Boundary Of Feasible Region Research Articles

A boundary identification approach for the feasible space of structural optimization using a virtual sampling technique-based support vector machine

To improve the computational efficiency of structural optimization, this study treats the feasibility evaluation of the solutions as a two-class classification problem and proposes a boundary identification approach (BIA) to identify the feasible region boundary of search space. The BIA includes a virtual sampling technique (VST), an improved Latin hypercube sampling (ILHS) method, and a support vector machine (SVM) classifier. The VST can generate cheap samples based on a mapping strategy from actual samples without time-consuming structural analysis. To enhance the global performance of the SVM, the ILHS yields the sample set on the normalized hypersphere of the original design space. An optimization framework based on the BIA hybridized with the harmony search algorithm is presented, and two numerical and three truss examples are utilized to examine the performances of the proposed optimization framework. The prediction accuracy of the BIA reaches about 99% in two numerical examples, and 97%, 90%, and 80% in the 10-bar, 72-bar, and 600-bar truss optimization examples, respectively. The results also show that the number of structural analyses required by the proposed optimization approach is reduced by more than 80% compared to the conventional metaheuristics optimization algorithms while obtaining a similar quality of optimal designs.

Globalized Knowledge-Based, Simulation-Driven Antenna Miniaturization Using Domain-Confined Surrogates and Dimensionality Reduction

The design of contemporary antenna systems encounters multifold challenges, one of which is a limited size. Compact antennas are indispensable for new fields of application such as the Internet of Things or 5G/6G mobile communication. Still, miniaturization generally undermines electrical and field performance. When attempted using numerical optimization, it turns into a constrained problem with costly constraints requiring electromagnetic (EM) simulations. At the same time, due to the parameter redundancy of compact antennas, size reduction poses a multimodal task. In particular, the achievable miniaturization rate heavily depends on the starting point, while identifying a suitable starting point is a challenge on its own. These issues indicate that miniaturization should be addressed using global optimization methods. Unfortunately, the most popular nature-inspired algorithms cannot be applied for solving size reduction tasks because of their inferior computational efficacy and difficulties in handling constraints. This work proposes a novel methodology for the globalized size reduction of antenna structures. Our methodology is a multi-stage knowledge-based procedure, initialized with the detection of the approximate location of the feasible region boundary, followed by the construction of a dimensionality-reduced metamodel and global optimization thereof; the last stage is the miniaturization-oriented local refinement of geometry parameters. For cost reduction, the first stages of the procedure are realized with the use of a low-fidelity EM antenna model. Our approach is verified using four broadband microstrip antennas and benchmarked against multi-start local search as well as nature-inspired methods. Superior size reduction rates are demonstrated for all considered cases while maintaining reasonably low computational costs.

Fast characterization of nonlinear feasible region based on deep neural network association mining

Dispatches of tie-line power between regional grids promote the use of natural resources. Therefore, the exact characterization of nonlinear tie-line feasible region becomes an important guarantee to ensure the power interaction. However, solving nonlinear problems using traditional methods usually requires a solver with powerful computational capabilities. We herein propose a feature association mining for nonlinear constraints and feasible region boundary to directly identify the boundary points with deep neural network (DNN) assisted prediction, which divides the identification of feasible region into two stages. Firstly, the cardinal decision variables are identified using the DNN to alleviate the numerical annihilation problem. Secondly, under the guidance of the characteristics of the description results, the association between the input constraints and the output feasible region is obtained and the block feature library of the sample data is constructed to reduce the learning difficulty. Finally, the block mapping of some key decision variables is completed. In the second stage, some cardinal decision variables are used as indicators to straightly locate the points. Moreover, a round of accuracy rectification is carried out using segment translation method and the results are corrected for ensuring the accuracy. Case studies demonstrate the effectiveness of the proposed methods.

Globalized simulation-driven miniaturization of microwave circuits by means of dimensionality-reduced constrained surrogates

Small size has become a crucial prerequisite in the design of modern microwave components. Miniaturized devices are essential for a number of application areas, including wireless communications, 5G/6G technology, wearable devices, or the internet of things. Notwithstanding, size reduction generally degrades the electrical performance of microwave systems. Therefore, trade-off solutions have to be sought that represent acceptable compromises between the ability to meet the design targets and physical compactness. From an optimization perspective, this poses a constrained task, which is computationally expensive because a reliable evaluation of microwave components has to rely on full-wave electromagnetic analysis. Furthermore, due to its constrained nature, size reduction is a multimodal problem, i.e., the results are highly dependent on the initial design. Thus, utilization of global search algorithms is advisable in principle, yet, often undoable in practice because of the associated computational expenses, especially when using nature-inspired procedures. This paper introduces a novel technique for globalized miniaturization of microwave components. Our technique starts by identifying the feasible region boundary, and by constructing a dimensionality-reduced surrogate model therein. Global optimization of the metamodel is followed by EM-driven local tuning. Application of the domain-confined surrogate ensures low cost of the entire procedure, further reduced by the incorporation of variable-fidelity EM simulations. Our framework is validated using two microstrip couplers, and compared to nature-inspired optimization, as well as gradient-based size reduction. The results indicate superior miniaturization rates and low running cost, which make the presented algorithm a potential candidate for efficient simulation-based design of compact structures.

Direct constraint control for EM-based miniaturization of microwave passives

Handling constraints imposed on physical dimensions of microwave circuits has become an important design consideration over the recent years. It is primarily fostered by the needs of emerging application areas such as 5G mobile communications, internet of things, or wearable/implantable devices. The size of conventional passive components is determined by the guided wavelength, and its reduction requires topological modifications, e.g., transmission line folding, or utilization of compact cells capitalizing on the slow-wave phenomenon. The resulting miniaturized structures are geometrically complex and typically exhibit strong cross coupling effects, which cannot be adequately accounted for by analytical or equivalent network models. Consequently, electromagnetic (EM)-driven parameter tuning is necessary, which is computationally expensive. When the primary objective is size reduction, the optimization task becomes far more challenging due to the presence of constraints related to electrical performance figures (bandwidth, power split ratio, etc.), which are all costly to evaluate. A popular solution approach is to utilize penalty functions. Therein, possible violations of constraints degrade the primary objective, thereby enforcing their satisfaction. Yet, the appropriate setup of penalty coefficients is a non-trivial problem by itself, and is often associated to extra computational expenses. In this work, we propose an explicit approach to constraint handling, which is combined with the trust-region gradient-search procedure. In our technique, the decision about the adjustment of the search radius is determined based on the reliability of rendering the feasible region boundary by linear approximation models of the constraints. Comprehensive numerical experiments conducted using three miniaturized coupler structures demonstrate superiority of the presented method over the penalty function paradigm. Apart from the efficacy, its appealing features include algorithmic simplicity, and no need for tailoring the procedure for a particular circuit to be optimized.

An efficient global optimization algorithm for expensive constrained black-box problems by reducing candidate infilling region

Surrogate-based optimization methods are usually employed to solve expensive black-box optimization problems. Constraints bring more challenges for optimization than unconstrained problems. This study proposes a novel three-stage infilling framework to solve expensive single-objective problems with equality and/or inequality constraints. In the first stage, a criterion for locating a feasible region is designed. Until a feasible solution is found, the first stage is removed in the subsequent process. The second stage exploits the current best feasible solution and explores potentially better solutions. If the infilled site is infeasible, the third stage will proceed to improve the surrogate accuracy around the feasible region boundary and an extra constraint derived from the objective is proposed to reduce the candidate infill region in this stage. Otherwise, the process stays in stage two. Stage two continues once one third-stage point has been sampled. For brevity, the three-stage framework is called CEGO-DI. The efficacy of CEGO-DI is demonstrated by comparing it with two variants of it. In addition, the method is also compared with several state-of-the-art algorithms on extensive problems. The experimental results show that CEGO-DI has a better or competitive performance on most problems.

An adaptive refined grid search strategy for assessing operational flexibility and application on refrigerant selection

AbstractA novel adaptive refined grid search strategy is developed for representative characterization of process feasible region boundaries and accurate estimation of its hypervolume. In particular, a linked list data structure adopted from the field of computer science is used to maintain the grid connectivity information. A uniform perturbation scheme is used to refine the search only near the boundaries. The volumetric flexibility index (FIV) is calculated directly from a summation of feasible hypercubes in the grid, without the need to apply shape reconstruction techniques. The proposed adaptive grid search strategy can capture complex region shapes with reduced sampling costs and without randomness, increasing reproducibility. Operational flexibility is optimized traditionally at a process scale. A case study on refrigerant selection is presented to demonstrate that the developed strategy can be combined within a computer‐aided molecular design framework for operational flexibility optimization at the molecular scale.

A double-model differential evolution for constrained waterflooding production optimization

Recently, evolutionary algorithms (EAs) are becoming more and more popular in oil industry. It should be noted that the existence of various state constraints largely decreases the efficiency of EAs. In this paper, a double-model differential evolution (CSDE) is proposed for waterflooding production optimization with nonlinear inequality constraints. There are two main stages in CSDE: 1) the boundary of feasible region is explicitly constructed by a classifier, support vector machine (SVM), to prescreen the feasible solutions from current population, and 2) the objective function is approximated by radial basis function (RBF) surrogate model which can be used to select the best individual among feasible solutions. It is worth noticing that problems with a large number of constraints can be significantly simplified by distinguishing the feasible solutions and infeasible solutions with one unique SVM classifier. To the best of our knowledge, this is the first foray to integrate SVM and RBF into evolutionary algorithm for waterflooding optimization problem. The CSDE method has been tested on three artificial cases: three-channel, PUNQ-S3 and SPE9. The test results demonstrate that CSDE algorithm can handle constraints more efficient and achieve higher net present value (NPV) compared with the original EAs and other single-model algorithms.

Energy Harvesting and Resource Allocation for Cache-Enabled UAV Based IoT NOMA Networks

This paper investigates a novel joint content caching and energy harvesting scheme to enhance unmanned aerial vehicle (UAV) communications in Internet of Things non-orthogonal multiple access (NOMA) network, where a UAV is acted as an aerial relay to serve users on demand. In particular, a neoteric gravitational search-based multi-constraint optimization algorithm is designed to maximize the throughput of the served users by jointly optimizing power allocation, energy harvesting, and time scheduling schemes. The algorithm engages two main characteristics: 1) classification of multiple constraints, which is for reducing the complexity of the problem solving process due to multiple iterations, and 2) design of force sets, which aims to enhance the global search for the optimal solution at the feasible region boundary. Finally, simulations are provided to show the effective convergence and superiority of the proposed algorithm.

Research on Unmanned Static Trajectory

With the development of science and technology, the intelligence of society is getting higher and higher. The development of safe and reliable intelligent driving has become one of the important topics in today’s era. As a high-tech complex integrating environmental awareness, planning decision-making, control execution and information interaction, driverless cars are increasingly becoming the needs of the times.[1] How to accurately extract effective information to provide safe and reliable control instructions for the next decision-making of vehicles in complex multi-source and heterogeneous environment is the technical basis of intelligent driving.In this paper, a certain amount of research has been done on lane change trajectory planning in different environments. In the aspect of static driving environment, a lane-changing trajectory planning method based on the fifth-order Bessel curve is planned. The physical problems are transformed into optimization problems of coordinate points of Bessel curve expression by planning the left and right boundaries of feasible region through lane-changing trajectory. [2]In the aspect of dynamic driving, based on the model predictive control theory, a lane-changing trajectory optimization method for multi-lane and multi-surrounding vehicles is proposed.

Research and Application of Back Propagation Neural Network-Based Linear Constrained Optimization Method

A back propagation (BP) neural network-based linear constrained optimization method(BPNN-LCOM) was proposed for to solve the problems in linear constraint black box in this paper,hoping to improve the shortcoming of BP neural network-based constrained optimization method (BPNN-COM). In view of minimizing the mathematic model of network output, the basic ideas of BPNN-LCOM wereilluminated,includingmodel design and training, and BP neural network-based global optimization. Firstly, the iteration step size was calculated by optimal step size, and the adjustment step size was calculated by interpolation method, also the iteration speed was accelerated. Secondly, the search direction that iteration point locates on the boundary offeasible region was determined by gradient projection method, which ensured that the iteration process continued along a feasible search direction, and effectively solved the defect of BPNN-COM that sometimes fails to find thetrue optimal solutions. At the same time, the iteration step size along the gradient projection direction was calculated by the optimal constraint step size, which ensured the new iteration point located in the feasible region. Thirdly, the Kuhn-Tucker conditions were introduced to verify whether the iteration point is theoptimization solution that locates on the boundary of feasible region, and it made the termination criterion perfect for BPNN-LCOM.The computation results of two examples showed the effectiveness and feasibility of BPNN-LCOM. The BPNN-LOCM was used to optimize the roller-type bailing mechanism,and the optimal parameters were obtained as follows: round disc diameter was 360 mm, rotationalspeed of the steel rollerwas 250 rpm, feeding quantity was1.7 kg/s, and length-width ratio was 0.8. The corresponding minimum power consumption was 45.8 kJ/bundle. The optimization results were superior to regression analysis and BPNN-COM.The verification test was carried out and the optimization results could improve roller-type bailing mechanism. Verification results showed that the BPNN-LCOM is a feasible method for solving problems in linear constraint black box.

A novel adaptive sampling based methodology for feasible region identification of compute intensive models using artificial neural network

AbstractIdentification of feasible region of operations in multivariate processes is a problem of interest in several fields. This is particularly challenging when the process model is black‐box in nature and/or is computationally expensive, as analytical solutions are not available and the number of possible model evaluations is limited. An efficient methodology is required to identify samples where the model is evaluated for developing a computationally efficient surrogate model. In this work, an artificial neural network based surrogate model is proposed which is integrated with a statistical‐based approach (Jack‐knifing) to estimate the variance of the surrogate model prediction. This allows implementation of an adaptive sampling approach where new samples are identified close to the feasible region boundary or in regions of high prediction uncertainty. The proposed approach performs better than a previously published kriging based method for different dimensionality case studies.

On the Stability and Multistability in a Duopoly Game with R&D Spillover and Price Competition

In this paper, a dynamical two-stage game with R&D competition and joint profit maximization is built. The stability of all the equilibrium points is discussed through Jury condition, and the stability region of the Nash equilibrium point is then given. The influence of the parameters on the system is discussed, and we find that the firm can even benefit from chaos, when it has higher innovation efficiency and higher adjusting speed. And then the coexistence of multiple attractors is studied using basin of attraction. Our research result shows that the coexisting attractors can be observed in the two-parameter bifurcation diagram. At last, the boundary of feasible region, global bifurcations, and formation mechanism of fractal structure of attracting basin are analyzed through critical curves and noninvertible map theory.

Analysis of the change of orbital elements in the process of gravity assist

Gravity assist is widely applied in the deep space exploration because of its reliability and practicability. There are lots of research in the literature about the nearly coplanar situations. In this work, a three-dimensional model of gravity assist model is developed in a semi-analytical manner on the basis of the geometry relationship between the parameters of spacecraft before gravity assist and the orbital elements after gravity assist. The parameters include V∞in (the hyperbolic excess velocity vector of the spacecraft before fly-by), H (the height of fly-by) and θ (the dihedral angle between approach plane and fly-by plane). These equations can be used for analyzing the change of orbital elements in the process of gravity assist, discussing the influence of different parameters on them and deriving the condition that remains the semi-major axis unchanged. Curve fitting of the feasible region boundary of Δi and contour plot of Δi are utilized to analyze the pattern of Δi changing with different parameters. This method is a valuable reference for designing gravity assist trajectories to high inclination targets in the Solar system.

Simplified performance-based optimal seismic design of reinforced concrete frame buildings

This paper presents a simplified performance-based optimal seismic design approach for multi-story reinforced concrete moment frames. The proposed approach minimizes construction cost and takes member plastic rotation and optionally inter-story drift as optimization constraints. Other seismic design requirements reflecting successful design practice are also incorporated. Simplification is made by reducing design variables into two, one for overall system stiffness and the other for overall system strength. The optimization contains two stages, the determination of feasible region boundary in strength and stiffness domain and optimization in material consumption domain. Capacity spectrum method, which jointly considers nonlinear static analysis and inelastic design spectrum, is used to estimate the global and local deformation demands at peak dynamic response. The proposed optimization approach is applied to the design of a six-story reinforced concrete frame. The design results indicate that 30% of needed flexural strength and 26% of cross-sectional area can be reduced from the initial strength-based design. Nonlinear time-history analyses are conducted on the optimized structure using ten historical ground motions scaled to represent three levels of seismic hazard.

Reduced-Cost Constrained Miniaturization of Wideband Antennas Using Improved Trust-Region Gradient Search With Repair Step

In this letter, an improved algorithm for electromagnetic (EM)-driven size reduction of wideband antennas is proposed. Our methodology utilizes variable-fidelity EM simulation models, auxiliary polynomial regression surrogates, as well as multipoint response correction. The constraint handling is implicit, using penalty functions. The core optimization algorithm is a trust-region gradient search with a repair step added in order to facilitate exploration of the feasible region boundary. The latter results in considerable reduction of the computational cost of the optimization process. The proposed methodology is demonstrated using two wideband antennas and compared to both direct optimization of the high-fidelity model and the surrogate-assisted framework without the aforementioned repair step. The results indicate superiority of the presented approach. Experimental validation of the fabricated prototypes of the optimized antennas is also provided.

Pareto front generation for bridge deck management system using bi-objective optimization

Bi-objective Optimization (BOO) method for the allocation of bridge deck Maintenance, Repair, and Rehabilitation (MR&R) budget is proposed using Bridge Management System (BMS) models. BOO problem is usually solved by using weighted sum method due to simple and easy of application. However, it is generally known that weighted sum method with linear objective functions finds the optimum solution which always lies on the boundary of feasible region. This phenomenon doesn't help the bridge engineers to have the choices when trade-off has to be made between objectives. Moreover, evenly distributed weights on objective functions does not guarantee the uniform distribution of optimized solution sets. This paper compares several multi-objective optimization techniques and proposes the improved solution technique that can be competent in terms of applicability for non-convex problem as well as production of only Pareto optimal solution sets. The proposed optimization technique is based on modification of well recognized method of “Normal Boundary Intersection” by Das and Dennis (1998). Using bi-objective optimization technique on bridge MR&R, decision maker will have more choice for the allocation of budget. Data obtained from Wyoming Department of Transportation (WYDOT) are used to validate the feasibility of application of proposed method for the maintenance of bridge decks.

A novel feasibility analysis method for black‐box processes using a radial basis function adaptive sampling approach

Feasibility analysis is used to determine the feasible region of a multivariate process. This can be difficult when the process models include black‐box constraints or the simulation is computationally expensive. To address such difficulties, surrogate models can be built as an inexpensive approximation to the original model and help identify the feasible region. An adaptive sampling method is used to efficiently sample new points toward feasible region boundaries and regions where prediction uncertainty is high. In this article, cubic Radial Basis Function (RBF) is used as the surrogate model. An error indicator for cubic RBF is proposed to indicate the prediction uncertainty and is used in adaptive sampling. In all case studies, the proposed RBF‐based method shows better performance than a previously published Kriging‐based method. © 2016 American Institute of Chemical Engineers AIChE J, 63: 532–550, 2017

A novel surrogate-based approach for optimal design of electromagnetic-based circuits

A new geometric design centring approach for optimal design of central processing unit-intensive electromagnetic (EM)-based circuits is introduced. The approach uses norms related to the probability distribution of the circuit parameters to find distances from a point to the feasible region boundaries by solving nonlinear optimization problems. Based on these normed distances, the design centring problem is formulated as a max–min optimization problem. A convergent iterative boundary search technique is exploited to find the normed distances. To alleviate the computation cost associated with the EM-based circuits design cycle, space-mapping (SM) surrogates are used to create a sequence of iteratively updated feasible region approximations. In each SM feasible region approximation, the centring process using normed distances is implemented, leading to a better centre point. The process is repeated until a final design centre is attained. Practical examples are given to show the effectiveness of the new design centring method for EM-based circuits.

Evaluation of Dynamic Load-Carrying Capacity for Free-Floating Space Manipulators

Two kinds of dynamic load-carrying capacity (DLCC) evaluation methods for free-floating space manipulators (FFSM) in two typical on-orbit operating missions are proposed in this paper. DLCC evaluation is transformed into nonlinear programming problem (NPP) by introducing load-carrying coefficient to measure DLCC: in point-to-point task, penalty function method is adopted to approach the boundary of feasible region rapidly, then DLCC can be obtained through following iterations; in trajectory tracking task, NPP is solved by using multiple one-dimensional search, the dynamic load-carrying coefficient in discontinuous feasible region can be quickly solved through adjusting the searching boundary constantly. The effectiveness of the mentioned methods is verified by simulations.