Relaxation Algorithm Research Articles

A decomposition approach to solve the individual railway crew Re-planning problem

Crew re-planning is an important and difficult task in railway crew management. In this paper, we establish a path-based model solving the Individual Crew Re-planning Problem (ICRP). The individual indicates that we focus the problem on specific (non-anonymous) crew members, considering their roles (leader and cabin crew) and qualifications. This problem is inspired by the crew planning problem faced in Chinese high-speed railway operations. To generate feasible paths, we construct a multi-layer time-space connection network and develop a heuristic algorithm. To decrease the complexity and scale of the model, we decompose the ICRP into two sub-problems (for leaders and for cabin crew members respectively) which can be solved in sequence. In addition, we develop a Lagrangian relaxation (LR) algorithm to get valid paths quickly for both sub-problems. We combine the LR algorithm with solving the restricted decomposed models to get a good quality solution for the studied ICRP problem. We test our methods on several real-world instances from Chinese high-speed railways. The computational experiments show that our LR algorithm with a decomposition strategy can solve the decomposed models in a relatively short computation time compared to solving the original model directly, while obtaining (near-)optimal solutions for all instances.

Research on frequency shift signal detection algorithm for jointless track circuits based on improved relaxation algorithm

The accuracy of ZPW-2000 frequency shift signal demodulation is related to the safety and efficiency of high-speed trains. This paper proposed a kind of ZPW-2000 frequency-shift signal detection algorithm based on improved Relaxation algorithm (ZFSD-IR) to address the issue of low accuracy in detecting ZPW-2000 frequency shift signal under strong noise interference, as the traditional fast Fourier transform (FFT) spectrum analysis methods are susceptible to fence effects and spectrum leakage effects. Firstly, the principle of ZPW-2000 jointless track circuit was analyzed, and then the ideal and simplified models of ZPW-2000 frequency shift signal were established, respectively. Finally, the simulation experiments were conducted on ZPW-2000 frequency shift signal detection under different sampling durations and signal-to-noise ratios (SNR). The effectiveness of the proposed algorithm was verified through comparative analysis with the traditional algorithms. The research results indicated that the ZFSD-IR algorithm has better accuracy in carrier-frequency and low-frequency estimation than traditional algorithms, and can achieve accurate detection of ZPW-2000 frequency shift signal under the lower SNR conditions. It has high detection accuracy and good anti-interference ability, ensuring the safe operation of high-speed trains.

Approach for multi-valued integer programming in multi-material topology optimization: Random discrete steepest descent (RDSD) algorithm

The present study models the multi-material topology optimization problems as the multi-valued integer programming (MVIP) or named as combinatorial optimization. By extending classical convex analysis and convex programming to discrete point-set functions, the discrete convex analysis and discrete steepest descent (DSD) algorithm are introduced. To overcome combinatorial complexity of the DSD algorithm, we employ the sequential approximate integer programming (SAIP) to explicitly and linearly approximate the implicit objective and constraint functions. Considering the multiple potential changed directions for multi-valued design variables, the random discrete steepest descent (RDSD) algorithm is proposed, where a random strategy is implemented to select a definitive direction of change. To analytically calculate multi-material discrete variable sensitivities, topological derivatives with material contrast is applied. In all, the MVIP is finally transferred as the linear 0–1 programming that can be efficiently solved by the canonical relaxation algorithm (CRA). Explicit nonlinear examples demonstrate that the RDSD algorithm owns nearly three orders of magnitude improvement compared with the commercial software (GUROBI). The proposed approach, without using any continuous variable relaxation and interpolation penalization schemes, successfully solves the minimum compliance problem, strength-related problem, and frequency-related optimization problems. Given the algorithm efficiency, mathematical generality and merits over other algorithms, the proposed RDSD algorithm is meaningful for other structural and topology optimization problems involving multi-valued discrete design variables.

Expectation analysis for bounding solutions of the 0–1 knapsack problem

In this paper, an entirely novel discrete probabilistic model is presented to generate 0–1 Knapsack Problem instances. We analyze the expected behavior of the greedy algorithm, the eligible-first algorithm and the linear relaxation algorithm for these instances; all used to bound the solution of the 0–1 Knapsack Problem (0–1 KP) and/or its approximation. The probabilistic setting is given and the main random variables are identified. The expected performance for each of the aforementioned algorithms is analytically established in closed forms in an unprecedented way.

A trust region algorithm for finite-strain plasticity with strongly coupled hardening

As extensions to our Lagrangian finite-strain plasticity framework based on the approximate exponential integrator, we introduce two new algorithms: (i) a fixed-radius trust region root finder for the nonlinear system involving the elastic right Cauchy Green tensor and plastic multiplier (ii) a partitioned approach for the hardening variables, which are determined in a staggered form using the strongly-coupled concept typically adopted for multiphysics problems. This allows the use of intricate hyperelastic laws combined with recent yield functions, which otherwise would involve a laborious treatment, and the use of corresponding work-hardening. Work-hardening would introduce significant nonlinearities in the constitutive system if used in a fully-coupled form. For the partitioned approach, a dynamic relaxation algorithm is adopted. This allows the efficient solution of the two nonlinear equations without significant drifting. Results show that robustness and efficiency are significantly improved. Herein, algorithms are described in detail. Significant testing is performed with imposed strains up to 100 for a carbon steel. This contributes to the robustness of equilibrium iterations. Drifting is also assessed as a function of number of steps in the dynamic relaxation algorithm. Numerical experimentation is performed in the 3D tension test for an anisotropic yield function.

Relaxed inertial self-adaptive algorithm for the split feasibility problem with multiple output sets and fixed-point problem in the class of demicontractive mappings

The purpose of this paper is to study the split feasibility problem with multiple output sets and fixed point problem in the class of demicontractive mappings and propose relaxed inertial self-adaptive algorithms that do not use the least squares method. Under some appropriate assumptions, we establish a strong convergence result for the sequence generated by the proposed algorithm. Our result generalizes and extends several results existing in the literature. Finally, we illustrate the convergence of the proposed algorithm by using a numerical example.

Modelling an emission trading scheme based on a dual-market mechanism in multimode networks with customised bus services

ABSTRACT The transport-related emissions are one of the main contributors to air pollution. In this paper, we construct an efficient and stable emission trading scheme (ETS) to reduce emissions. We build a dual-market mechanism for carbon emission permit (CEP) in the transportation system to control emissions at source, where CEPs are issued in a paid way in the primary market and traded freely in the secondary market. At the same time, we include customised bus (CB) and describe the competitive relationship between CB and private car (PC) in a multimode network. The market trading process and travel choice behaviours are formulated as a variational inequality problem (VIP). The VIP is solved using a relaxation algorithm, and the multi-round iteration strategy is used for updating permit volumes. Finally, we conduct numerical experiments based on Braess and Sioux Falls networks to demonstrate the merits of the ETS based on a dual-market mechanism.

A distribution-free-based approach for stochastic food closed-loop supply chain

ABSTRACT Resource scarcity has driven growing interest in circular economy (CE). Closed-loop supply chain (CLSC) with returnable transport items (RTIs) in the food industry is an important component of CE. However, existing works on food CLSC with RTIs have not simultaneously considered the perishability, facility location, and uncertain demand under limited information. Therefore, this work addresses a new food CLSC optimisation problem. We first propose a non-linear chance-constrained programming model. It is then transformed into a mixed-integer linear programming model via using the distribution-free (DF) method and sample average approximation (SAA) method, respectively. An illustrative example reveals that the DF method needs only 10.50% of the computation time of the SAA method. To address large-scale problems, an improved Lagrangian relaxation (LR) method is developed. To address the computational challenge in large-scale problems, an improved Lagrangian relaxation (LR) algorithm is developed. Results show that CPLEX achieves a gap of 75.57%, while the LR surpasses it by finding near-optimal solutions with a gap of 1.22%, using only 31.82% of the computation time required by CPLEX. For this work, the main insights are summarised: (1) extending product shelf life can reduce the total cost; and (2) to alleviate uncertain demand and production risks, production capacity and product inventory capacity can be appropriately expanded, but excessive investment may not improve returns.

A scenario-based decision framework for the order promising process in hybrid MTS/MTO production systems considering product substitution

ABSTRACT Considering the increasing competition among manufacturers and the diversification of customer orders, it is important to use the optimal production system. Hybrid manufacturing systems have proven to be a viable solution to achieve a satisfactory level of customization while maintaining adequate production volumes. This article determines the optimal strategy for decision makers in order to choose the appropriate method of supplying customers’ orders. In this article, a hybrid MTS-MTO production system has been studied in two different scenarios. For this purpose, a mixed-integer linear bi-objective model with product substitution and replaceable materials has been developed and solved by a Lagrangian Relaxation algorithm. The findings of this study reveal that enabling product substitution by manufacturers leads to an increase in the number of accepted orders, along with resulting in a higher average level of customer dissatisfaction. The system prioritizes the fulfillment of orders from permissive customers. Also, with the increase of uncertainty in each of the supplying methods, manufacturers are using other sources to supply raw materials to satisfy the accepted orders.

An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery

An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery

A High-Resolution Multipath Delay Measurement Method Using KFSC-WRELAX Algorithm.

Given the challenges associated with the low accuracy, complexity of the equipment, and poor interference resistance observed in current wireless multipath channel measurements, this study introduces a novel algorithm called KFSC-WRELAX. This algorithm integrates techniques involving pseudorandom noise (PN) sequences, Kalman filtering (KF), sliding correlation, and weighted Fourier transform combined with the RELAXation (WRELAX) algorithm. An m-sequence is employed as the probing sequence for channel detection. The effectiveness of the KFSC-WRELAX algorithm is demonstrated through both simulation experiments and corridor testing, showing that it can accurately determine the delays in various paths with robust performance at a signal-to-noise ratio (SNR) of -5 dB or higher.

Power-Efficient Resource Allocation for Active STAR-RIS-Aided SWIPT Communication Systems

Simultaneous wireless information and power transfer (SWIPT) has emerged as a pivotal technology in 6G, offering an efficient means of delivering energy to a large quantity of low-power devices while transmitting data concurrently. To address the challenges of obstructions, high path loss, and significant energy consumption associated with long-distance communication, this work introduces a novel alternating iterative optimization strategy. The proposed approach combines active simultaneous transmission and reflection of reconfigurable intelligent surfaces (STAR-RIS) with SWIPT to maximize spectrum efficiency and reduce overall system energy consumption. This method addresses the considerable energy demands inherent in SWIPT systems by focusing on reducing the power output from the base station (BS) while meeting key constraints: the communication rate for information receivers (IRs) and minimum energy levels for energy receivers (ERs). Given complex interactions between variables, the solution involves an alternating iterative optimization process. In the first stage of this approach, the passive beamforming variables are kept constant, enabling the use of semi-definite relaxation (SDR) and successive convex approximation (SCA) algorithms to optimize active beamforming variables. In the next stage, with active beamforming variables fixed, penalty-based algorithms are applied to fine-tune the passive beamforming variables. This iterative process continues, alternating between active and passive beamforming optimization, until the system converges on a stable solution. The simulation results indicated that the proposed system configuration, which leverages active STAR-RIS, achieves lower energy consumption and demonstrates improved performance compared to configurations utilizing passive RIS, active RIS, and passive STAR-RIS. This evidence suggests that the proposed approach can significantly contribute to advancing energy efficiency in 6G systems.

A novel treatment planning method via scissor beams for uniform-target-dose proton GRID with peak-valley-dose-ratio optimization.

Proton spatially fractionated RT (SFRT) can potentially synergize the unique advantages of using proton Bragg peak and SFRT peak-valley dose ratio (PVDR) to reduce the radiation-induced damage for normal tissues. Uniform-target-dose (UTD) proton GRID is a proton SFRT modality that can be clinically desirable and conveniently adopted since its UTD resembles target dose distribution in conventional proton RT (CONV). However, UTD proton GRID is not used clinically, which is likely due to the lack of an effective treatment planning method. This work will develop a novel treatment planning method using scissor beams (SB) for UTD proton GRID, with the joint optimization of PVDR and dose objectives. The SB method for spatial dose modulation in normal tissues with UTD has two steps: (1) a primary beam (PB) is halved with interleaved beamlets, to generate spatial dose modulation in normal tissues; (2) a complementary beam (CB) is added to fill in previously valley-dose positions in the target to generate UTD, while the CB is angled slightly from the PB, to maintain spatial dose modulation in normal tissues. A treatment planning method with PVDR optimization via the joint total variation and L1 (TVL1) regularization is developed to jointly optimize PVDR and dose objectives. The plan optimization solution is obtained using an iterative convex relaxation algorithm. The new methods SB and SB-TVL1 were validated in comparison with CONV. Compared to CONV of relatively homogeneous dose distribution, SB had modulated spatial dose pattern in normal tissues with UTD and comparable plan quality. Compared to SB, SB-TVL1 further maximized PVDR, with comparable dose-volume parameters. A novel SB method is proposed that can generate modulated spatial dose pattern in normal tissues to achieve UTD proton GRID. A treatment planning method with PVDR optimization capability via TVL1 regularization is developed that can jointly optimize PVDR and dose objectives for proton GRID.

RELAXED DOUBLE INERTIA AND VISCOSITY ALGORITHMS FOR THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

In this paper, we investigate a multiple-sets split feasibility problem with multiple output sets in infinite-dimensional Hilbert spaces. To address this problem, we propose relaxed inertial self-adaptive algorithms that do not use the least squares method and prove strong convergence results for the sequences generated by these algorithms. Finally, we validate the performances of the proposed algorithms by using numerical examples.

Decentralized Operations of Industrial Complex Microgrids Considering Corporate Power Purchase Agreements for Renewable Energy 100% Initiatives in South Korea

With the rise of environmental policies and advanced technologies, power systems are transitioning from centralized to decentralized systems, incorporating more distributed energy resources (DERs). This shift has increased interest in the operational functions of microgrids (MGs). The “Renewable Energy 100%” (RE100) campaign is pushing companies to adopt renewable energy. In South Korea, industrial complex microgrids (ICMGs) aim to achieve RE100 through corporate power purchase agreements (PPAs) with renewable energy providers. ICMGs need to operate in both grid-connected and islanded modes, facing challenges in power transactions due to different operating agents. This study proposes a decentralized optimal power flow (OPF) method using the separable augmented Lagrangian relaxation (SALR) algorithm to solve these power transaction problems without disclosing internal information. The proposed method decomposes the centralized OPF problem into subproblems for each ICMG and solves them in a distributed manner, sharing only transaction prices and amounts. Numerical results from the case study validate the effectiveness of the proposed method.

GPU-accelerated relaxed graph pattern matching algorithms

GPU-accelerated relaxed graph pattern matching algorithms

View-unaligned clustering with graph regularization

In current multi-view clustering modeling scenarios, the cross-view correspondence of the data is generally presumed in advance. However, this assumption is inevitably violated in practical applications as each view is independently processed during data collection and transmission, thus resulting in the view-unaligned problem (VuP). The absence of cross-view correspondence between the data renders most existing multi-view clustering methods ineffective in addressing the VuP. To address this problem, we propose a novel view-unaligned clustering method, termed View-unaligned Clustering with Graph regularization (VuCG), which performs latent embedding learning on manifold, latent embedding alignment and partition generation in a one-stage manner. Specifically, we implement the latent embedding learning on manifold by seeking a matrix factorization respecting the graph structure, and perform latent embedding alignment by identifying the counterpart from a selected template of the shuffled embedding using global and local information of the data in the latent space. Additionally, we obtain the partition of the aligned data by applying the relaxed k-means algorithm to the aligned embeddings. Extensive experimental results on four practical datasets demonstrate the effectiveness of the proposed method.

A virtual wind tunnel for deforming airborne wind energy kites

This paper presents a quasi-steady simulation framework for soft-wing kites with suspended control unit employed for airborne wind energy. The kites are subject to actuation-induced and aero-elastic deformation and are described by a coupled aero-structural model in a virtual wind tunnel setup. Key contributions of the present work are a kinetic dynamic relaxation algorithm and a procedure to define a physically consistent initial state. For symmetric actuation, the kite is pitch-statically stable and the simulations converge to a static equilibrium state. Most soft-wing kites are not roll-statically stable and do not find a static equilibrium without a symmetry assumption, as this introduces non-zero roll- and yaw moments. Another important contribution is the introduction of a steady circular flight state that enables convergence without a symmetry assumption. By neglecting gravity, the kite can fly in a perfectly circular turning motion around the wind vector with a constant radius and constant rotational velocity without requiring active control input. In an idealized wind-aligned tether case, the difference in aerodynamic- and centrifugal force application centers makes it impossible to achieve both a force- and moment equilibrium. This was resolved by including an elevation angle that introduces a radial tether force component, which introduces a centrifugal and aerodynamic force difference. Therefore, an operating point with roll equilibrium can be found where the kite finds a static equilibrium, enabling the first quasi-steady simulations of turning flights. Simulated quantifications of soft-wing kite turning behavior, i.e., turning laws, contribute to better kite- and control design.

Dynamics of the ohmic heating and chemically reactive time-dependent flow of magnetized Casson fluid inside a rectangular pipe

Chemical reaction and ohmic heating can significantly influence the flow behavior and heat transfer characteristics in industrial processes involving non-Newtonian fluids. These processes include polymer processing, food processing, and manufacturing processes where non-Newtonian fluids are commonly encountered. Therefore, the impacts of chemical reaction and ohmic heating on the unsteady flow of an incompressible magnetized non-Newtonian Casson liquid through a rectangular pipe with a variable pressure gradient is scrutinized in this article. The impacts of heat generation/absorption and viscous dissipation are also incorporated through the energy equation. The numerical simulations of partial differential equations (PDEs) are acquired utilizing the finite difference method with the incorporating relaxation (SOR) algorithm. The impacts of dissimilar imperative parameters on various flow fields are scrutinized through graphs. Outcomes indicate that liquid velocity decreases with enhancing values of the Casson parameter. Furthermore, the liquid temperature has an enhancing behavior with the impact of the heat source/sink parameter. Comparisons of numerical results with previously published results show an excellent agreement. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.

Joint uplink-downlink user-cell association for ultra-dense NOMA networks

As wireless communication systems evolve, the transition from homogeneous structures to heterogeneous ones intensifies. The need for continuous connectivity, fairness, and spectrum efficiency, such as in massive Internet of Things (IoT) networks and ultra reliable low latency communications (uRLLC), necessitates the utilization of base stations with diverse capabilities and coverage areas. As a result, the need for advanced interference management, user-cell association, and resource allocation techniques increases. This study proposes an innovative solution for the problem of non-orthogonal multiple access (NOMA) user-cell association in multi-tier ultra-dense heterogeneous networks (UD-HetNet). The proposed network constitutes a general framework that can be applied to next generation cellular communications, massive IoT, non-terrestrial and uRLLC type communications. Differing from previous studies that ignore interference and primarily focus on the received signal powers for user-cell association, this investigation advances the subject by considering the interplay between downlink received signal/interference power and uplink inter-cell interference. Due to the non-convex integer programming nature of the problem, it is proposed to employ an innovative relaxation algorithm to obtain a sub-optimal solution for the total signal-to-interference-plus-noise ratio (SINR). As verified through simulation results, the proposed association method permits concurrent communication participation of multiple users while managing the interference, rendering it as an ideal approach for systems emphasizing fairness and continuous connectivity.