optimisation models for maintenance scheduling and routing at offshore windfarms. A tactical model is formulated to find the optimal schedule for preventive maintenance over a medium-term planning horizon (one month). The schedule is produced assuming a weather forecast for the entire planning horizon, which in practice will be uncertain. However, for each day, an operational maintenance routing model is solved to obtain optimal vessel routes with a one-day planning horizon, assuming an updated weather forecast for that day. In the operational routing model, the turbines scheduled for preventive maintenance are provided by the tactical scheduling model, whereas the turbines requiring corrective maintenance are provided by information about failures and alarms updated on a daily basis. In the case that the solution generated by the routing model contains turbines that cannot be maintained, the monthly maintenance activities are rescheduled by solving the tactical scheduling model considering the delayed activities. As the routing problem is too time consuming to solve exactly, we propose efficient matheuristic solution methods incorporating Variable Neighbourhood Search and an exact method. Computational experiments have been carried out to assess the performance of the tactical-operational framework.

Coordinated Planning of Electric Power and Natural Gas Distribution Systems With Refueling Stations for Alternative Fuel Vehicles in Transportation System

The alternative fuel vehicles (AFVs) which include electric vehicles (EVs) and natural gas vehicles (GVs) have gained much attention in recent years for delivering a clean and low-carbon urban mobility. The AFV development is promoting the coordination among electric power, natural gas, and transportation (ENT) networks. This paper proposes a coordinated planning method for investment on and operation of emerging urban energy infrastructures. The sites and sizes of refueling stations are optimized along with the expansion strategies for electric power distribution network (PDN) and natural gas distribution network (GDN). First, AFV refueling demands are analyzed according to the refueling station constraints and options, and transportation network (TN) constraints. Second, the coordinated planning model for PDN and GDN is formulated along with respective operation constraints in PDN, GDN, and TN. An efficient MILP solution method is developed for the proposed optimization problem. Finally, several case studies verify the effectiveness of the proposed model and its solution method. Compared with existing solutions, the proposed panning method offers a more accurate AFV refueling demand model with various refueling options. It is demonstrated that the coordinated planning can reduce investment and operation costs of urban energy infrastructures by exploring the pertinent interactions among constrained PDN, GDN, and TN.

Efficient Global Solutions to Single-Input Optimal Control Problems via Approximation by Sum-of-Squares Polynomials

Optimal control problems are prevalent in model-based control, state and parameter estimation, and experimental design for complex dynamical systems. An approach for obtaining solutions to these problems is based on the notion of parsimonious input parameterization and comprises two tasks: the enumeration of arc sequences followed by the computation of optimal values of a small number of decision variables for each sequence. This article proposes an efficient global solution method for single-input optimal control problems for nonlinear dynamical systems with a potentially large number of states or complex dynamics via sum-of-squares polynomials and parallel computing. The method approximates the problem for a given arc sequence as a polynomial optimization problem that can be efficiently solved to global optimality via semidefinite programming. It is established that the difference between the cost obtained by the proposed method and the globally optimal cost of the original problem is bounded and depends on the polynomial approximation error. The method is illustrated by simulation examples of a reaction system and a rocket.

Design and optimization of nanooptical couplers based on photonic crystals involving dielectric rods of varying lengths

This study presents design and optimization of compact and efficient nanooptical couplers involving photonic crystals. Nanooptical couplers that have single and double input ports are designed to obtain efficient transmission of electromagnetic waves in desired directions. In addition, these nanooptical couplers are cascaded by adding one after another to realize electromagnetic transmission systems. In the design and optimization of all these nanooptical couplers, the multilevel fast multipole algorithm, which is an efficient full-wave solution method, is used to perform electromagnetic analyses and simulations. A heuristic optimization method based on genetic algorithms is employed to obtain effective designs that provide the highest efficiency values. Two types of optimization strategies are applied using nanorods with a fixed length and using nanorods with varying lengths. This way, photonic crystals consisting of irregular arrays of both identical and nonidentical dielectric elements are designed for the realization of nanooptical couplers. The designs and their numerical results show that it is possible to design and further improve efficient nanooptical couplers with simple and compact geometries based on the principles of photonic crystals. Using relatively simple geometries and a single material, the designed nanooptical couplers are more preferable than the available designs in the literature.

Investigations of Couette Flow Unsteady Radiative Convective Heat Transfer in a Vertical Channel Using the Generalized Method of Lines (MOL)

This study describes a very efficient and fast numerical solution method for the non-steady free convection flow with radiation of a viscous fluid between two infinite vertical parallel walls. The method of lines (MOL) is used together with the Runge-Kutta ODE Matlab solver to investigate this problem numerically. The presence of radiation adds more stiffness and numerical complexity to the problem. A complete derivation in dimensionless form of the governing equations for momentum and energy is also included. A constant heat flux condition is applied at the left wall and a transient numerical solution is obtained for different values of the radiation parameter (<i>R</i>). The results are presented for dimensionless velocity, dimensionless temperature and Nusselt number for different values of the Prandtl number (<i>Pr</i>), Grashof number (<i>Gr</i>), and the radiation parameter (<i>R</i>). As expected, the results show that the convection heat transfer is high when the Nusselt number is high and the radiation parameter is low. It is also shown that the solution method used is simple and efficient and could be easily adopted to solve more complex problems.

In-plane instability of shallow layered arches with interlayer slip

In this paper, a beam theory for predicting limit point buckling and bifurcation buckling of shallow arches composed of two layers flexibly bonded is presented. The flexibility of layer bond results in interlayer slip, which significantly affects the critical transverse loads. The presented theory is based on a layerwise assumption of the Euler–Bernoulli theory and a linear behavior of the interlayer. After establishing the equilibrium equations and boundary conditions, a numerical method for efficient solution of these equations is provided. In a first example, the presented theory is validated by comparative computations with a much more elaborate finite element analysis assuming a plane stress state. In several other examples, the effect of interlayer stiffness, load distribution and boundary conditions on the stable and unstable equilibrium paths of shallow arches with interlayer slip is investigated.

Block preconditioners for linear systems in interior point methods for convex constrained optimization

In this paper, we address the preconditioned iterative solution of the saddle-point linear systems arising from the (regularized) Interior Point method applied to linear and quadratic convex programming problems, typically of large scale. Starting from the well-studied Constraint Preconditioner, we review a number of inexact variants with the aim to reduce the computational cost of the preconditioner application within the Krylov subspace solver of choice. In all cases we illustrate a spectral analysis showing the conditions under which a good clustering of the eigenvalues of the preconditioned matrix can be obtained, which foreshadows (at least in case PCG/MINRES Krylov solvers are used), a fast convergence of the iterative method. Results on a set of large size optimization problems confirm that the Inexact variants of the Constraint Preconditioner can yield efficient solution methods.

Frequency response function method for dynamic gas flow modeling and its application in pipeline system leakage diagnosis

Timely diagnosing leakages is significant for the safety and reliability of gas pipeline systems, where an efficient and accurate modeling and solution method is critical to identify the leakage rate and location. Here, a frequency response function-based modeling method for dynamic gas flow in pipelines is proposed. Based on the frequency-domain flow resistance of pipelines and Fourier Transform, original dynamic flow model is transformed into the frequency response function model consisting of linear lumped transmission constraints, nonlinear frequency response function, and nonlinear pipeline resistance characteristics, which are efficiently solved according to their different mathematical properties. Dynamic simulation cases show the proposed modeling and solution method greatly improves the computational efficiency keeping the accuracy. Besides, taking the difference between measurements and simulation results under leakage condition as objective, an iterative bilayer optimization algorithm is proposed based on the mathematical categorization of system constraints to efficiently diagnose leakages. Four leakage diagnosis cases in single pipeline and pipeline network with measurement noise and transient boundary conditions are studied to validate the leakage diagnosis method. Absolute location errors in the results are all within 1%, demonstrating the accuracy and robustness of the proposed method for single leakages and multiple leakages occurring successively or simultaneously.

The discrete time break scheduling problem under fatigue and no preemption: solution methods and impact of work regulations

We address the discrete time break scheduling problem with no preemption when workers' fatigue impacts their productivity. We propose a Mixed Integer Linear Programming model to solve the one break problem to optimality, using a lexicographic approach where the production amount is maximised first, and then the break length over a discrete time horizon. We develop a Variable Neighbourhood Search algorithm to solve the multiple break problem. In addition to proposing efficient solution methods to the problem, our incentive is to assess the impact on the production amount and on workers' welfare of rest break regulations laid down in legislation or collective agreements. We conducted an extensive simulation study to represent a wide range of workers' profiles defined in terms of fatigability and recovery speed. Simulation results show that regulations slightly affect the production amount whereas they allow for large improvements of workers' welfare as long as breaks are optimised as a second objective. The production amount is also shown to be quite sensitive to the break timing. Finally, multiple breaks can improve the production amount and workers' welfare in many situations, which questions the widespread belief that endowing workers with a single short break would optimise the production amount.

A heuristic-based hybrid algorithm to configure a sustainable supply chain network for medical devices considering information-sharing systems.

In today’s hyper-competitive marketplace, the crucial role of the sustainability concept has been highlighted more. Hence, managers’ attention has been attracted to the concept of sustainable supply chains. On the other hand, after the COVID-19 outbreak, the importance of medical devices and their demand has drastically enhanced, which has led to shifting the attention of researchers toward this industry. In this regard, based on the importance of the mentioned points, the current study configures a sustainable supply chain network for the medical devices industry. In this way, given the crucial role of the oxygen concentrator during the COVID-19 outbreak, the present study investigates the supply chain of the mentioned goods as a case study. Also, this research develops an efficient hybrid solution method based on goal programming, a heuristic algorithm, and the simulated annealing algorithm to solve the suggested model. Eventually, sensitivity analysis is conducted to examine the influence of the crucial parameters of the model on the outputs, and managerial insights are provided. According to the achieved results, the suggested model and the developed hybrid method demonstrate a good performance which shows their efficiency.

An efficient numerical solution method for detailed modelling of large 5th generation district heating and cooling networks

Numerical simulations of district heating and cooling networks constitute a valuable tool for system design and optimization. This paper presents a novel thermo-hydraulic network model, which addresses particularly large 5th generation district heating and cooling (5GDHC) networks. We take into account the current flow regime for heat loss calculation, which significantly improves accuracy during zero mass flux compared to a widely used literature model. We demonstrate our model's capability on a real-world 5GDHC network with 6 km length and 180 distributed heat pumps. In contrast to existing models, we take into account the temperature dependency of the viscosity, which leads to a deviation of up to 65% in pressure drop in the given example. Yet, the performance of our implementation is considerably higher in comparison to simplified models of similar size that use generic equation solver, such as Modelica, as we avoid typical performance issues due to tight coupling and solution of large equation systems. The model is implemented using error-controlled, adaptive time step solver CVODE and made available as open-source project for reference and general usage.

Stochastic RWA and Lightpath Rerouting in WDM Networks

In a telecommunication network, routing and wavelength assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity because of stranded bandwidth. At this point, service providers try to recover the capacity via a defragmentation process. We study this setting from two perspectives: (i) while granting the connection requests via the RWA problem and (ii) during the defragmentation process by lightpath rerouting. For both problems, we present the first two-stage stochastic integer programming model incorporating incoming request uncertainty to maximize the expected grade of service. We develop a decomposition-based solution approach, which uses various relaxations of the problem and a newly developed problem-specific cut family. Simulation of two-stage policies for a variety of instances in a rolling-horizon framework of 52 stages shows that our stochastic models provide high-quality solutions when compared with traditionally used deterministic ones. Specifically, the proposed provisioning policies yield improvements of up to 19% in overall grade of service and 20% in spectrum saving, while the stochastic lightpath rerouting policies grant up to 36% more requests, using up to just 4% more bandwidth spectrum.Summary of Contribution: For handling the intrinsic uncertainty of demand in the telecommunications industry, this paper proposes novel stochastic models and solution methodology for two fundamental problems in telecommunications at operational level: (i) routing and wavelength assignment (RWA) and (ii) lightpath rerouting problem. Despite the vast literature on the RWA problem, stochastic optimization has not been considered as a viable solution for resource allocation in optical networks. We propose two-stage stochastic programming models for both problems and design efficient decomposition-based solution methods that use various relaxations of the models and a new family of cutting planes. Our extensive and rigorous numerical experiments show the significant merit of incorporating uncertainty into decision making, as well as the effectiveness of the decomposition framework and our newly designed family of cuts in enhancing the solvability of both models. This work opens new avenues to explore where the powerful stochastic programming literature can be leveraged to make operational decisions in telecommunications problems, a field that currently relies mostly on deterministic and heuristic solution methods.