Penalty Function Method Research Articles

An objective penalty function method for biconvex programming

An objective penalty function method for biconvex programming

Multi-objective Optimization of High Speed Milling Parameters Based on Genetic Algorithm

In order to optimize the high-speed milling parameters and reduce the experimental work in the actual processing, a multi-objective optimization model is established. The improved genetic algorithm NSGA-II combined with penalty function method is used to solve the mathematical model, and the optimal cutting parameters are obtained when the high-speed milling conditions are known, which provides guidance for the process decision-making of high-speed milling.

A Computational Approach to Optimal Control Problems with Almost Smooth Controls

In this paper, we consider a class of optimal control problems involving continuous control and state inequality constraints where the control is almost smooth. We first employ the control parametrization technique via approximating the control signal by a piecewise linear function. Then, we develop a time scaling transformation procedure for transforming the approximate problem into an equivalent problem that can be solved readily using conventional methods. On this basis, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. The gradient formulas and convergent properties ensure that the transformed unconstrained optimal parameter selection problems can be solved by existing optimization algorithms or software packages. Finally, an example is solved showing the effectiveness and applicability of the approach proposed.

Trade-off analysis between delay and throughput of RAN slicing for smart grid

Emerging power services with massive connections and real-time control have different requirements on delay, rate, reliability, etc. In order to meet the diversified requirements of power services, network slicing can provide guarantee for the wide application of 5G in power. The current research on network slicing adapting power services is still in its infancy. This paper proposes a trade-off analysis method for radio access network (RAN) slice delay and throughput based on dynamic intelligent resource allocation to meet the different QoS requirements of different services in smart grid scenarios. Firstly, clustering analysis is used to classify the communication requirements of smart grid services. A throughput demand model for enhanced mobile broadband (eMBB) slice users based on importance and a delay constraint model for ultra-reliable and low latency communication (uRLLC) slice users are constructed, and a throughput model for slice users based on cell capacity limitation is constructed. Then, the problem model of maximizing the throughput of the eMBB slice by reasonably allocating resource blocks and power under the premise of ensuring the delay of the uRLLC slice is established. The Lyapunov drift plus penalty function method is used to convert the above problem into a tractable form, and then the problem is solved by the active set method. Simulation results show that the different QoS requirements of smart grid services will significantly affect the actual queue length of the uRLLC slice as well as the throughput of the eMBB slice.

Improved Symbiotic Organisms Search Algorithm for Optimal Operation of Active Distribution Systems Incorporating Renewables and Emerging Data‐Center Resources

AbstractThe optimal operation analysis plays an important role in estimating the expected return of investment for power systems. However, this work could be highly challenging under the context of active distribution network, where a variety of renewable energy sources and emerging active loads (such as Internet data centers) could be penetrated that introduce a high level of nonlinearity and nonconvexity characteristics into the system modeling. To overcome such challenge, this paper presents a new methodological framework based on the improvements of symbiotic organisms search (SOS) algorithm to address the optimal operation problem of active distribution systems containing renewable energy sources and datacenter resources, aiming to provide a practical tool for system analysis, particularly subject to nonconvexity nature of system components. For this purpose, a generic model for the distribution system including wind power, PV, and datacenter resources is first developed, which not only captures the uncertain nature of system components but also accounts for their spatiotemporal flexibility during operation. On this basis, in order to improve the computation efficiency of the problem, the SOS algorithm is improved by designing the selection strategy of random parameters. By using the penalty function method, the concerned problem is expressed as a nonlinear unconstrained optimization problem. The performance of the proposed model and algorithm is examined through comparative studies. It is shown that the proposed method is able to schedule the renewable energy resources and flexible demand of datacenters coordinately to reduce the operation cost of the system significantly in the case study. In addition, the proposed algorithm demonstrates a higher level of accuracy as well as better convergence efficiency compared to other conventional techniques.

Joint Beamforming and Power-Splitting Design for Cooperative Nonorthogonal Multicast

We propose a cooperative nonorthogonal multicast scheme for multiple-input-single-output (MISO) systems, where the transmitter sends the superimposed signal to two multicast groups. After successfully detecting all signals, the cell-center users (CCUs) in one multicast group help relay signal to the cell-edge users (CEUs) in another group to enhance signal reception. Simultaneous wireless information and power transfer is adopted at CCUs to assist information relaying. In such a system, to minimize the transmission power of the system while satisfying the quality of service requirements of all the users, an optimization problem is formulated to jointly design the transmitter beamformers, distributed CCUs beamformer, as well as the power-splitting (PS) ratios. To solve the nonconvex problem, we first equivalently transform it into a difference of convex (DC) programming. Then, a low-complexity iterative algorithm based on the constrained concave convex procedure (CCCP) is proposed to solve the DC programming one. In addition, a robust joint beamforming and PS scheme is proposed by assuming imperfect channel state information (CSI). The infinite constraints caused by CSI uncertainties are converted into finite ones utilizing the S-procedure. To obtain a rank-one locally optimal solution, the penalty function method and CCCP algorithm are adopted. The simulation results reveal that the proposed cooperative scheme can greatly reduce the transmission power and outperform the baselines within a certain range. Moreover, the robustness and effectiveness of the robust design under imperfect CSI case have been validated.

An efficient numerical method for dynamic analysis of polygonal plate under moving loads

Plate structures under moving loads are frequently encountered in practical engineering. Over the past decades, the moving-load models for plates are mainly developed for rectangular plates. In this study, an efficient numerical method is developed for triangular and quadrilateral plates, which are the two most representative polygonal plates and also the basic elements to form general polygon plates. To avoid the mismatch between the moving load and nodes that encountered in Finite Element Method (FEM), the entire domain of the plate is firstly mapped into a square domain using the isoparametric shape functions. The domain decomposition method is also introduced to handle the general polygon shaped plates, whereas the penalty function method is adopted to handle arbitrary boundary conditions. The first-order shear deformation theory (FSDT) is used to describe the elastic deflection of the plates, and then the deformation fields in the mapped domain are spatially discretized by using Chebyshev polynomials of the first kind (CPOFK). Afterwards, the governing equations of motion is derived using Lagrange’s equation, in which the inertia force, Coriolis force and centrifugal force due to the interactions between the moving load and supporting plates are taken into account simultaneously. The mode reduction method is employed to reduce the dimension of dynamic equations, and then the first-order generalized-α method is used to solve the dynamic response in time domain. Finally, the correctness and efficiency of the presented method are validated from convergence analysis and comparisons.

Penalty function method for the minimal time crisis problem

In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem. The interest of this approach is illustrated on numerical examples for which optimal trajectories can leave and enter the crisis set tangentially.

Series solution to fractional contact problem using Caputo’s derivative

Abstract In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs). The series solution of this system of FBVPs is acquired by using the variational iteration method (VIM). The performance as well as precision of the applied method is gauged by means of significant numerical tests. We further study the convergence and residual errors of the solutions by giving variation to the fractional parameter, and graphically present the solutions and residual errors accordingly. The outcomes thus obtained witness the high effectiveness of VIM for solving FBVPs.

ALGORITHMS AND SOFTWARE OF BUILDINGS INTERMITTENT THERMAL CONDITIONS OPTIMAL CONTROL

The actual problem of synthesizing the optimal control law for the intermittent heating mode of office buildings is considered, which consists in the programmed reduction of the room temperature during off-hours. The analysis of information sources showed the absence of sufficiently justified methods for solving the problem of optimizing the thermal processes of buildings, which provide comfortable conditions for the functioning of personnel, on the one hand, and save costs for buildings maintenance, on the other hand. The statement of the building thermal state optimal control problem is formulated, which contains a mathematical model of the process, a control goal, constraints on control actions and an integral quadratic quality criterion, including deviations of the room temperature from a given program and heat consumption. The limitation on the control action is taken into account by the method of penalty functions. As a mathematical model of the optimized thermal process, a two-dimensional controlled system of differential equations with constant coefficients is applied. The values of these coefficients are determined on the basis of building similarity criteria, which allows solving the optimization problem in a dimensionless form. The model includes a control action - the supplied heat flux, and a disturbing action - the ambient temperature, changing according to a given harmonious law. The numerical solution of the optimal control problem is implemented by the Chernous'ko method of successive approximations. A description of the user interface is given, as well as examples of the implementation of the thermal state optimal control. The proposed software allows on the stage of designing the heating system to obtain express assessments of various thermal modes of the building, and can also be used as computer support for automated individual heating points.
 Keywords: intermittent heating mode, optimal control, mathematical model, control quality criterion, control constraints, penalty function, successive approximations, program interface, automated individual heating point.

An exact penalty function method for optimal control of a dubins airplane in the presence of moving obstacles

An exact penalty function method for optimal control of a dubins airplane in the presence of moving obstacles

A Penalty Function Method for the Principal-Agent Problem with an Infinite Number of Incentive-Compatibility Constraints under Moral Hazard

A Penalty Function Method for the Principal-Agent Problem with an Infinite Number of Incentive-Compatibility Constraints under Moral Hazard

Robust penalty function method for an uncertain multi-time control optimization problems

This paper gives some new results on multi-time first-order PDE constrained control optimization problem in the face of data uncertainty (MCOPU). We obtain the robust sufficient optimality conditions for (MCOPU). Further, we construct an unconstrained multi-time control optimization problem (MCOPU)ϱ corresponding to (MCOPU) via absolute value penalty function method. Then, we show that the robust optimal solution to the constrained problem and a robust minimizer to the unconstrained problem are equivalent under suitable hypotheses. Moreover, we give some non-trivial examples to validate the results established in this paper.

Ascent Trajectory Optimization for Air-Breathing Hypersonic Vehicles Based on IGS-MPSP

This paper proposes an improved Generalized Quasi-Spectral Model Predictive Static Programming (GS-MPSP) algorithm for the ascent trajectory optimization for hypersonic vehicles in a complex flight environment. The proposed method guarantees the satisfaction of constraints related to the state and control vector while retaining its high computational efficiency. The spectral representation technique is used to describe the control variables, which reduces the number of decision variables and makes the control input smooth enough. Through Taylor expansion, the constraints are transformed into an inequality containing only decision variables, such that it can be added into GS-MPSP framework. By Gauss quadrature collocation method, only a few collocation points are needed to solve the sensitivity matrix, which greatly accelerates the calculation. Subsequently, the analytical expression is obtained by combining the static optimization with the penalty function method. Finally, the simulation results demonstrate that the proposed improved GS-MPSP algorithm can achieve both high computational efficiency and high terminal precision under the constraints.

Study on the optimization algorithm of the cross-sectional layout of an umbilical based on the layering strategy

As a key device in subsea production system of the offshore hydrocarbon resources exploitation, the umbilical consists of a variety of functional components such as hydraulic tubes, electrical cables and optical cables. The cross-sectional layout design plays an important role in the performance of an umbilical. Considering the mechanical and geometrical properties as the quantitative design objectives, the mathematical model of multi-objective optimization of the cross-sectional layout of an umbilical is described. Meanwhile, the algorithm of smallest radius of the enclosing circle and the multiplier penalty function method are proposed. Then, the manufacture factor is considered and the layering strategy based on the identification of contact points is introduced to modify implement algorithm to obtain the optimal cross-sectional layout with layering characteristic. Finally, some case studies are performed, the optimal cross-sectional layouts with layering characteristic are obtained. Comparing with the initial design and cross-sectional layouts without layering, the results verify the feasibility of the presented optimization design algorithm, which can improve the design efficiency of an umbilical and avoid the manual process.

A Method for Nonlinear Error Compensation of Load Cell Based on Neural Network With Second Derivative Constraints

This paper presents a method for compensating the load cell's nonlinear error based on neural network with the second derivative constraints. In this method, for improving the ability of the neural network in the case of lack of samples, the prior knowledge of load cell, i.e., the second derivative of the load cell's input-output function is less than zero, is used to construct the constraint of neural network. The augmented performance index of training neural network with penalty function method is founded, and its detailed training algorithm is given. In addition, the performance of neural network affected by the punishing factor is discussed. This proposed method can reduce the NN's generalization error when the training samples are insufficient. The experimental results show that the generalization ability of this proposed neural network is better than that of the conventional data inducing neural network (DINN, i.e. training neural network by only using data samples and not any constraints), and the nonlinear error of load cell with this proposed method is far less than that of DINN.

Design and analysis of the mandrel structure for a composite S-shaped inlet

Automated fiber placement (AFP) combining with the autoclave curing process is the main manufacturing method for large-scale rotary composite parts. During the forming process, the mandrel plays an important role that affects the forming quality of the part directly. In this study, design and analysis of the mandrel structure for a composite S-shaped inlet are carried out. The preforming process of the rotary composite part using the AFP technique is introduced first. Then, design principles of the shaft are presented and applied to the shaft design for the mandrel of the S-shaped inlet, which then is transformed into an optimization problem. The internal penalty function method is adopted to solve this optimization problem in order to obtain the optimal axis position and axle diameter. Moreover, detailed structure design of the mandrel is proposed which takes the demolding into consideration, and the wall thickness is designed considering the total weight and the stiffness. The static analysis and modal analysis are also carried out by the finite element method to verify the feasibility of the proposed mandrel structure.

A new methodology for buckling, postbuckling and delamination growth behavior of composite laminates with delamination

A methodology for predicting the buckling and postbuckling behavior of composite plates with delamination is proposed. The novelty of the new methodology lies in the built-in capability of addressing the fracture mechanics phenomena involved in the postbuckling regime. The formulation is derived based on a new laminate partitioning scheme which offers better displacement consistency in the vicinity of the crack tip and provides access to interlaminar tractions. The sublaminates created by the partitioning scheme are modeled using the first-order shear deformation theory. The continuity of the displacement field across the interfaces of the sublaminates is enforced using a penalty function method which is equivalent to considering high stiffness elastic bonds between the sublaminates. The equilibrium equations are derived using the stationary total potential energy principle and through the application of the Ritz method. The derived system of nonlinear equations is solved using an arc-length method. Irwin’s crack closure integrals are employed for calculating the distribution of energy release rates corresponding to the three fracture modes individually. The validity of the fracture mechanics results is examined through the comparison of sample results with finite element results. The postbuckling results are verified through comparisons made with experimental data available in the literature.

Dynamic ultimate bearing capacity of beam-plate coupled structures with deformable connection under uniaxial compression, compression-bending and compression–shear loadings

This paper presents a generalized constrained differential quadrature method to investigate the elastoplastic dynamic response and ultimate bearing capacity of beam-plate coupled structures under uniaxial compression, compression-bending and compression–shear loadings, considering the interaction between plates and beams. A beam-plate coupled structure is divided into some plate elements, considering the compatibility between contiguous plate elements using the penalty function method which can solve the problem of beam-plate deformable connection of different materials. Virtual work principle and generalized constrained differential quadrature method are used to derive the dynamic governing equations of the beam-plate in which the geometrical and material nonlinearity is considered in the paper. The iterative Newmark/Newton–Raphson method is used to solve the governing equations of the beam-plate. The verification analysis is carried out to demonstrate the accuracy of the proposed method by comparison with the results from FEM. Then, various effects of the rotational spring stiffness, width-to-thickness ratio, aspect ratio, impact time and coupling load on the elastoplastic dynamic response and ultimate bearing capacity of beam-plates are evaluated.

Dynamic analysis of arbitrarily restrained stiffened plate under moving loads

This paper develops a unified method for the vibration analysis of stiffened plate subjected to moving loads traveling along arbitrary paths. The stiffened plate is modeled as the main/secondary built-up structure in which the plate is selected as the main structure, whereas the stiffeners treated as the beam are selected as the secondary structures. The stiffeners are allowed to be arbitrarily distributed in terms of the number, length, location and orientation. The connection joint between the plate and beam is described by considering the motion compatibility conditions at the interface on the basis of the first order shear deformation theory (FSDT). Both the torsion, bending and warping of the stiffeners are taken into account. To deal with the spatial discretization of the displacement field, the displacements of plate are expressed as the expansions of Chebyshev polynomials of the first kind (CPOFK). Penalty function method using artificial springs is used to realize the various boundary conditions. Afterward, the finite-dimensional governing equations of motion are obtained by means of the Lagrange’s equation. To improve the computational efficiency, the mode reduction technique is used to obtain the reduced-order dynamic model. The first-order generalized-α time integration scheme is then employed to solve the reduced-order governing equations of motion in time domain. The convergence and accuracy of the presented method are verified by comparing with Finite Element Method (FEM) and published literature. Finally, the effects of stiffeners, boundary condition, moving speed and inertia interaction on the dynamic response of stiffened plate are examined by parametric studies.