Efficient Solution Method Research Articles

Algorithm Portfolios for Solving the Quadratic Assignment Problem

Introduction. The quadratic assignment problem is a well-established NP-hard problem in combinatorial optimization with applications in diverse fields like economics, archaeology, and chemistry. Due to its complexity, research on efficient solution methods remains active, including efforts for parallelization on multiprocessor computing systems. However, effective parallel algorithms are crucial to fully leverage these computational resources. In this context, algorithm unions (portfolios and teams) play a significant role in achieving parallel execution for solving such problems. Research objectives. This work investigates the application of portfolios constructed from modifications of the repeated iterated tabu search algorithm to the quadratic assignment problem. The effectiveness of these portfolios was evaluated through experimental computations. Results. The portfolios, derived from modifications of the repeated iterated tabu search algorithm, were applied to the quadratic assignment problem. For the most demanding test instances, the proposed algorithms were evaluated on the SCIT-4 supercomputer, alongside previously published results from the authors, confirming their competitive performance. Additionally, we assessed the parallel efficiency of these portfolios in solving instances of the quadratic assignment problem. The results demonstrate their ability to accelerate the optimization process (with speedup dependent on problem size and utilized processors), enabling the solution of large-scale problems. Conclusions. The conducted studies demonstrate that employing algorithm portfolios significantly accelerates the solution process for the quadratic assignment problem. Analysis of the results reveals a near-linear speedup factor achieved by the portfolio. For the challenging test instance tai100a, a new best solution value of 21040996 was obtained using a portfolio of 16 algorithms. Keywords: quadratic assignment problem, algorithm portfolios, experimental research, algorithm portfolios efficiency.

Elastodynamic behaviors of steady moving straight dislocation within thin nano film

The elastodynamic dislocation behaviors are of great interest for understanding the performances of structural alloys under intense dynamic loading conditions. The formation, propagations, and interactions of dislocations (such as injected dislocation, accelerating dislocation, steady moving dislocation at high constant speed) are quite different from static dislocations. For steady-moving dislocation within the isotropic infinite medium, the effects of surface and interface on steady-moving dislocations within limited space are still known. In this paper, we investigate the elastodynamic image stress simulation of steady moving dislocation within film of limited thickness at constant speed using Eigenstrain theory, Lorentz transformation, and steady dynamic equilibrium equations. We propose an efficient solution method that involves complex Fourier series, transforming partial differential equations into ordinary differential equations, and ultimately into a set of algebraic equations in spectral space. The effects of dislocation speed and position near the free surface on the image stress of steady-moving climbing and gliding dislocations within the thin film are examined. The results show that relativistic effects are significant for certain dislocation configurations and stress components, whereas other stress components are less sensitive to relativistic effects near the transonic speed region.

Three-phase power flow using binary tree search algorithm for unbalanced distribution networks

The main objective of this study is to examine a binary tree (BT) three-phase (3Φ) power flow analysis method for unbalanced distribution networks. A simple and efficient 3Φ power flow solution method for unbalanced radial distribution networks was proposed. This method is based on the BT search structure. Large-scale distribution network problems can be evaluated using current-injection techniques and two-port network models. The power flow solution process was simplified into a set of 3 × 3 matrix operations using the BT-based method. The solution complexity remained unchanged, regardless of the size of the power system. In other words, the performance and robustness of the proposed algorithm were maintained at relatively high values with increasing system size. Furthermore, programming complexity was reduced by standardising the solution process. The effectiveness and accuracy of the proposed model and algorithm were validated using four IEEE standard benchmark feeders and a series of random cases.

Dynamic Operations of a Mobile Charging Crowdsourcing Platform

This paper investigates the operation of a novel electric vehicles (EVs) charging service mode, that is, crowdsourced mobile charging service for EVs, whereby a crowdsourcing platform is established to arrange suppliers (crowdsourced chargers) to deliver charging service to customers’ electric vehicles (parked EVs) at low-battery levels. From the platform operator’s perspective, we aim to determine the optimal operation strategies for mobile charging crowdsourcing platforms to achieve specific objectives. A mathematical modeling framework is developed to capture the interactions among supply, demand, and service operations in the crowdsourced mobile charging market. To design an efficient solution method to solve the formulated model, we first analyze the model properties by rigorously proving that a crucial variable set for operating the mobile charging crowdsourcing system includes charging price, commission control, and period-specific aggregate demand control. Besides, we provide both an equivalent condition and a necessary condition for checking the feasibility of these crucial variables. On top of this, we construct a search tree according to the operation periods in a day to solve the optimal operation strategies, wherein a nondominated principle is adopted as an accelerating technique in the searching process. The solution obtained from the proposed solution algorithm is proved to be sufficiently close to the actual global optimal solutions of the formulated model up to the resolution of the discretization scheme adopted. Numerical examples provide evidence verifying the model’s validity and the solution method’s efficiency. Overall, the research outcome of this work can offer service operators structured and valuable guidelines for operating mobile charging crowdsourcing platforms. Funding: This work was supported by the Singapore Ministry of Education [Grant RG124/21]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0126 .

Transparent boundary condition and its effectively local approximation for the Schrödinger equation on a rectangular computational domain

The transparent boundary condition for the free Schrödinger equation on a rectangular computational domain requires implementation of an operator of the form ∂t−i△Γ where △Γ is the Laplace-Beltrami operator. It is known that this operator is nonlocal in time as well as space which poses a significant challenge in developing an efficient numerical method of solution. The computational complexity of the existing methods scale with the number of time-steps which can be attributed to the nonlocal nature of the boundary operator. In this work, we report an effectively local approximation for the boundary operator such that the resulting complexity remains independent of number of time-steps. At the heart of this algorithm is a Padé approximant based rational approximation of certain fractional operators that handles corners of the domain adequately. For the spatial discretization, we use a Legendre-Galerkin spectral method with a new boundary adapted basis which ensures that the resulting linear system is banded. A compatible boundary-lifting procedure is also presented which accommodates the segments as well as the corners on the boundary. The proposed novel scheme can be implemented within the framework of any one-step time marching schemes. In particular, we demonstrate these ideas for two one-step methods, namely, the backward-differentiation formula of order 1 (BDF1) and the trapezoidal rule (TR). For the sake of comparison, we also present a convolution quadrature based scheme conforming to the one-step methods which is computationally expensive but serves as a golden standard. Finally, several numerical tests are presented to demonstrate the effectiveness of our novel method as well as to verify the order of convergence empirically.

An efficient numerical method for modeling silver powder heat exchanger in dilution refrigerator

Dilution refrigerator provides continuous ultralow temperature environments as low as 10 mK. It has been widely used in a variety of important applications such as quantum computations. The silver powder heat exchanger in a dilution refrigerator plays a crucial role in realizing ultralow temperatures on the order of 10 mK by precooling the circulation of helium mixtures. To study the silver powder heat exchanger quantitatively, we have proposed an efficient numerical solution method for its thermodynamic model. This method utilizes constraint conditions cleverly to convert the initial value problem of differential equations into a boundary value problem, allowing us to solve the control equations using the existing ODE function quickly. Furthermore, we demonstrate the application of this method in the evaluation and design of silver powder heat exchanger. The research results of this paper have certain significance for the development of dilution refrigerator.

Nonstationary response statistics of structures with hysteretic damping to evolutionary stochastic excitation

The damping of a structure has often been modeled as linear hysteretic damping (LHD), so its corresponding equation of motion (EOM) is an integro-differential equation that involves the Hilbert transform of response displacement. As a result, the system is non-causal in nature, and it is challenging to compute its nonstationary response statistics under evolutionary stochastic excitation. This article develops an efficient solution method to obtain closed-form solutions for various nonstationary response statistics, including the evolutionary power spectrum (EPS), correlation function and mean square values. The novel solution method utilizes the concept of causalization time to introduce a “causalized” impulse response function (IRF), by which causal response statistics are computed based on a pole-residue approach. This approach requires obtaining a pole-residue form of the transfer function (TF) from the frequency response function (FRF) of the system, which is readily obtained from the EOM. Subsequently, the desired response statistics are obtained by shifting the causal response statistics back to the original time. To obtain the pole-residue form of the TF, two steps are necessary: (1) taking the inverse Fourier transform of the FRF of the oscillator to obtain a discrete IRF and (2) using the Prony-SS method to decompose this discrete IRF to obtain the pole residues associated with the TF. The correctness of the proposed method is numerically verified by Monte Carlo simulations through examples of hysteretic damping and mixed viscous-hysteretic damping oscillators that are subjected to white noise, modulated white noise and modulated Kanai–Tajimi model random excitations.

Discrete cutting path problems: a general solution framework and industrial applications

The optimal tool routing for cutting machines, also known as cutting path optimisation is an important problem in production research. This problem is relevant in various manufacturing environments such as aeronautic, automotive, garment and semiconductor industries. In this paper, we introduce a general solution framework for the discrete Cutting Path Problem which includes: (i) the universal approach to reduce numerous settings of this problem to the appropriate auxiliary instances of the well-known Precedence Constrained Generalized Traveling Salesman Problem; (ii) the proposition of efficient solution methods for finding (sub-) optimal solutions. We carry out extensive computational experiments in order to evaluate performance of the proposed framework and the obtained results demonstrate its efficiency for real-life industrial instances.

Review on Current Issues related to Work Related Musculoskeletal Disorders

Work-related musculoskeletal disorders (WMSDs) are one of the most common occupational ailments in recent decades, significantly limiting people's daily lives. Globally, WMSDs are the major cause of employee pain, impairment, absenteeism, reduced productivity, and large financial costs. WRMSDs are illnesses that develop over time because of long-term occupational exposure to varying-intensity loads. WRMSDs are produced by discomfort or injury to the muscles and bones of the upper limbs because of activity. Low-extremity illnesses, like upper-limb diseases, may be just as dangerous, There is a high prevalence of neck and upper extremity problems among computer users. Upper extremities diseases were more common in older personnel. The physiological outcome of prolonged, repetitive, or repeating muscle contractions with insufficient recovery is localised muscular fatigue (WMSDs). Muscle tiredness has a substantial impact on occupational task performance, hence preventing it is crucial. The key challenge in ergonomics is to create work that avoids WMSDs while retaining high levels of output quality and productivity. Uncomfortable postures are commonly recognised as a major contributor of MSD among construction workers. Because of their linearity, ergonomic metrics can be incorporated into assembly line design models. They can also be utilised to take use of efficient solution methods established for optimal line design which are beneficial in the assembly line industry. Real-time risk assessment for work-related musculoskeletal disorders (MSDs) has proven to be challenging to research. Working at a fast speed and performing repetitive activities, as well as maintaining non-neutral body postures, are all physical risk factors for WMSDs. This review discuses common issue related to WMSDs which includes upper extremity, upper limbs, carpal tunnel syndrome, awkward postures, muscle activity, muscle fatigue, assembly line and risk assessment. The aim is to provide an overview of the problems related to the subject matter.

A unified framework for symmetry handling

AbstractHandling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods. While these methods are mostly discussed independently from each other, our framework allows to apply different methods simultaneously and thus outperforming their individual effect. Moreover, most existing symmetry handling methods only apply to binary variables. Our framework allows to easily generalize these methods to general variable types. Numerical experiments confirm that our novel framework is superior to the state-of-the-art symmetry handling methods as implemented in the solver on a broad set of instances.

MATRICS: The implicit matrix-free Eulerian hydrodynamics solver

Context. There exists a zoo of different astrophysical fluid dynamics solvers, most of which are based on an explicit formulation and hence stability-limited to small time steps dictated by the Courant number expressing the local speed of sound. With this limitation, the modeling of low-Mach-number flows requires small time steps that introduce significant numerical diffusion, and a large amount of computational resources are needed. On the other hand, implicit methods are often developed to exclusively model the fully incompressible or 1D case since they require the construction and solution of one or more large (non)linear systems per time step, for which direct matrix inversion procedures become unacceptably slow in two or more dimensions. Aims. In this work, we present a globally implicit 3D axisymmetric Eulerian solver for the compressible Navier–Stokes equations including the energy equation using conservative formulation and a fully simultaneous approach. We use the second-order-in-time backward differentiation formula for temporal discretization as well as the κ scheme for spatial discretization. We implement different limiter functions to prohibit the occurrence of spurious oscillations in the vicinity of discontinuities. Our method resembles the well-known monotone upwind scheme for conservation laws (MUSCL). We briefly present efficient solution methods for the arising sparse and nonlinear system of equations. Methods. To deal with the nonlinearity of the Navier–Stokes equations we used a Newton iteration procedure in which the required Jacobian matrix-vector product was reconstructed with a first-order finite difference approximation to machine precision in a matrix-free way. The resulting linear system was solved either completely matrix-free with a combination of a sufficient Krylov solver and an approximate Jacobian preconditioner or semi-matrix-free with the incomplete lower upper factorization technique as a preconditioner. The latter was dependent on a standalone approximation of the Jacobian matrix, which was optionally calculated and needed solely for the purpose of preconditioning. Results. We show our method to be capable of damping sound waves and resolving shocks even at Courant numbers larger than one. Furthermore, we prove the method’s ability to solve boundary value problems like the cylindrical Taylor-Couette flow (TC), including viscosity, and to model transition flows. To show the latter, we recover predicted growth rates for the vertical shear instability, while choosing a time step orders of magnitude larger than the explicit one. Finally, we verify that our method is second order in space by simulating a simplistic, stationary solar wind.

Assessing the effectiveness of static heuristics for scheduling lumber orders in the sawmilling production process

Although optimization models can be used to plan the production process, in most cases static heuristics, such as earliest due date (E), longest processing time (L), and shortest processing time (S), are used because of their simplicity. This study aims to analyze the production cost of the static heuristics and to determine how this cost relates to the size of the production orders in the sawmilling industry. We set a planning problem with different orders and due dates and solved it using two cost-minimization models to compare their solutions. The first was a planning model (PL) where orders were split up into products demand by period, and the second, a planning scheduling (PS) where the sequence of processing orders based on static heuristics was assumed as known. In the latter, the minimum production cost for each static heuristic was found. In both models, the same resource constraints were assumed. The costs showed no significant changes based on order sizes. However, 0,5 % of orders were delayed using PS-E, and 17 % of orders were delayed using PL. PL was an efficient solution method when changing the orders´ size and when looking for the best static heuristic to process the orders. However, PS-E showed the ability to reduce the backlog close to zero while the PL backlog ratio was 17 %. No penalties were applied to backlogs due to their subjective nature; however, when shortages occurred, the demand was unmet or backlogged with substantial costs. Thus, in case the proposed method is adopted using a conservative backlog cost, a sawmill producing under the cut-to-order environment that produces 300000 m3 /year would reduce backlogged orders by 51000 m3. If the holding lumber cost is 2 $/m3, annual savings would be $408000.

A method for nonlinear electric-thermal coupling calculations of bushings based on unbiased gradient-free smooth domains.

High-voltage dry-type bushings, serving as the crucial junctions in DC power transmission, represent equipment with the highest failure rate on the DC primary side, underscoring the critical importance of monitoring their condition. Presently, numerical simulation methods are commonly employed to assess the internal state of bushings. However, due to limitations in the efficiency of multi-physics field computations, the guidance provided by numerical simulation results in the field of power equipment condition assessment is relatively weak. This paper focuses on solving the electrical-thermal coupling in high-voltage dry-type bushings. Addressing the most widely used tetrahedral mesh in numerical computations, we propose an efficient solution method based on the concept of "smooth domains." This method involves partitioning the volume centroids of the elements into multiple smooth domains within the computational domain. Electric and thermal conduction matrix calculations occur within these smooth domains, rather than within the grid or element interiors. This approach eliminates the need for traditional element mapping and complex volume integration. To demonstrate the effectiveness of this method, we use high-voltage dry-type bushings as a case study, comparing the performance of our approach with traditional finite element algorithms. We verify the algorithm's computational efficiency and apply it to the analysis of typical temperature anomalies in bushings, further illustrating its suitability for electrical equipment condition assessment.

An efficient generator maintenance scheduling model based on unit clustering and linear relaxation

The formulation of periodic maintenance schedules for generators is crucial for the efficient and reliable operation of power systems. Traditional generator maintenance scheduling models often have low temporal resolution and ignore significant information. To solve this problem, this paper proposes a mid/ long-term generator maintenance scheduling model with an hourly time resolution. Given the challenges of large integer variable quantities and computational complexity in directly solving mid/ long-term maintenance schedules for power system generation units, an efficient solution method is proposed based on unit clustering and linear relaxation. Initially, a basic maintenance model is established based on the Unit Commitment (UC) model. Subsequently, the basic UC maintenance model is linearly relaxed to obtain an efficient approximate model, termed the Relaxed Clustered Unit Commitment (RCUC) maintenance model, which involves the operation of annual regulating hydropower stations, energy storage devices, pumped storage stations, wind power plants, and photovoltaic (PV) plants. Simulation results from an adapted IEEE RTS-79 system and a provincial scale system case study are provided to demonstrate the effectiveness of the proposed model in coping with mid/long-term maintenance scheduling and annual hydropower allocation problems of large-scale power systems.

Robust Kalman filters under epistemic uncertainty for non‐Gaussian systems with multiplicative noise

AbstractThis article proposes two robust Kalman filters to solve the issue of inaccurate modeling in multiplicative noise systems due to epistemic limitations. First, we construct all conceivable state/measurement transition probability densities as an ambiguity set. This ambiguity set chooses the Wasserstein distance or the moment‐based metric as the distance metric. Besides, this set is an inequality set with a chosen tolerance, which can be seen as a non‐negative radius ball. Then, by combining the robust solution of the least favorable model in that ball with the alternating direction method of multipliers or an efficient direct solution method, we propose two robust Kalman filters based on the minimum mean square error criterion. A classical example is provided to verify the effectiveness of the proposed robust filters in comparison to existing state‐of‐the‐art filters.

A joint solution framework for the optimal operation and evaluation of integrated energy systems based on exergy

Exergy analysis provides a unified scale for evaluating the quality and quantity of energy, and is suitable and essential for scientifically and rationally guiding the optimization and evaluation of integrated energy systems with intricate multi-component configurations. The present work proposes an exergy analysis model and joint solution framework for integrated energy systems based on exergy, and presents an efficient and accurate solution method. The exergy analysis model is analogous to the energy-based model and possesses a succinct form. This model is then applied to establish an input exergy model defining the exergy of inputs, a destroyed exergy model defining the exergy lost due to the conversions, transmissions, and storages, and a benefit exergy model defining the remaining useful exergy for the loads. The joint solution framework optimizes the system from the basis of exergy conservation, and evaluates the destroyed exergy of each link and the prices of the various exergy products from an economic perspective based on the established exergy analysis model. The complexity of the framework is then reduced by establishing a sequential optimization and evaluation model. The optimization model is solved accurately and efficiently using a stringent cutting plane method to address the problem of relaxation inaccuracy, and piecewise linearization to accommodate the non-convex constraints. Numerical computations on a 97-node system demonstrate the accuracy of the proposed models in exergy-based optimization, destruction, and price evaluation, preventing substantial deviations (e.g., a 23% discrepancy in total destroyed exergy). The adopted cost allocation method based on energy quality reflects fair pricing, rectifying conventional pricing disparities (e.g., a 47.56% underestimation of the electric load using energy-based pricing). Therefore, the accuracy and efficiency of the developed exergy analysis model, solution framework, and solution method are validated.

Modeling and solving a corporate vehicle-sharing problem combined with other modes of transport

We consider a car-sharing problem in a company during business hours. The employees, located at one or several offices, have to travel to one or more appointments each with a fixed location and fixed start and end times and return to one of the offices afterwards. Each employee trip can be carried out with one out of several alternative modes of transport. The considered modes of transport are a company car from the company car pool, walking, public transport, bike, and taxi. The aim is to assign modes of transport to employee trips such that the total costs of covering the trips is minimized.We first consider that the company is operating a shared fleet of a single type of vehicle and then that the fleet consists of different vehicle types. By relying on minimizing the savings when using a vehicle compared to the cheapest alternative available mode of transport (which is used if no vehicle is assigned to a trip), we do not need to model the alternative modes explicitly. For the case where the vehicle fleet consists of a single type of vehicle, we model the vehicle-sharing problem as a minimum-cost flow problem. Secondly, if multiple types of vehicles are available the problem can be formulated as a multi-commodity flow problem. Since very efficient solution methods are available for these formulations, they are applicable in daily operations.We provide a comprehensive computational study for both cases on instances based on demographic, spatial, and economic data of Vienna. We show that our formulations for the problem solve these instances in a few seconds, which makes them usable in an online booking system. In the analysis, we discuss different potential settings. We study different sizes and compositions of the shared fleet, restricted sets of modes of transport, and variations of the objective function.

The Nature of Ideological and Political Education in Colleges and Universities Based on Deep Learning Models and Its Development

Abstract In this paper, first of all, after extracting the character sequence information, a certain scale of the corpus is obtained by using a crawler, and a corpus in the field of ideological and political education, as well as a participle system, is constructed. Then, the sequence decoding problem is solved by combining the idea of dynamic programming, based on the word level N-gram language algorithm, to design and implement an efficient solution method and calculate the final result of the participle. Finally, the keywords of related literature are classified, the essential dimensions of ideological and political education can be derived, and the essence of ideological and political education is explored and analyzed by using the word division algorithm. The results show that the most important essence of ideological and political education is “educating people’s feelings” with a weight value of 0.46, and among the 24 secondary nodes, there are 19 items with coefficients of variation less than or equal to 0.3, which shows that the degree of consistency is high, indicating that the degree of importance of the essence of ideological and political education is also high.

An Efficient Optimal Solution Method for Neutrosophic Transport Models: Analysis, Improvements, and Examples


 Transport issues aim to determine the number of units that will be transferred from the production centers to consumption areas so that the cost of transportation is as low as possible, taking into account the conditions of supply and demand. Due to the great importance of these issues and to obtain more accurate results that take into account all circumstances, we conducted two research studies. In the first research, we presented a formulation of neutrosophic transport issues, and in the second research, we presented some ways to find a preliminary solution to these issues, but we do not know whether the preliminary solution is optimal or not, so we will present in this research a study whose purpose is to shed light on some important methods used to improve the optimal solution to transportation issues and then reformulating them using the concepts of neutrosophic science, a science that leaves nothing to chance or circumstances but rather provides solutions with neutrosophic values. Unspecified values take into account the best and worst conditions.

Adaptive MPC for Burst Incident Management in Water Distribution Networks

This paper investigates an adaptive control strategy which takes advantage of remotely actuated pumps and valves to improve the performance of water distribution networks (WDN) during burst incidents. The proposed strategy relies on model predictive control (MPC) to switch between problem formulations corresponding to normal operating conditions and burst conditions. The optimal control problems are formulated as non-convex non-linear programs (NLP), where the action of fixed-speed pumps and control valves (non-return and bi-directional) is modeled exactly and burst remedial interventions are represented using time-dependent connectivity matrices. We propose an efficient solution method based on reformulations and approximations of the non-convex objectives and constraints and apply the proposed strategy to the adaptive control of an operational WDN during a burst incident. The numerical experiments show that the computed burst control settings allow to partially or completely restore customer supply following the detection of a burst while maintaining minimum water levels in the network tanks and without increasing the cost of pumping operations. The results suggest that the proposed adaptive control strategy can be implemented alone, to mitigate the impact of bursts incidents in WDNs at minimum cost, or to complement traditional remedial interventions.