Parameter Optimization Problem Research Articles

Multi-objective trajectory planning for industrial robots using a hybrid optimization approach

Abstract In this paper, a hybrid approach organized in four phases is proposed to solve the multi-objective trajectory planning problem for industrial robots. In the first phase, a transcription of the original problem into a standard multi-objective parametric optimization problem is achieved by adopting an adequate parametrization scheme for the continuous robot configuration variables. Then, in the second phase, a global search is performed using a population-based search metaheuristic in order to build a first approximation of the Pareto front (PF). In the third phase, a local search is applied in the neighborhood of each solution of the PF approximation using a deterministic algorithm in order to generate new solutions. Finally, in the fourth phase, results of the global and local searches are gathered and postprocessed using a multi-objective direct search method to enhance the quality of compromise solutions and to converge toward the true optimal PF. By combining different optimization techniques, we intend not only to improve the overall search mechanism of the optimization strategy but also the resulting hybrid algorithm should keep the robustness of the population-based algorithm while enjoying the theoretical properties of convergence of the deterministic component. Also, the proposed approach is modular and flexible, and it can be implemented in different ways according to the applied techniques in the different phases. In this paper, we illustrate the efficiency of the hybrid framework by considering different techniques available in various numerical optimization libraries which are combined judiciously and tested on various case studies.

A comprehensive review of parametric optimization of electrical discharge machining processes using multi-criteria decision-making techniques

Optimization of electrical discharge machining (EDM) processes is a critical issue due to complex material removal mechanism, presence of multiple input parameters and responses (outputs) and interactions among them and varying interest of different stakeholders with respect to relative importance assigned to the considered responses. Multi-criteria decision making (MCDM) techniques have become potent tools in solving parametric optimization problems of the EDM processes. In this paper, more than 130 research articles from SCOPUS database published during 2013–22 are reviewed extracting information with respect to experimental design plans employed, materials machined, dielectrics used, process parameters and responses considered and MCDM tools applied along with their integration with other mathematical techniques. A detailed analysis of those reviewed articles reveals that the past researchers have mostly preferred Taguchi’s L9 orthogonal array as the experimental design plan; EDM oil as the dielectric fluid; medium and high carbon steels as the work materials; peak current and pulse-on time as the input parameters; material removal rate, tool wear rate and surface roughness as the responses; and grey relational analysis as the MCDM tool during conducting and optimizing EDM operations. This review paper would act as a data repository to the future researchers in understanding the stochastic behaviour of EDM processes and providing guidance in setting the tentative operating levels of varying input parameters along with achievable response values. The extracted dataset can be treated as an input to any of the machine learning algorithms for subsequent development of appropriate prediction models. This review also outlines potential future research avenues, emphasizing advancements in EDM technology and the integration of innovative multi-criteria decision-making tools.

Rational design of the aerodynamic rudder structure taking into account strength, rigidity and aeroelastic stability

The paper considers a design process of an aerodynamic rudder, which structure comprises the skin of constant thickness, a load-bearing structure and a trimmed nose that plays the role of an anti-flutter balancer. The aim of the work is to set and solve the design problem of a rational structural and technological solution of the rudder that meets the requirements of strength, rigidity, aeroelastic stability and minimum mass. To solve this problem, a design algorithm for the rudder, using topological and parametric optimization, is proposed. The main parameters of the design area and the trimmed nose required for topological optimization are determined. The ANSYS Workbench software package was used for the finite element analysis and topological optimization. Based on the results of optimization, post-processing was carried out. A structural and technological solution, that combines structural layouts with constant and variable width of the trimmed nose, was proposed. An analysis of the stress-strain state was carried out, and it was found that the designed structure meets the strength requirements for the given design case. A scheme for solving the parametric optimization problem of the rudder under the condition of aeroelastic stability is proposed. Within the framework of solving this problem, a flutter study was conducted, using a multi-mode model, which makes it possible to study the rudder and body-rudder flutter forms of an unmanned aerial vehicle (UAV) equipped with aerodynamic rudders. The results of the flutter study for the design mode of the UAV flight are obtained in the form of dependencies of the critical flutter velocity and frequency on the average width of the trimmed nose. The analysis of these dependencies allowed us to derive the optimal values of the trimmed nose parameters from the minimum weight condition for two rudder configurations: with a constant and variable width of the trimmed nose.

Continuity of the solutions sets for parametric set optimization problems

The current study focuses on exploring the stability of solution sets pertaining to set optimization problems, particularly with regard to the set order relation outlined by Karaman et al. 2018. Sufficient conditions are provided for the lower semicontinuity, upper semicontinuity, and compactness of m-minimal solution mappings in parametric set optimization, where the involved set-valued mapping is Lipschitz continuous.

Data poisoning attacks on traffic state estimation and prediction

Data has become ubiquitous nowadays in transportation, including vehicular data and infrastructure-generated data. The growing reliance on data poses potential cybersecurity issues to transportation systems, among which the so-called “data poisoning” attacks by adversaries are becoming increasingly critical. Such attacks aim to compromise a system’s performance by adding systematic and malicious noises, perturbations, or deviations to the dataset used by the system. Formal investigations of data poisoning attacks are essential for understanding the attacks and developing effective defense methods. This study develops a general data poisoning attack model for traffic state estimation and prediction (TSEP) that is a basic application in transportation. We first formulate data poisoning attacks as a general sensitivity analysis of parameterized optimization problems over parameter changes (i.e., data perturbations) and study the Lipschitz continuity property of the solution with the presence of general (equality and inequality) constraints. Then, we develop attack models that fit a broader spectrum of learning applications (such as TSEP) by extending existing models that only focus on learning problems with no or equality constraints (widely used in the cybersecurity field). Since the solution of such general problems is often continuous but not differentiable with data changes, we apply the generalized implicit function theorem to compute the semi-derivatives that express how the TSEP solution responds to data perturbations. The semi-derivatives enable us to evaluate TSEP models’ vulnerability (at each data point) and solve the proposed attack model. We demonstrate the generality and effectiveness of the proposed method on two TSEP models using mobile sensing data.

A Multi-level Surrogate-assisted Algorithm for Expensive Optimization Problems

With the development of computer science, more and more complex problems rely on the help of computers for solving. When facing the parameter optimization problem of complex models, traditional intelligent optimization algorithms often require multiple iterations on the target problem. It can bring unacceptable costs and resource costs in dealing with these complex problems. In order to solve the parameter optimization of complex problems, in this paper we propose a multi-level surrogate-assisted optimization algorithm (MLSAO). By constructing surrogate models at different levels, the algorithm effectively explores the parameter space, avoiding local optima and enhancing optimization efficiency. The method combines two optimization algorithms, differential evolution (DE) and Downhill simplex method. DE is focused on global level surrogate model optimization. Downhill simplex is concentrated on local level surrogate model update. Random forest and inverse distance weighting (IDW) are constructed for global and local level surrogate model respectively. These methods leverage their respective advantages at different stages of the algorithm. The MLSAO algorithm is evaluated against other state-of-the-art approaches using benchmark functions of varying dimensions. Comprehensive results from the comparisons showcase the superior performance of the MLSAO algorithm in addressing expensive optimization problems. Moreover, we implement the MLSAO algorithm for tuning precipitation parameters in the Community Earth System Model (CESM). The outcomes reveal its effective enhancement of CESM's simulation accuracy for precipitation in the North Indian Ocean and the North Pacific region. These experiments demonstrate that MLSAO can better address parameter optimization problems under complex conditions.

A novel method for reference parameters identification and electrical property estimation of PV modules under varying operating conditions

The parameters identification of the diode model under reference condition are crucial and have significant impact on output characteristics estimation of photovoltaic (PV) module under varying operating conditions. The traditional methods of extracting model parameters have always focused on solving the parameter optimization problem only under some certain condition, which neglects their effect of performance estimation under other operating condition. In this paper, a novel method is proposed to identify the reference physical parameters and enhance the accuracy of electrical property estimation for PV modules under varying operating conditions. New objective function with penalty function is constructed by considering the estimated performance not only under reference condition but also under multiple real operating conditions. The maximum permissible error (MPE) is proposed to constrain the accuracy for key electrical output indicators and added in penalty function to ensure the accuracy under reference condition. Taking into account the inequality constraints, the guaranteed convergence particle swarm optimization with penalty function (P-GCPSO) is introduced for parameter identification. A set of comparisons between the measured and calculated results of PV modules indicate that the proposed method substantially more accurate than other documented methods for both single and double diode model. For the six different materials tested, the root mean square error (RMSE) was compared. The RMSE of the single-diode model is reduced by at least 57.98% compared to the compared method, with a maximum reduction of 86.57%. Similarly, the RMSE of the double -diode model was reduced by at least 47.24% with a maximum reduction of 88.71% compared to the compared methods. Additionally, the tests with six different types of PV modules at varying environmental conditions for over one year prove that the proposed method is reliable and practical for real-world applications. The relative error of power generation reached a minimum of 2.20%. This proves the reliability and practicability of the proposed method in practical applications. The proposed method is envisaged to be valuable for both offline analysis and online monitoring applications where an accurate, fast and consistent performance estimation tool is required.

Optimality conditions for bilevel optimal control problems with non-convex quasi-variational inequalities

We establish Pontryagin optimality conditions for a generalized bilevel optimal control problem in which the leader is subject to a pure state inequality constraint, while the follower is governed by a non-convex quasi-variational inequality parameterized by the final state. To simplify the problem at hand, we convert it into a single-level optimal control problem by mapping the solution set of the quasi-variational inequality to a parametric optimization problem and employing the value function reformulation. Furthermore, we introduce certain regularity conditions to ensure that the derived maximum principle remains non-degenerate. Finally, we provide an illustrative example to elucidate our research findings.

Optimization design of brushless DC motor based on improved JAYA algorithm

Brushless direct current motor is widely used in industrial production because of its simple structure, wide speed range and low noise. To improve the operation efficiency of brushless DC motor and reduce the production and application costs, the optimization of brushless DC motor is analyzed by introducing the JAYA algorithm. This method determines the optimal parameters of a brushless DC motor using the theory of electromagnetic structure parameter selection and efficiency calculation. The population diversity of the JAYA algorithm is improved through an empirical learning strategy, and an adaptive strategy is introduced to balance the development ability and search performance of the algorithm. This ensures population diversity and improves convergence speed. The experiment showcases that the improved JAYA algorithm has a lower rank average in unimodal function operations, demonstrating stronger local development ability and better stability. It exhibits strong search ability in many local optima of multimodal functions. Moreover, the motor's average efficiency after optimization is 94.48%. The algorithm reaches the global optimum after approximately 40 iterations and offers faster convergence speed and higher accuracy. The adaptive JAYA algorithm is stable at around 93% when the number of iterations reaches 90, with a maximum efficiency of 95.3%. It is 5–12 percentage points higher than the other three comparison algorithms. The optimal solution of the motor parameters in the adaptive JAYA algorithm is closest to the theoretical parameter optimization value, meeting both the constraints of variables and the constraints of the model. The stator diameter, tooth magnetic induction, winding current density, air gap magnetic induction, and stator yoke magnetic induction values are 201.5 mm, 1.8 T, 2.049 A/mm2, 0.63 T, and 0.91 T, respectively. The research overcomes the problem of parameter optimization in the optimization design of brushless DC motor, improving their economic value of brushless DC motor in industrial production and application.

Set-valued parametric optimization problems with higher-order $$\rho $$-cone arcwise connectedness

Set-valued parametric optimization problems with higher-order $$\rho $$-cone arcwise connectedness

Parameter and Topology Optimization of Structures in the Frequency Domain under Nevanlinna–Pick Interpolation Constraints

The design optimization of structures can be conducted in either the time domain or the frequency domain. The frequency domain approach is advantageous compared to its time domain counterpart, especially if the degree of freedom is large, the objectives and/or constraints are formulated in the frequency domain, or the structure is subject to random loading. In this paper, an attempt is undertaken to obtain feasible optimal solutions by implementing the Nevanlinna–Pick (NP) interpolation theory across multi-objective structural optimization problems in the frequency domain. The NP equations introduce a trade-off that originates from the interpolation theory for complex variables. According to the NP theory, a complex function cannot have an independent amplitude from its derivative at a certain frequency. Consequently, the frequency response of a physical system cannot be shaped arbitrarily at discrete frequencies. Our objectives within this paper include calculating the weight, natural frequency, fatigue life, frequency domain response, and its derivative. To illustrate our claims, sample parameter and topology optimization problems were formulated and solved, both with and without the NP constraints. It was found that the inclusion of NP constraints induced a considerable improvement in the optimal solutions, while also causing the convergence to the optimal solution to become smoother.

Optimization of Ship Power Supply Network and Intelligent Energy Management Strategy Under Multiple Energy Modes

<p>Purpose: This article aims to address the issues of incomplete management models and slow convergence speed of optimization models in energy management in ship multi energy systems, and to construct a comprehensive dynamic optimization objective model. Method: Firstly, establish an optimization design model with the objective functions of energy storage system cost, grid power fluctuation smoothing, and energy supply and demand balance; Then, in the optimization process of the objective function, a bus voltage coordination control strategy is adopted, and for the parameter optimization problem in the strategy, a cuckoo search algorithm based on population feature feedback is used for optimization. Result: Through simulation experiments, the method proposed in this article provides effective guidance for capacity configuration and energy management of multi energy ship microgrids, improving quality and efficiency.</p> <p> </p>

Research on Optimization Design Based on Heliostat Field

This study aims to deeply explore the mathematical modeling and performance optimization of solar heliostat fields, in order to improve their energy output efficiency. The solar heliostat field is an innovative solar heating system that focuses solar radiation on the absorption tower through a reflector, thereby generating high-temperature heat energy. This article mainly discusses the performance analysis and parameter optimization of the heliostat field to achieve optimal performance while meeting the rated power requirements. A simulated solar model was established using a three-dimensional Cartesian coordinate system, taking into account the effects of solar altitude angle and direct normal irradiance (DNI). The model in this paper comprehensively considers the effects of shadow occlusion loss, cosine efficiency, atmospheric transmittance, collector truncation efficiency, and mirror reflectance on the mirror field. The specific values of each parameter were calculated using model algorithms such as the HFLCAL model, To provide a basis for accurate performance analysis and solve the problem of parameter optimization, this article defines an objective function aimed at improving the energy utilization efficiency of the heliostat field by adjusting the parameters of the reflector, in order to achieve optimal performance. The above parameters are determined by establishing a genetic algorithm to define constants and initial parameters, and initializing the overall layout of the heliostat field to calculate the optical efficiency of the heliostat. In each iteration, the optimal heliostat field layout can be recorded. The final optimal solution includes parameters such as the position coordinates of the absorption tower, heliostat size, installation height, number of heliostats, and heliostat position.

The Flood Simulation of the Modified Muskingum Model with a Variable Exponent Based on the Artificial Rabbit Optimization Algorithm

In order to further improve the accuracy of flood routing, this article uses the Variable Exponential Nonlinear Muskingum Model (VEP-NMM), combined with the Artificial Rabbit Optimization (ARO) algorithm for parameter calibration, to construct the ARO-VEP-NMM flood routing model. Taking Wilson’s (1974) flood as an example, the model calculation results were compared and analyzed with the Muskingum model constructed with seven optimization algorithms. At the same time, six measured floods in the Zishui Basin were selected for model applicability testing. The results show that the ARO algorithm exhibits stronger robustness and search ability compared with other optimization algorithms and can better solve the parameter optimization problem of the Muskingum model. The use of the ARO-VEP-NMM model for flood routing accurately reflects the movement patterns of floods. The Nash coefficient of the Wilson section reached 0.9983, and the average Nash coefficient during the flood validation period in the Zishui Basin was 0.9, further verifying the adaptability and feasibility of the ARO-VEP-NMM model in flood routing. The research results can provide certain references and a theoretical basis for improving the accuracy of flood forecasting.

Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization

Stability analysis for nonlinear programming systems deals with the possible changes of the system parameters and/or equations that maintain the stability of the solutions. It is a crucial requirement to study the nonlinear system and its practical values, specifically the economic impact in most real-world applications. This paper presents some outcomes in connection with stability analysis corresponding to parametric conic vector optimization problems. For these last optimization problems, two novel types of P-Stability maps, which are the P-Stability notion map and the P-Stability perturbation map, are considered based on six kinds of sets: P-feasible set, P-solvability set, the first, second, third, and fourth kinds of P-Stability notion sets with respect to a specific domination cone P. Furthermore, qualitative characteristics of the P-Stability maps under some continuity and convexity assumptions on the objective function are provided and proved. Specifically, the connections between the P-Stability maps and the P-Stability notion set are investigated. Accordingly, these characteristics were extended to the P-perturbation maps. In addition, the idea of Pstability has heavily used in different applications like network privacy, engineering fields, and some business financial models. 

Research on Multi-Objective Optimization on Explosion-Suppression Structure-Nonmetallic Spherical Spacers

Intense burning phenomena (fire disasters) need to be prevented in the combustible gas utilization and transportation processes to ensure industrial safety. Nonmetallic spherical spacers (NSSs) have been investigated and applied in lots of explosive atmospheres to prevent explosion execution in a confined space. In this work, a novel fuzzy-based analytic hierarchy process (FAHP) is developed to take into account the uncertainty in decision-making and effectively solve the problem of factor weight allocation in multi-objective optimization. Optimal Latin Hypercube Design (Opt LHD), Chebyshev Orthogonal Polynomials (COP), and Adaptive Simulated Annealing (ASA) were combined. A multi-objective optimization method is proposed for the structural parameter optimization problem on NSSs in order to achieve conflicting multiple-objective optimization of low displacement rate and minimal deformation. That is to say, the small volume (low displacement rate) and high explosion-suppression performance (minimal deformation) of NSSs were optimized simultaneously. The results show that, compared with the original NSS model’s deformation (2.85 mm) and displacement rate (3.63%), the optimized NSSs with weight allocation had optimized the deformation by 12.98% and displacement rate by 6.1%. Compared with the optimized design model of NSSs without weight allocation with a deformation of 2.75 mm and a displacement rate of 3.48%, the deformation has been optimized by 9.82%, and the displacement rate has been optimized by 2.0%. It was verified that the proposed method is effective. At the same time, it was verified that the suppression effect of NSSs can be enhanced by changing the shape of the NSS spacer reasonably by experimental verification.

Cam Profile Design of Low-Speed Marine Diesel Engine Based on the Grey Theory

The camshaft profile is one of the important parameters of the engine, the reasonableness or otherwise of its design directly influences the engine’s power output, fuel consumption, emissions, noise and reliability. However, most existing cam profile optimization designs are based on the basic software operation, profile parameter selection and tuning lack a scientific theoretical basis. In order to address this issue, this study establishes a single valve kinematic model of the gas delivery mechanism of diesel engines by using the AVL-EXCITE Timing Drive, and performs a model-based multinomial kinematic acceleration cam profile design. Subsequently, an orthogonal design method is employed to obtain the parameter combinations that can satisfy the dynamic requirements. The research investigates the influence of cam profile design parameters (C 4, p, q, r, and s) on valve fullness, maximum jerk, cam contact stress, and valve seating force through a systematic study. Lastly, based on the grey correlation theory, a thorough analysis of the performance indices of cams with different profile parameter combinations is conducted. The optimization problem of the profile parameters with multiple performance indicators is transformed into a single-objective grey relational optimization problem, resulting in the optimal cam profile parameter combination of C4 =0.1, p=14, q=20, r=28 and s=36. The optimal method proposed in the paper is straightforward to implement and is applicable to the optimum design of cam profiles of the engine, which is of great importance for the optimal design of cam fabrication processes.

To the question of parameter optimization of hydraulic transportation technology

Background. The selection of rational schemes for the technology of hydraulic transportation of rock mass requires optimization of the main parameters of this technology. A large number of factors determining the efficiency of hydraulic transportation hamper the formalization of relationships of the main transportation processes both between themselves and other mining and processing processes.Aim. To identify specific features of the main processes in hydraulic transportation technology, to establish the factors and parameters that determine their optimal operation, and to propose an optimization tool for both individual links and the entire chain of hydraulic transportation of rock mass.Materials and methods. The problem of parameter optimization of hydraulic transportation of mineral raw materials is solved based on the integral characteristics of the pressure movement of ore and rock hydraulic mixtures. These characteristics were previously obtained empirically or theoretically by the authors of the present paper and other researchers at various mining companies.Results. Among the variety of factors determining the efficiency of hydraulic transportation, the size of the transported piece (ore, rock, coal) was found to play the major role. At the same time, the nature of changes in economic expenditures and results of evaluating the effectiveness of hydraulic transportation technology will always relate to a specific field, the accepted technological scheme, and the equipment used.Conclusion. The problem of parameter optimization of hydraulic transportation processes can be solved using digital twin technology. This technology can be used to address the issues of managing complicated technological processes, as the same time allowing timely adjustments to the modes and parameters of operational processes both on individual production lines and at the enterprise as a whole.

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

Fracturing parameter optimization technology for highly deviated wells in complex lithologic reservoirs

Highly-deviated wells are the key technology to reduce the risk of drilling accidents and improve the utilization of reservoirs. However, for reservoirs with complex lithology, highly-deviated wells are faced with the problems of geomechanical transformation and fracturing parameter optimization. The research on fracturing parameter optimization technology of high-deviated wells in complex lithologic reservoirs is helpful to the research and application of geomechanics in deep unconventional reservoirs. This paper is based on geological mechanics laboratory experiments and logging interpretation, combined with regional geological background, to clarify the geological and mechanical characteristics of the Fengcheng Formation shale oil region in the Mabei Slope. On this basis, based on the current geostress field and natural fracture distribution pattern of the Mabei Slope, an integrated model of shale oil geological engineering in local well areas was established. Based on the finite element method, optimization design was carried out for the cluster spacing, construction fluid volume, displacement, and sand volume of highly deviated well fracturing, and three-dimensional simulation of fracturing fractures was completed. The research results indicate that: (1) The current dominant direction of the maximum principal stress in the Fengcheng Formation on the Mabei Slope is from northeast to southwest, with the maximum horizontal principal stress generally ranging from 90 to 120 MPa and the minimum horizontal principal stress generally ranging from 70 to 110 MPa. (2) The difference in stress between the two horizontal directions is relatively large, generally greater than 8 MPa. Two sets of natural fractures have developed in the research area, one with a northwest southeast trend and the other with a northeast southwest trend. The natural fracture density of the Fengcheng Formation shale reservoir in the Mabei Slope is 0.32–1.12/m, with an average of 0.58/m, indicating a moderate to high degree of fracture development. (3) The geological model and three-dimensional geo-mechanical model are established according to the actual drilling geological data, and different schemes are designed to carry out single parameter optimization. The optimization results show that the optimal cluster spacing of the subdividing cutting volume pressure of the highly deviated wells in the Fengcheng Formation of the Mabei Slope is 12 m, the optimal construction fluid volume is 1400–1600 m3/section, the optimal construction displacement is 8 m3/min, and the optimal sanding strength is 2.5 m3/m. At the same time, by comparing the fracturing implementation effect with the fracturing scheme design, it is proven that the artificial parameter optimization method for highly deviated wells based on the finite element method based on the regional stress background and the natural fracture development law proposed in this paper is feasible and can provide a scientific basis for the fracturing development of highly deviated wells in complex lithologic reservoirs. This research has been well applied in Mahu area of Xinjiang oilfield.