Nonlinear Constrained Optimization Research Articles

Collaborative Beamforming Aided Fog Radio Access Networks

The success of fog radio access networks (F-RANs) is critically dependent on the potential quality of service (QoS) that they can offer to users in the face of capacity-constrained fronthaul links and limited caches at their remote radio heads (RRHs). In this context, the collaborative beamforming design is very challenging, since it constitutes a large-dimensional nonlinearly constrained optimization problem. The paper develops a new technique for tackling these critical challenges in fog computing. We show that all the associated constraints can be efficiently dealt with maximizing the geometric mean (GM) of the user throughputs (GM-throughput) subject to the affordable total transmit power constraints. To elaborate, the GM-throughput maximization judiciously exploits the fronthaul links and the RRHs’ caches by relying on our novel algorithm, which evaluates low-complexity closed-form expressions in each of its iterations. The problem of F-RAN energy-efficiency is also addressed while maintaining the target throughput. Numerical examples are provided for quantifying the efficiency of the proposed algorithms.

Data-Driven Model Predictive Control for Wave Energy Converters Using Gaussian Process

The energy harvested by an ocean wave energy converter (WEC) can be enhanced by a well-designed wave-by-wave control strategy. One of such superior control methods is model predictive control (MPC), which is a nonlinear constrained optimization control strategy. A limitation of the classical MPC algorithm is its requirement of an accurate WEC dynamic model for real-time implementation. This article overcomes this challenge by proposing a data-driven MPC scheme for wave energy converters. The data-based WEC model is developed by a Gaussian process (encompassing mean predictions and symmetric uncertainties) for a more accurate description of nonlinear and unmodeled system dynamics. A cross-entropy solver for data-driven MPC is employed for rapid, high-performance results, which samples trajectories from Gaussian distributions based on the concept of the symmetry principle. The proposed strategy is verified numerically by simulations which demonstrate its superior performance over a classical complex-conjugate controller.

COMPARING FUEL-OPTIMAL AND SHORTEST PATHS WITH OBSTACLE AVOIDANCE

This paper presents a comparison of fuel-optimal and shortest paths of an unmanned combat aerial vehicle (UCAV) with obstacle avoidance. A nonlinear constrained optimization algorithm is applied to obtain the optimal paths. An initial value problem (IVP) and an inverse-dynamics approach are used separately to determine optimal paths for various scenarios and in order to reduce computation time. While inputs of the optimization algorithm are discrete control variables in the IVP method, discrete state variables are used as inputs in the inverse-dynamics method. The minimized path segments of the geometrical model provide an initial estimation of the heading angle for the aircraft flight mechanics model. The number of variables used by the optimization algorithm has a direct effect upon the optimal accuracy; however, the computation time is inversely proportional to the number of the variables. Simulation results demonstrate that the proposed IVP method effectively converges to optimal solutions.

Advances in the application of the Principal Static Wind Loads: A large-span roof case

In this paper, a procedure to define a small set Multi-target Equivalent Static Wind Loads (M-ESWLs) that allows for the verification of a large set of structural elements of a stadium roof is presented and applied to a real case. The methodology, based on the combination of the so-called Principal Static Wind Loads (PSWLs), is aimed at reducing the subjectivity of the designer in the identification of the most challenging structural conditions induced by wind actions, and therefore it allows to simplify and speed up the wind-resistant design process of roof structures.Starting from wind tunnel tests on a scaled rigid model of a stadium, the dynamic response of its roof is computed by loading the finite element model of the structure with the time histories of the spatially averaged net pressures acting on its surface. The time histories of the internal forces acting in a set of structural members are reconstructed, and the target envelope is built by identifying, for each of them, a maximum and a minimum value through a statistical analysis of the time series. For each of these extreme conditions an ESWL is identified, PSWLs are computed and combined by means of a genetic algorithm, and the set of M-ESWLs, able to match the envelope, is defined. To limit the number of M-ESWLs, a nonlinear constrained optimization is implemented in the PSWLs combination, also introducing the possibility to over-dimension some structural members.It is concluded that the application of this methodology allows the designer to select a limited number of M-ESWLs that can be used in an automated way in order to verify the response of a defined set of structural elements.

Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

Integrated Conceptual Mechatronic Design of a Delta Robot

In this paper, a conceptual design of a Delta robot is developed by means of a mechatronic design methodology. A fully integrated conceptual design, clarifying the recurrence of the conceptual design process using black-box/white-box analysis, is presented using the Model Based Systems Engineering (MBSE) paradigm and the SysML language as the formal modeling tool. Multiple designs proposals are then evaluated by the non-linear Choquet integral in order to choose the most appropriate according to a multicriteria requirement. For a preliminary conceptual design, structural parameters for the Delta robot are determined by defining and solving a nonlinear constrained optimization problem, which considers the kinematic model of the robot maximizing its workspace. Both the decision making and the optimization problem are integrated and automated into a common software framework for the design process, by using a standard genetic algorithm and Monte Carlo method to set the optimized conceptual design to be rendered in Computer Aided Design (CAD) software and in a physical prototype, satisfying the technical specifications.

Optimization of Indoor Luminaire Layout for General Lighting Scheme Using Improved Particle Swarm Optimization

An improved mathematical model and an improved particle swarm optimization (IPSO) are proposed for the complex design parameters and conflicting design goals of the indoor luminaire layout (ILL) problem. The ILL problem is formulated as a nonlinear constrained mixed-variable optimization problem that has four decision variables. For a general lighting scheme (GLS), the number and location of luminaires can be uniquely determined by optimizing four decision variables, which avoid using program loops to determine the number of luminaires. We improve the particle swarm optimization (PSO) in three aspects: (1) up-down probabilistic rounding (UDPR) method proposed to solve mixed integer, (2) improving the velocity of the best global particle, and (3) using nonlinear inertia weights with random items. The IPSO has better optimization results in an office study compared with the PSO and genetic algorithm (GA). The results are validated by DIALux simulation software, and a maximum deviation of 2.2% is found. The validated results show that the method using four decision variables increased the speed by 10.6% and the success rate by 23.33%. Furthermore, Indoor Luminaire Layout System APP is designed to provide guidelines visually for lighting designers and related researchers.

Efficient Hybrid Algorithm Solution for Optimal Reactive Power Flow Using the Sensitive Bus Approach

This paper presents the design and application of an efficient hybrid algorithm for solving the Optimal Reactive Power Flow (ORPF) problem. The ORPF is formulated as a nonlinear constrained optimization problem where the active power losses must be minimized. The proposed approach is based on the hybridization of Particle Swarm Optimization (PSO) and Tabu-Search (TS) technique. The proposed PSO-TS approach is used to find the settings of the control variables (i.e. generation bus voltages, transformer taps, and shunt capacitor sizes) which minimize transmission active power losses. The bus locations of the shunt capacitors are identified according to sensitive buses. To show the effectiveness of the proposed method, it is applied to the IEEE 30 bus benchmark test system and is compared with PSO and TS without hybridization, along with some other published approaches. The obtained results reveal the effectiveness of the proposed method in dealing with the highly nonlinear constrained nature of the ORPF problem.

Fast and reliable transient simulation and continuous optimization of large-scale gas networks

We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of decreasing complexity and varying over time. Feasible work regions of compressor stations consisting of several turbo compressors are included by semiconvex approximations of aggregated characteristic fields. A discrete adjoint approach within a first-discretize-then-optimize strategy is proposed and a sequential quadratic programming with an active set strategy is applied to solve the nonlinear constrained optimization problems resulting from a validation of nominations. The method proposed here accelerates the computation of near-term forecasts of sudden changes in the gas management and allows for an economic control of intra-day gas flow schedules in large networks. Case studies for real gas pipeline systems show the remarkable performance of the new method.

A high accuracy modeling scheme for dynamic systems: spacecraft reaction wheel model

Reaction wheels are crucial actuators in spacecraft attitude control subsystem (ACS). The precise modeling of reaction wheels is of fundamental need in spacecraft ACS for design, analysis, simulation, and fault diagnosis applications. The complex nature of the reaction wheel leads to modeling difficulties utilizing the conventional modeling schemes. Additionally, the absence of reaction wheel providers’ parameters is crucial for triggering a new modeling scheme. The Radial Basis Function Neural Network (RBFNN) has an efficient architecture, alluring generalization properties, invulnerability against noise, and amazing training capabilities. This research proposes a promising modeling scheme for the spacecraft reaction wheel utilizing RBFNN and an improved variant of the Quantum Behaved Particle Swarm Optimization (QPSO). The problem of enhancing the network parameters of the RBFNN at the training phase is formed as a nonlinear constrained optimization problem. Thus, it is proposed to efficiently resolve utilizing an enhanced version of QPSO with mutation strategy (EQPSO-2M). The proposed technique is compared with the conventional QPSO algorithm and different variants of PSO algorithms. Evaluation criteria rely upon convergence speed, mean best fitness value, stability, and the number of successful runs that has been utilized to assess the proposed approach. A non-parametric test is utilized to decide the critical contrast between the results of the proposed algorithm compared with different algorithms. The simulation results demonstrated that the training of the proposed RBFNN-based reaction wheel model with enhanced parameters by EQPSO-2M algorithm furnishes a superior prediction accuracy went with effective network architecture.

A numerical algorithm for solving power-exponent type nonlinear inequalities with applications in calculating stabilizing parameters for LTI systems

The paper proposes a numerical algorithm for finding a solution set of a class of power-exponent type nonlinear inequalities. The proposed numerical algorithm applies specifically to the case when the power-exponent is positive irrational number, which can’t be effectively solved by using the existing methods. Firstly, by introducing a novel concept of margin variable and using the monotonicity of power-exponent function, this paper converts the problem of solving the nonlinear inequalities into a constrained nonlinear optimization (CNO) problem. Then the obtained CNO problem is solved by using the MATLAB function fmincon. Finally, a numerical algorithm to solve this class of inequalities is obtained. The proposed algorithm can find a solution set of the considered inequalities, not just one or few solutions. Further, the derived algorithm can be easily used to calculate the stabilizing parameter ranges for LTI systems based on the Routh-Hurwitz criterion. Moreover, an example of calculating the stabilizing parameters of a LTI system and an example of solving power-exponent type nonlinear inequalities are provided to show the effectiveness of the proposed algorithm.

Real coded self-organising migrating genetic algorithm for nonlinear constrained optimisation problems

The objective of this article is to propose a new hybrid algorithm named as real coded self-organising migrating genetic algorithm (C-RCSOMGA) by combining real coded genetic algorithm (RCGA) and modified self-organising migrating algorithm (SOMA) for solving the nonlinear constrained optimisation problems. In RCGA, a modified mutation operator called as double mutation operator has been introduced combining two different existing mutation operators, whereas in SOMA, a modified strategy has been proposed. To test the performance of the proposed algorithm, a set of test problems taken from the existing literature has been solved and the simulated results have been compared numerically as well as graphically with the existing algorithms. In the graphical comparison, a modification of performance index (PI) has been made. Finally, with the help of modified performance index (MPI), it has been shown that the proposed hybrid algorithm has performed much better than the existing algorithms.

Limiting reactive power flow peaks in wave energy systems

Optimal control of wave energy converters has been shown to require an injection of power into the WEC system to maintain an optimal velocity profile. While this consumption of power results in an overall increase in energy capture, it also brings more stringent requirements on the power take-off (PTO) system. Specifically, the PTO must cater for bi-directional power flow and a source available for the provision of this reactive power, either via a storage device, or the electrical grid itself. However, one aspect which has received relatively little attention is the magnitude of the reactive power peaks, which may have implications for the required overall power rating of the system. In particular, though reactive power flow may only be required for a small fraction of the wave period, reactive power peaks well in excess of active power levels bring a potentially significant capital cost in terms of system power rating, along with a unfavourable capacity factor rating. This paper examines the circumstances under which reactive power flow peaks exceed active power levels and proposes a solution which puts a finite (nonzero) limit on reactive power flow, consistent with active power levels. The problem is solved as a nonlinear constrained optimisation problem, while the consequences of imposing such a limit on energy capture are also examined.

Area Optimisation of Two Stage Miller Compensated Op-Amp in 65 nm Using Hybrid PSO

Analog circuit design can be formulated as a nonlinear constrained optimisation problem that can be solved using any suitable optimisation algorithms. Different optimisation techniques have been reported to reduce the design time of analog circuits. A hybrid particle swarm optimisation algorithm with linearly decreasing inertia weight for the optimisation of analog circuit design is proposed in this study. The proposed method is used to design a two-stage operational amplifier circuit with Miller compensation. The results show that the proposed optimisation method can substantially reduce the design time needed for analog circuits.

An area-type nonmonotone filter method for nonlinear constrained optimization

<abstract><p>In this paper, we define a new area-type filter algorithm based on the trust-region method. A relaxed trust-region quadratic correction subproblem is proposed to compute the trial direction at the current point. Consider the objective function and the constraint violation function at the current point as a point pair. We divide the point pairs into different partitions by the dominant region of the filter and calculate the contributions of the point pairs to the area of the filter separately. Different from the conventional filter, we define the contribution as the filter acceptance criterion for the trial point. The nonmonotone area-average form is also adopted in the filter mechanism. In this paper, monotone and nonmonotone methods are proposed and compared with the numerical values. Furthermore, the algorithm is proved to be convergent under some reasonable assumptions. The numerical experiment shows the effectiveness of the algorithm.</p></abstract>

Semi-Automatic Planning and Three-Dimensional Electrospinning of Patient-Specific Grafts for Fontan Surgery.

This paper proposes a semi-automatic Fontan surgery planning method for designing and manufacturing hemodynamically optimized patient-specific grafts. Fontan surgery is a palliative procedure for patients with a single ventricle heart defect by creating a new path using a vascular graft for the deoxygenated blood to be directed to the lungs, bypassing the heart. However, designing patient-specific grafts with optimized hemodynamic performance is a complex task due to the variety of patient-specific anatomies, confined surgical planning space, and the requirement of simultaneously considering multiple design criteria for vascular graft optimization. To address these challenges, we used parameterized Fontan pathways to explore patient-specific vascular graft design spaces and search for optimal solutions by formulating a nonlinear constrained optimization problem, which minimizes indexed power loss (iPL) of the Fontan model by constraining hepatic flow distribution (HFD), percentage of abnormal wall shear stress (%WSS) and geometric interference between Fontan pathways and the heart models (InDep) within clinically acceptable thresholds. Gaussian process regression was employed to build surrogate models of the hemodynamic parameters as well as InDep and [Formula: see text] (conduit model smoothness indicator) for optimization by pattern search. We tested the proposed method on two patient-specific models (n=2). The results showed the automatically optimized (AutoOpt) Fontan models hemodynamically outperformed or at least are comparable to manually optimized Fontan models with significantly reduced surgical planning time (15 hours versus over 2 weeks). We also demonstrated feasibility of manufacturing the AutoOpt Fontan conduits by using electrospun nanofibers.

Constrained nonlinear optimization method for accurate calibration of a bi-telecentric camera in a three-dimensional microtopography system.

Telecentric cameras are widely used in the field of microscopic imaging because of their constant magnification and tiny distortion in the depth of field. Camera calibration has always been a key step in the field of computer vision. Usually, the precise parameters of the telecentric camera are obtained by nonlinear optimization; however, the randomness of the optimization algorithm without proper constraints will cause the results to be inconsistent with reality. Existing studies paid little attention to this issue; therefore, we show a reliable optimization approach for the bi-telecentric camera in a structured illumination three-dimensional microtopography measurement system. In this method, the distortion-free camera parameters are solved through a closed-form solution. Then a nonlinear optimization algorithm with constraining the world coordinates of the precise calibration target is proposed to refine the global parameters, leading to the calibration results being more accurate and authentic. The real experiments are conducted to verify the feasibility of the proposed method. The comparative experiments with the exiting approach are then carried out, manifesting that the proposed method enjoys advantages in terms of both reprojection error and operating efficiency. Additionally, the average offset of the world coordinates on the calibration target derived from the proposed method verifies its effectiveness and reasonability.

Integration of solar field with multiple stage evaporator to sustain eco-energy in pulp and paper plant

Deploying renewable energy to unit design energy-efficient technologies may fulfill the additional demand of various energy-intensive industries for their sustainability and resiliency. Multiple Stage Evaporator (MSE) is one of the most energy-intensive units used to extract the water content of the weak liquor in various industries, including the paper industry. This energy intensiveness may be reduced by integrating various Energy Reduction Schemes (ERSs). Hence, this work proposes a ERSs integrated MSE model to analyze its energy efficiency. These ERSs includes Thermo-Vapor Compressor, Steam-, Feed- Split, Feed Preheater, and Flash Tanks. Further, the performance of the proposed model is investigated under two important real-time plant complexities: Boiling Point Elevation and Fouling to achieve more realistic results. The performance analysis is initiated with the formulation of a nonlinear constrained optimization problem to increase the steam economy (SE). Also, the simulation is extended to validate at two different product concentrations (52% and 65%) by employing state-of-art optimization algorithms: CONOPT, and SCA in GAMS and MATLAB respectively. The simulated results shows an increment 1.64% and 1.37% of SE for both 52% and 65% concentration of weak liquor respectively in case of CONOPT than SCA. Also, the waste heat of the condensate, feed, and product may be further utilized for the heat recovery by incorporating the flash tanks which leads to a countable energy saving. Eventually, integrating the solar fields: PTC and LFR ensures a notable reduction in conventional heat utilization by 85.96% and 92.85%, respectively and hence, enhance the energy efficiency.

Ensemble-based constrained optimization using an exterior penalty method

In science and engineering, non-linear constrained optimization has been a useful mathematical technique for many practical applications. Of interest to us is its applicability in the modeling and prediction of hydrocarbon reservoir production. In this paper, a new efficient, robust, and accurate optimal solution strategy based on the exterior penalty function (EPF) method and the adaptive ensemble-based optimization (EnOpt) approach (with backtracking line-search technique) for non-linear constrained optimization problems is presented. The purpose of this work is to provide a better user-friendly strategy which mitigates the problem often faced with the current constraints handling technique utilized when using the EnOpt method to solve constrained problems of water or EOR flooding. This study notes that the problem contributes to uncertainties in the gradient computation of the objective function and hence leads to the poor convergence rate of the standard EnOpt method. In this work, we used the EPF method to transform a given constrained optimization problem to a sequence of unconstrained subproblems and then sequentially solve the subproblems by unconstrained EnOpt procedure until convergence to the solution of the original problem. To demonstrate the advantage of the proposed methodology, we used it to solve analytical 2D bound constrained Rosenbrock’s problem and a practical high dimensional bound constrained water flooding optimization problem associated with a 2D 5Spot field and a 3D Reek reservoir field. The numerical results are compared with EnOpt using classical Lagrangian approach, as well as the traditional EnOpt. Our findings showed that the proposed solution method has a fast convergence rate and is more accurate and robust.

Principal Component Analysis Applied to Gradient Fields in Band Gap Optimization Problems for Metamaterials

A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based iterative optimization algorithms to the numerical solution of such problems is typically highly demanding, due to the complexity of the underlying physical models. Nevertheless, supervised machine learning techniques can reduce such a computational effort, e.g., by replacing the original objective functions of such optimization problems with more-easily computable approximations. In this framework, the present article describes the application of a related unsupervised machine learning technique, namely, principal component analysis, to approximate the gradient of the objective function of a band gap optimization problem for an acoustic metamaterial, with the aim of making the successive application of a gradient-based iterative optimization algorithm faster. Numerical results show the effectiveness of the proposed method.