Parameter Optimization Problem Research Articles

Parametric optimization of bar structures with discrete and continuous design variables using improved gradient projection method

The paper considers a parametric optimization problem for the bar structures formulated as nonlinear programming task, where the purpose function and non-linear constraints of the mathematical model are continuously differentiable functions of the design variables. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A discretization technique for the design variables that should vary discretely has been proposed. The discretization of the optimal design solution obtained in the continuous space of the design variables is performed by the purposefully selecting discrete points around the point of the continuous optimum. The comparison of the optimization results presented by the paper demonstrates that improved gradient method together with proposed discretization technique for the discrete design variables converges to better solutions of the problem comparing to the meta-heuristic algorithms.

Efficient Bi-objective SQL Optimization for Enclaved Cloud Databases with Differentially Private Padding

Hardware-enabled enclaves have been applied to efficiently enforce data security and privacy protection in cloud database services. Such enclaved systems, however, are reported to suffer from I/O-size (also referred to as communication-volume)-based side-channel attacks. Albeit differentially private padding has been exploited to defend against these attacks as a principle method, it introduces a challenging bi-objective parametric query optimization (BPQO) problem and current solutions are still not satisfactory. Concretely, the goal in BPQO is to find a Pareto-optimal plan that makes a tradeoff between query performance and privacy loss; existing solutions are subjected to poor computational efficiency and high cloud resource waste. In this article, we propose a two-phase optimization algorithm called TPOA to solve the BPQO problem. TPOA incorporates two novel ideas: divide-and-conquer to separately handle parameters according to their types in optimization for dimensionality reduction; on-demand-optimization to progressively build a set of necessary Pareto-optimal plans instead of seeking a complete set for saving resources. Besides, we introduce an acceleration mechanism in TPOA to improve its efficiency, which prunes the non-optimal candidate plans in advance. We theoretically prove the correctness of TPOA, numerically analyze its complexity, and formally give an end-to-end privacy analysis. Through a comprehensive evaluation on its efficiency by running baseline algorithms over synthetic and test-bed benchmarks, we can conclude that TPOA outperforms all benchmarked methods with an overall efficiency improvement of roughly two orders of magnitude; moreover, the acceleration mechanism speeds up TPOA by 10-200×.

Deriving Controllable Local Optimal Solutions through an Environment Parameter Fixed Algorithm

This paper addresses the challenge of optimizing objective functions in engineering problems influenced by multiple environmental factors, such as temperature and humidity. Traditional modeling approaches often struggle to capture the complexities of non-ideal situations. In this research, we propose a novel approach called the Environment Parameter Fixed Algorithm (EPFA) for optimizing the objective function of a deep neural network (DNN) trained in a specific environment. By fixing the environmental parameters in the DNN defined objective function, we transform the original optimization problem into a control parameter optimization problem. We integrate EPFA-CLS (Controllable local-Optimal Solution) with Gradient Descent and algorithms such as Adagrad to obtain the optimal solution. To demonstrate the concept, we apply our approach to an optimal course model and validate it using optimal course and Boston house price datasets. The results demonstrate the effectiveness of our approach in handling optimization problems in complex environments, offering promising outcomes for practical engineering applications.

Resource Constrained Vehicular Edge Federated Learning With Highly Mobile Connected Vehicles

This paper proposes a vehicular edge federated learning (VEFL) solution, where an edge server leverages highly mobile connected vehicles’ (CVs’) onboard central processing units (CPUs) and local datasets to train a global model. Convergence analysis reveals that the VEFL training loss depends on the successful receptions of the CVs’ trained models over the intermittent vehicle-to-infrastructure (V2I) wireless links. Owing to high mobility, in the full device participation case (FDPC), the edge server aggregates client model parameters based on a weighted combination according to the CVs’ dataset sizes and sojourn periods, while it selects a subset of CVs in the partial device participation case (PDPC). We then devise joint VEFL and radio access technology (RAT) parameters optimization problems under delay, energy and cost constraints to maximize the probability of successful reception of the locally trained models. Considering that the optimization problem is NP-hard, we decompose it into a VEFL parameter optimization sub-problem, given the estimated worst-case sojourn period, delay and energy expense, and an online RAT parameter optimization sub-problem. Finally, extensive simulations are conducted to validate the effectiveness of the proposed solutions with a practical 5G new radio (5G-NR) RAT under a realistic microscopic mobility model.

Optimization of drilling processes of aluminium metal matrix composites using the robust ordinal priority approach

In the present-day automobile, aviation, marine, defence and manufacturing industries, aluminium metal matrix composites (Al-MMCs) have found immense applications due to their higher strength-to-weight ratio, toughness, thermal stability, and excellent corrosion and wear resistance properties. Non-uniform metallurgical structure due to presence of agglomerated reinforcement elements in the matrix is responsible for poor machinability of Al-MMCs leading to reduced tool life, poor surface integrity, higher energy consumption, increased cutting force etc. during drilling operations. This paper proposes application of a newly developed multi-criteria decision making tool, in the form of ordinal priority approach (OPA), for solving two parametric optimization problems for drilling operations of Al-MMCs. In this method, the optimal intermix of various drilling parameters is identified based on ordinal preference of the experts with respect to criteria importance and preference of the conducted experiments against each of the criteria. In the first example, a combination of drilling parameters as cutting speed = 87.96 mm/min, feed rate = 0.050 mm/min and point angle = 140° provides compromised values of average surface roughness (Ra), cutting force and torque. On the other hand, in the second example, the most preferred values of thrust force, Ra and burr height can be obtained at an optimal parametric intermix of spindle speed = 2000 rpm, feed rate = 0.2 mm/rev, Al2219 work material and carbide drill bit. The robustness and solution accuracy of OPA while solving parametric optimization problems are also validated against other criteria weight measurement techniques and MCDM tools respectively.

Optimization features of an aperture antenna with field variable-phase distribution

The solution of a number of tasks at maximum ranges in a wide sector of angles requires the use by radio engineering systems of an antenna with a quasi-sector directional pattern, the formation of which is provided by an variable-phase distribution of excitation sources (currents or fields). Taking into account the ambiguous influence of many parameters of such a distribution on the shape of the realized radiation pattern, the traditional optimization criteria for such an antenna are unacceptable. The possibilities and criteria of parametric optimization can be determined using numerical methods of mathematical modeling. In order to solve the problem of parametric optimization of an aperture microwave antenna with a quasi-sector radiation pattern and to select a criterion that allows achieving the best design solution of the projected antenna in this sense, its mathematical model has been developed. It is proposed to use a complex quality criterion for optimization in a uniform approximation of antennas with variable-phase field distribution in the aperture. The constructed mathematical model of a microwave antenna describing the quasi-sector radiation pattern and the corresponding field distribution in its aperture is presented, which makes it possible to determine the controlled parameters that ensure the achievement of a given optimization criterion. The determining influence of the fraction and amplitude of the antiphase section in the field distribution on the main parameters of the radiation pattern is shown. The results of mathematical modeling indicate the possibility of controlling the parameters of the quasi-vector radiation pattern of the aperture antenna and achieving a given criterion for its optimization. The results obtained can be recommended for practical use in the design of aperture antennas with variable-phase distribution of field.

Comparative study on manifold learning approaches for parametric topology optimization problem via unsupervised deep learning

Comparative study on manifold learning approaches for parametric topology optimization problem via unsupervised deep learning

An approximate solution for variable‐order fractional optimal control problem via Müntz‐Legendre wavelets with an application in epidemiology

A class of variable‐order fractional optimal control problems (VO‐FOCPs) is solved by applying Müntz‐Legendre wavelets. Different from classical wavelets (such as Legendre and Chebyshev), the Müntz‐Legendre wavelets have an extra parameter representing the fractional order; therefore, they provide more reliable results for certain fractional calculus problems. Using the regularized beta function, the Riemann‐Liouville fractional integral operator (RLFIO) of these wavelets is precisely determined. We then transform the given VO‐FOCPs into parameter optimization problems that can be easily solved. The convergence analysis and error estimation of the proposed method are provided. Four examples are solved to illustrate the high accuracy of the approach. The method is also applied to a cancer‐obesity interaction model to analyze the interactions between the tumor, immune, normal, and fat cells when the chemotherapeutic drugs are injected into a body.

Optimal switching control of 1,3-propanediol fed-batch production with a cost on smooth feeding rate variation

In this paper, we propose a nonlinear switched control system for microbial 1,3-propanediol (1,3-PD) fed-batch production, where the smooth feeding rate of glycerol as well as the switching instants between batch process and feeding process are taken as control variables. To maximize 1,3-PD yield and minimize the fluctuation of feeding rate, we then present an optimal switching control problem with a cost on the smooth feeding rate variation and subject to path constraints reflecting the operational requirements. For solving this problem, we convert it to a series of parameter optimization problems by using a novel control parameterization scheme, a time-scaling transformation and a constraint transcription technique. An analytical expression of the total variation for the smooth feeding rate is also derived. On this basis, we develop a parallel Particle Swarm Optimization (PSO) algorithm together with the gradient-based optimization to solve the resulting problem. Finally, numerical simulations indicate that sacrificing a small amount of 1,3-PD can reduce the feeding rate variation significantly.

Comparing solution paths of sparse quadratic minimization with a Stieltjes matrix

This paper studies several solution paths of sparse quadratic minimization problems as a function of the weighing parameter of the bi-objective of estimation loss versus solution sparsity. Three such paths are considered: the “ℓ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _0$$\\end{document}-path” where the discontinuous ℓ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _0$$\\end{document}-function provides the exact sparsity count; the “ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path” where the ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-function provides a convex surrogate of sparsity count; and the “capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path” where the nonconvex nondifferentiable capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-function aims to enhance the ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-approximation. Serving different purposes, each of these three formulations is different from each other, both analytically and computationally. Our results deepen the understanding of (old and new) properties of the associated paths, highlight the pros, cons, and tradeoffs of these sparse optimization models, and provide numerical evidence to support the practical superiority of the capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path. Our study of the capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path is interesting in its own right as the path pertains to computable directionally stationary (= strongly locally minimizing in this context, as opposed to globally optimal) solutions of a parametric nonconvex nondifferentiable optimization problem. Motivated by classical parametric quadratic programming theory and reinforced by modern statistical learning studies, both casting an exponential perspective in fully describing such solution paths, we also aim to address the question of whether some of them can be fully traced in strongly polynomial time in the problem dimensions. A major conclusion of this paper is that a path of directional stationary solutions of the capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-regularized problem offers interesting theoretical properties and practical compromise between the ℓ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _0$$\\end{document}-path and the ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path. Indeed, while the ℓ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _0$$\\end{document}-path is computationally prohibitive and greatly handicapped by the repeated solution of mixed-integer nonlinear programs, the quality of ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path, in terms of the two criteria—loss and sparsity—in the estimation objective, is inferior to the capped ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-path; the latter can be obtained efficiently by a combination of a parametric pivoting-like scheme supplemented by an algorithm that takes advantage of the Z-matrix structure of the loss function.

Dam Safety Evaluation Method after Extreme Load Condition Based on Health Monitoring and Deep Learning.

The safety operation of dams after extreme load is an important frontier research topic in the field of dam engineering. The dam health monitoring provides a reliable data basis for a safety evaluation after extreme loads. This study proposes a novel data-driven fusion model for a dam safety evaluation after extreme load based on monitoring data derived by sensors. First, the relationship between dam environmental quantity and effect quantity is deeply excavated based on bidirectional long short-term memory (BiLSTM) network, which is a deeply improved LSTM model. Aiming at the parameter optimization problem of BiLSTM model, sparrow search algorithm (SSA), which is an advanced optimization algorithm, is integrated. Second, conducting the constructed SSA-BiLSTM model to estimate the change law of dam effect quantity after the extreme load. Finally, the Mann-Whitney U-test theory is introduced to establish the evaluation criterion of the dam safety state. Project case shows that the multiple quantitative prediction accuracy evaluation indicators of the proposed method are significantly superior to the comparison method, with mean absolute percentage error (MAPE) and mean absolute error (MAE) values decreasing by 30.5% and 27.8%, respectively, on average. The proposed model can accurately diagnose the dam safety state after the extreme load compared with on-site inspection results of the engineering department, which provides a new method for dam safety evaluation.

Dimension synthesis of a 2T2R curved layer FDM 3D printer

3D printing or Additive Manufacturing (AM) is significant in various applications. The authors’ previous research indicates that higher-degree-of-freedom (DOF) 3D printers have the potential for curved layer printing and multi-direction AM. Hence, this paper focuses on designing a novel 2T2R FDM 3D printer. Performance-chart-based design methodology (PCbDM) has been used for multiple parameters optimization problems due to its reliability, globality, and intuition. While its limitation is the number of optimization parameters less than four. The printer’s print head is attached to a planar parallel 1T1R mechanism (4R1P, 3R1P, and passive P). Objectives and requirements require the print head to move over a more considerable distance with a constant swing range and proper pressure angle. So, the 4R1P five-bar (virtual double-rocker, crank-rocker, and rocker-crank) has been investigated to facilitate PCbDM. Meanwhile, one DOF remote center of motion (RCM) mechanism has been integrated for decoupling motion control. Finally, the selected parameters are verified by comparing the numerical and simulation results and experiments. Besides, this novel 3D printer’s initial feasibility of flat and curved layer printing is studied with several printed parts to give qualitative analyses. This early-stage work generally intends to investigate the dimension synthesis and show the resulting 2T2R-type rotary 3D printer’s initial feasibility for curved printing. The research can help people understand how to carry out the dimension synthesis of 4R1P and a novel mechanism with multi-chain with the help of Grashof criteria to reduce the design space dimensionality.

PID parameter tuning based on improved particle swarm optimization algorithm

To address the shortcomings of the particle swarm algorithm in solving the PID controller parameter optimization problem in the late stage, an improved particle swarm algorithm is proposed for solving the problem. The particle swarm algorithm is optimized by introducing a nonlinear decreasing inertia weight adjustment strategy so that the pre-flight speed of the particles does not drop too fast, thus balancing the global search ability of the particles with the local search ability and avoiding falling into a local optimum. Simulation experiments were conducted in Matlab/Simulink using the standard PSO, ZN formula method, and the improved PSO, respectively. The results show that the improved algorithm enhances the stability, convergence speed, and search accuracy of the PID parameters with better performance indicators.

Parametric Optimization on HPC Clusters with Geneva

Many challenges of today’s science are parametric optimization problems that are extremely complex and computationally intensive to calculate. At the same time, the hardware for high-performance computing is becoming increasingly powerful. Geneva is a framework for parallel optimization of large-scale problems with highly nonlinear quality surfaces in grid and cloud environments. To harness the immense computing power of high-performance computing clusters, we have developed a new networking component for Geneva—the so-called MPI Consumer—which makes Geneva suitable for HPC. Geneva is most prominent for its evolutionary algorithm, which requires repeatedly evaluating a user-defined cost function. The MPI Consumer parallelizes the computation of the candidate solutions’ cost functions by sending them to remote cluster nodes. By using an advanced multithreading mechanism on the master node and by using asynchronous requests on the worker nodes, the MPI Consumer is highly scalable. Additionally, it provides fault tolerance, which is usually not the case for MPI programs but becomes increasingly important for HPC. Moreover, the MPI Consumer provides a framework for the intuitive implementation of fine-grained parallelization of the cost function. Since the MPI Consumer conforms to the standard paradigm of HPC programs, it vastly improves Geneva’s user-friendliness on HPC clusters. This article gives insight into Geneva’s general system architecture and the system design of the MPI Consumer as well as the underlying concepts. Geneva—including the novel MPI Consumer—is publicly available as an open source project on GitHub (https://github.com/gemfony/geneva) and is currently used for fundamental physics research at GSI in Darmstadt, Germany.

Multi-objective optimization of process parameters of laser cladding 15-5PH alloy powder based on gray-fuzzy taguchi approach

Laser cladding is a new surface treatment technology that is widely used for surface modification of metal parts, and the high quality of the surface geometry of the cladding layer can save a lot of resources for the company. To obtain high quality of the clad layer, the L25 Taguchi experiment of laser cladding process parameters was designed to laser-clad a single 15-5PH layer on the surface of 45# steel; the effect of process parameters on the surface morphology and dilution rate of the coating was determined by ANOVA; the optimal combination of process parameters was obtained by combining gray correlation and fuzzy inference system method. The ANOVA results show that the scanning speed among the laser cladding process parameters plays a key role in obtaining the best superposition of the four geometrical features of the cladding layer simultaneously; With the optimization objectives of larger clad width and height, smaller clad depth, and 30% dilution rate, the optimal combination of process parameters, (P: 600W, V: 500 mm min−1, F −1 : 1.3 r min−1), obtained based on the Gray-fuzzy Taguchi Approach, was compared and analyzed to find a significant improvement in the geometric quality characteristics of the optimized clad layer. The analysis of microstructure, physical phase, hardness, wear resistance and corrosion resistance showed that the 15-5PH clad layer was able to effectively enhance the surface properties of the 12Cr13 substrate. The optimization method proposed in this study can solve the problem of parameter optimization in the industrial multi-parameter and multi-response processes.

Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles

Aiming at the cooperative guidance problem of multi-hypersonic glide vehicles, a cooperative guidance method based on a parametric design and an analytical solution of time-to-go is proposed. First, the hypersonic reentry trajectory optimization problem was transformed into a parameter optimization problem. The parameters were optimized to determine the angle of attack profile and the time to enter the altitude velocity reentry corridor. Then, using the quasi-equilibrium glide condition, the estimation form of the remaining flight time was analytically derived to satisfy accurately the cooperative time constraint. Using the remaining time-to-go and range-to-go, combined with the heading angle deviation corridor, the bank angle command was further calculated. Finally, the swarm intelligence optimization algorithm was used to optimize the design parameters to obtain the cooperative guidance trajectory satisfying the time constraint. Simulations showed that the analytical time reentry cooperative guidance algorithm proposed in this paper can accurately meet the time constraints and cooperative flight accuracy. Monte Carlo simulation experiments verified that the proposed algorithm demonstrates a robust performance.

Graphical multispectral radiation temperature inversion algorithm based on deep learning.

Neural networks are the most promising tool to solve the problem that an assumed emissivity model is needed in the field of multispectral radiometric temperature measurement. Existing neural network multispectral radiometric temperature measurement algorithms have been investigating the problems of network selection, network porting, and parameter optimization. The inversion accuracy and adaptability of the algorithms have been unsatisfactory. In view of the great success of deep learning in the field of image processing, this Letter proposes the idea of converting one-dimensional multispectral radiometric temperature data into two-dimensional image data for data processing to improve the accuracy and adaptability of multispectral radiometric temperature measurement by deep learning algorithms. Simulation and experimental validation are carried out. In the simulation, the error is less than 0.71% without noise and 1.80% with 5% random noise, which improves the accuracy by more than 1.55% and 2.66% compared with the classical BP (backpropagation) algorithm, and 0.94% and 0.96% compared with the GIM-LSTM (generalized inverse matrix-long short-term memory) algorithm. In the experiment, the error is less than 0.83%. This indicates that the method has high research value and is expected to lead multispectral radiometric temperature measurement technology to a new level.

Structural Changes in Nonlocal Denoising Models Arising Through Bi-Level Parameter Learning

We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a general topological space. Our focus lies on the situation with non-compact parameter domains, which is, for example, relevant when the commonly used box constraints are disposed of. To overcome this lack of compactness, we propose a natural extension of the upper-level functional to the closure of the parameter domain via Gamma-convergence, which captures possible structural changes in the reconstruction model at the edge of the domain. Under two main assumptions, namely, Mosco-convergence of the regularizers and uniqueness of minimizers of the lower-level problem, we prove that the extension coincides with the relaxation, thus admitting minimizers that relate to the parameter optimization problem of interest. We apply our abstract framework to investigate a quartet of practically relevant models in image denoising, all featuring nonlocality. The associated families of regularizers exhibit qualitatively different parameter dependence, describing a weight factor, an amount of nonlocality, an integrability exponent, and a fractional order, respectively. After the asymptotic analysis that determines the relaxation in each of the four settings, we finally establish theoretical conditions on the data that guarantee structural stability of the models and give examples of when stability is lost.

Multiobjective optimization of roadheader shovel-plate parameters based on improved particle swarm optimization and grey decision.

The development of tunneling equipment still lags behind, limiting rapid and accurate tunneling and restricting efficient production in coal mines. Thus, improving the reliability and design of roadheaders becomes essential. As the shovel plate is an essential part of a roadheader, improving its parameters can increase the roadheader performance. The parameter optimization of roadheader shovel plate is multi-objective optimization. Because of conventional multiobjective optimization requires strong prior knowledge, often provides low-quality results, and presents vulnerability to initialization and other shortcomings when used in practice. We propose an improved particle swarm optimization (PSO) algorithm that takes the minimum Euclidean distance from a base value as the evaluation criterion for global and individual extreme values. The improved algorithm enables multiobjective parallel optimization by providing a non-inferior solution set. Then, the optimal solution is searched in this set using grey decision to obtain the optimal solution. To validate the proposed method, the multiobjective optimization problem of the shovel-plate parameters is formulated for its solution. Before optimization shovel-plate most important parameters l is the width of the shovel plate = 3.2 m, is the inclination angle of the shovel plate and β = ,19°. When doing optimization, set accelerated factor , population size N = 20, and maximum number of iterations = 100. In addition, speed V was restricted by , and inertia factor W was dynamic and linearly decreasing, , with and . In addition, and were set randomly in [0, 1], while optimization degree η was set to 30%. And then we executed the improved PSO, obtaining 2000 non-inferior solutions. Apply grey decision to find the optimal solution. The optimal roadheader shovel-plate parameters are l = 3.144 m and β = 16.88°. Comparative analysis is made before and after optimization, the optimized parameters were substituted into the model and simulated. Obtained that the optimized parameters of shovel-plate can reduce the mass of the shovel plate decreases by 14.3%, while the propulsive resistance decreases by 6.62%, and the load capacity increases by 3.68%. Thus jointly achieving the optimization goals of reducing the propulsive resistance while increasing the load capacity. The feasibility of the proposed multiobjective optimization method with improved particle swarm optimization and grey decision is verified, and the method can provide convenient multiobjective optimization in engineering practice.

An infeasible interior-point technique to generate the nondominated set for multiobjective optimization problems

In this paper, an infeasible interior-point technique is proposed to generate the nondominated set of nonlinear multi-objective optimization problems with the help of the direction-based cone method. We derive the proposed method for both convex and nonconvex problems. In order to solve the parametric optimization problems of the cone method, the infeasible interior-point method starts with an initial iterate outside the feasible region, and then gradually reduces the primal and dual infeasibility measures and the objective function value across the iterations with the help of a merit function. Estimates of the reduction of primal and dual infeasibility parameters per iteration are given. The convergence analysis of the method and an estimate of the number of iterations to reach an ϵ-precise solution are also provided. We provide the performance of the proposed methods on a variety of convex and nonconvex multi-objective test problems. Performance comparison between the proposed method and popular existing solvers is provided with respect to two performance measures and the corresponding relative efficiency measures. The reduction of a combined infeasibility measure, as the iterations progress, on the test problems is also shown graphically.