Multidimensional Optimization Problem Research Articles

Blind NCS-Based Autofocus for Airborne Wide-Beam SAR Imaging

The improvement in azimuth resolution and/or the increase in the instantaneous beam width can result in a wide-beam autofocus problem in airborne synthetic aperture radar (SAR). Because of the assumption of central-beam approximation, the typical two-step motion compensation (MoCo) method and its extensions are unsuitable for the autofocus of wide-beam SAR imaging. In addition, existing MoCo algorithms for airborne wide-beam SAR imaging require high-precision inertial navigation data. To address these problems, we propose a wide-beam autofocus algorithm based on a blind nonlinear chirp scaling. First, based on the two-step MoCo method, the wide-beam autofocus in this study was modeled as a multiparameter optimization problem for an optimal overall imagery quality. Subsequently, we combine the well-known parametric and nonparametric methods in the SAR autofocus community to convert the multidimensional optimization problem into a two-dimensional optimization problem. Furthermore, we observe that this two-dimensional optimization problem can be further converted into two one-dimensional optimization problems, which can significantly increase the efficiency and robustness of autofocus processing. In addition, the proposed method is a full-aperture algorithm for wide-beam SAR autofocus, which can avoid the problems of image stitching and phase discontinuity compared with well-known subaperture autofocus algorithms (e.g., SATA, PTA, and FD). The processing results of the simulated and measured data verified the effectiveness of the proposed method.

A Machine Learning Generative Method for Automating Antenna Design and Optimization

To facilitate the antenna design with the aid of computer, one of the practices in consumer electronic industry is to model and optimize antenna performances with a simplified antenna geometric scheme. The ease of handling multi-dimensional optimization problems and the less dependence on the engineers' knowledge and experience are the key to achieve the popularity of simulation-driven antenna design and optimization for the industry. In this paper, we introduce a flexible geometric scheme with the concept of mesh network that can form any arbitrary shape by connecting different nodes. For such problems with high dimensional parameters, we propose a machine learning based generative method to assist the searching of optimal solutions. It consists of discriminators and generators. The discriminators are used to predict the performance of geometric models, and the generators to create new candidates that will pass the discriminators. Moreover, an evolutionary criterion approach is proposed for further improving the efficiency of our method. Finally, not only optimal solutions can be found, but also the well trained generators can be used to automate future antenna design and optimization. For a dual resonance antenna design, our proposed method is better than the other mature algorithms.

Design and Optimization of Enhanced Magnitude and Phase Response IIR Full-Band Digital Differentiator and Integrator Using the Cuckoo Search Algorithm

Design of full-band infinite impulse response (IIR) digital differentiator (DD) and digital integrator (DI) based on the L_k-norm and the min-max optimality criteria have been demonstrated in literature. However, the designed IIR DDs and DIs using these criteria do not have linear phase or have unsatisfactory magnitude response. In this paper, a novel approach to design, optimize and improve the magnitude response and the linearity of the phase response of IIR DD and DI using the cuckoo search (CS) optimization algorithm is proposed. The proposed approach is based on a varied L_<i>k</i>-norm where <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> linearly increases with the number of the frequency samples between the values 1 and 2. The design and optimization of DDs and DIs are carried out using the CS optimization method due to its simplicity, efficiency, and robustness in solving general multidimensional optimization problems. The performance of the designed DDs and DIs using the proposed approach is compared with designs based on different criteria and algorithms available in literature. The comparison shows that the designed DDs and DIs based on the proposed approach have better phase responses and better or at least comparable magnitude responses compared to those of DDs and DIs designed using other methods in the literature.

Better baboon break-ups: collective decision theory of complex social network fissions.

Many social groups are made up of complex social networks in which each individual associates with a distinct subset of its groupmates. If social groups become larger over time, competition often leads to a permanent group fission. During such fissions, complex social networks present a collective decision problem and a multidimensional optimization problem: it is advantageous for each individual to remain with their closest allies after a fission, but impossible for every individual to do so. Here, we develop computational algorithms designed to simulate group fissions in a network-theoretic framework. We focus on three fission algorithms (democracy, community and despotism) that fall on a spectrum from a democratic to a dictatorial collective decision. We parameterize our social networks with data from wild baboons (Papio cynocephalus) and compare our simulated fissions with actual baboon fission events. We find that the democracy and community algorithms (egalitarian decisions where each individual influences the outcome) better maintain social networks during simulated fissions than despotic decisions (driven primarily by a single individual). We also find that egalitarian decisions are better at predicting the observed individual-level outcomes of observed fissions, although the observed fissions often disturbed their social networks more than the simulated egalitarian fissions.

Improved arithmetic optimization algorithm and its application to discrete structural optimization

The arithmetic optimization algorithm (AOA) is a newly developed metaheuristic search technique that simulates the distribution characteristics of the basic arithmetic operations of addition, subtraction, multiplication, and division, and has been employed to solve some real-world optimization problems. However, it has been found that the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when applied to multi-dimensional optimization problems. In this paper, to overcome the shortcomings of the standard AOA, an improved variant of the AOA, called improved arithmetic optimization algorithm (IAOA), is proposed and then employed for optimization of skeletal structures with discrete design variables. Compared to the standard AOA, two major improvements are made in the proposed IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The proposed IAOA requires fewer algorithm-specific parameters compared with the standard AOA, making it easy to be implemented. To examine the efficiency and robustness of the proposed IAOA, three benchmark structural optimization problems with discrete design variables are investigated and the results are compared to those of the standard AOA and other methods available in the literature. To the best of our knowledge, this is the first attempt to apply AOA to structural optimization. The IAOA not only promotes the exploration capability of the search space but also overcomes the shortcoming of the premature convergence of the standard AOA. Experimental results indicate that IAOA significantly surpasses the standard AOA and achieves results comparable or superior to other state-of-the-art metaheuristics.

Application of genetic algorithms in optimization of SFR nuclear reactor design

Abstract This work presents a demonstrational application of genetic algorithms (GAs) to solve sample optimization problems in the generation IV nuclear reactor core design. The new software was developed implementing novel GAs, and it was applied to show their capabilities by presenting an example solution of two selected problems to check whether GAs can be used successfully in reactor engineering as an optimization tool. The 3600 MWth oxide core, which was based on the OECD/NEA sodium-cooled fast reactor (SFR) benchmark, was used a reference design [1]. The first problem was the optimization of the fuel isotopic inventory in terms of minimizing the volume share of long-lived actinides, while maximizing the effective neutron multiplication factor. The second task was the optimization of the boron shield distribution around the reactor core to minimize the sodium void reactivity effect (SVRE). Neutron transport and fuel depletion simulations were performed using Monte Carlo neutron transport code SERPENT2. The simulation resulted in an optimized fuel mixture composition for the selected parameters, which demonstrates the functionality of the algorithm. The results show the efficiency and universality of GAs in multidimensional optimization problems in nuclear engineering.

A contraction approach to dynamic optimization problems

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.

Improvement on optimal design of dynamic absorber for enhancing seismic performance of nuclear piping using adaptive Kriging method

For improving the seismic performance of the nuclear power plant (NPP) piping system, attempts have been made to apply a dynamic absorber (DA). However, the current piping DA design method is limited because it cannot provide the globally optimum values for the target design seismic loading. Therefore, this study proposes a seismic time history analysis-based DA optimal design method for piping. To this end, the Kriging approach is introduced to reduce the numerical cost required for seismic time history analyses. The appropriate design of the experiment method is used to increase the efficiency in securing response data. A gradient-based method is used to efficiently deal with the multi-dimensional unconstrained optimization problem of the DA optimal design. As a result, the proposed method showed an excellent response reduction effect in several responses compared to other optimal design methods. The proposed method showed that the average response reduction rate was about 9% less at the maximum acceleration, about 5% less at the maximum value of the response spectrum, about 9% less at the maximum relative displacement, and about 4% less at the maximum combined stress compared to existing optimal design methods. Therefore, the proposed method enables an effective optimal DA design method for mitigating seismic response in NPP piping in the future.

IBOA-Based Optimization of Cross-Sectional Dimension of Rods for a 3-RRR PPM to Minimize Energy Consumption

For obtaining optimal cross-sectional dimensions of rods for a 3-RRR planar parallel manipulator (PPM) to minimize energy consumption, the inverse dynamics of the manipulator is modeled based on the Newton–Euler method, after which the coefficient matrix of the inverse dynamics equation is decomposed based on matrix theory. Hence, the objective function, that is, the logical relationship between the energy consumption of the manipulator and the cross-sectional dimension of each rod, is established. However, in solving the multidimensional constrained single-object optimization problem, there are difficulties such as the penalty function’s sensitivity to the penalty factors if the problem is transformed into the one of unconstrained multiobjective optimization. Therefore, to properly handle the constraints, an improved butterfly optimization algorithm (IBOA) is presented to ensure that the new iterated point always falls into the feasible region according to the butterfly optimization algorithm (BOA). Finally, the comparisons among the IBOA, particle swarm optimization (PSO), and BOA and further experiments of the physical prototype are implemented to validate the effectiveness of the proposed theoretical model and numerical algorithm. Results indicate that the proposed IBOA is more suitable for solving the constrained single-object optimization problem with better convergence speed and accuracy.

Impact of Chinese and European Airspace Constraints on Trajectory Optimization

Air traffic trajectory optimization is a complex, multidimensional and non-linear optimization problem and requires a firm focus on the essential criteria. The criteria cover operational, economical, environmental, political, and social factors and differ from continent to continent. Since air traffic is a transcontinental transport system, the criteria may also change during a single flight. Historic flight track data allow observation and assess real flights, to extract essential criteria and to derive optimization strategies to increase air traffic efficiency. Real flight track data from the Chinese and European air traffic show significant differences in the routing structure in both regions. For that reason, reference trajectories of historic ADS-B 24-h air traffic data in China and Europe have been extracted and analyzed regarding horizontal flight efficiency and the most restrictive criteria of trajectory optimization. We found that prohibited areas might be the most powerful reason to describe deviations from the great circle distance in the Chinese air traffic system. Atmospheric conditions, network requirements, aircraft types and flight planning procedures are similar in China and Europe and only have a minor impact on flight efficiency during the cruise phase. In a multi-criteria trajectory optimization of the extracted reference trajectories considering the weather, operational constraints and prohibited areas, we found that flown ground distances could be reduced by 255 km in the Chinese airspace and 2.3 km in the European airspace. The resultant reference trajectories can be used for further analysis to increase the efficiency of continental air traffic flows.

A Literature Review of MADM Applications for Site Selection Problems — One Decade Review from 2011 to 2020

Site selection is a multi-dimensional optimization problem that influences a wide variety of stakeholders from local communities and authorities to governments, environmental protection agencies, etc. Locating an energy project as well as transportation infrastructure projects, for instance, are of great strategic importance and are connected to the top-level regulations and policy levels. These problems are significant from strategic levels to the productivity of a single construction project level, from energy to transportation and from infrastructure to residential buildings.A large number of publications in this field of study prove this significance. However, regarding the variety of applications, managerial decision levels, and the growing number of studies, it is important to comprehend the latest trends and conclude an appropriate research path in this field.This study is mainly focused on the application of MADM methodologies on locating problems by which many studies are carried out and have a high coincidence with the locating problem environment. Consequently, 425 studies are considered in this study, and 217 more relevant papers are selected for the subsequent reviews. Based on the results, Energy projects are by far the most frequent field of study in this regard which are considered as renewable and nonrenewable categories. Also, environmental planning and sustainable site selection are of secondary importance.

Will a Computer Design Your Next Transformer? [White Hot

The design of magnetics is a real challenge for power electronics engineers. To get a good design means finding the right combination of core material, core shape, bobbin/coil former, winding layup, winding wire or foil, insulation, and terminations. This makes even a one winding inductor a complex multidimensional optimization problem. The author gives a brief overview of several types of magnetics design automation highlighting their capabilities and limitations. It is concluded that these tools bode well and that power electronics designers can look forward to an ever evolving capability in the automated design of magnetic devices. So what do you think? Will a computer design your next transformer or inductor?

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

The present study aims to develop a risk-based approach to finding optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing a positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets and the second objective is to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life extension assessment considers the results of a detailed structural integrity analysis, a free-cash-flow analysis, the probability of project failure, and local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk–return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rates of return are recommended for different stages of life extension.

Fast Trajectory Optimization for Gliding Reentry Vehicle Based on Improved Sparrow Search Algorithm

In order to solve the problem of low convergence accuracy and easy to fall into local optimization when solving the reentry vehicle trajectory optimization problem for existing algorithms, an improved sparrow search algorithm (OTRSSA) is proposed. Firstly, the basic sparrow search algorithm is improved by the methods of opposition-based learning, adaptive T-distribution and random walk to improve the optimization accuracy and stability, and increase the global search ability, and the performance verification is carried out in 12 benchmark functions; secondly, the 3-DOF motion model of reentry trajectory optimization problem is established and transformed into multi-dimensional function optimization problem; finally, OTRSSA is applied to solve the trajectory optimization problem. The simulation results show that the optimization performance and convergence speed of OTRSSA are better, and a reentry trajectory with the farthest range and satisfying constraints can be obtained quickly.

On Robust Saddle-Point Criterion in Optimization Problems with Curvilinear Integral Functionals

In this paper, we introduce a new class of multi-dimensional robust optimization problems (named (P)) with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Moreover, we define an auxiliary (modified) class of robust control problems (named (P)(b¯,c¯)), which is much easier to study, and provide some characterization results of (P) and (P)(b¯,c¯) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to (P)(b¯,c¯). For this aim, we consider path-independent curvilinear integral cost functionals and the notion of convexity associated with a curvilinear integral functional generated by a controlled closed (complete integrable) Lagrange 1-form.

A new trisection method for solving Lipschitz bi-objective optimization problems

In this paper, we develop a branch and bounds algorithm to solve bound-construction bi-objective optimization problem. The proposed algorithm allows to determine an approximation of the Pareto optimal solutions sets in both spaces: decisions and objectives ones. By running α-dense space filling curves, we convert a multidimensional bi-objective optimization problem into a one-dimensional one. Hence it gets possible the implementation of the proposed algorithm when objectives depend on more than one decision variable. The proposed algorithm was applied on an engineering problem to find the working space of a robotic manipulator and the obtained results are promising.

Generalized Oppositional Moth Flame Optimization with Crossover Strategy: An Approach for Medical Diagnosis

In the original Moth-Flame Optimization (MFO), the search behavior of the moth depends on the corresponding flame and the interaction between the moth and its corresponding flame, so it will get stuck in the local optimum easily when facing the multi-dimensional and high-dimensional optimization problems. Therefore, in this work, a generalized oppositional MFO with crossover strategy, named GCMFO, is presented to overcome the mentioned defects. In the proposed GCMFO, GOBL is employed to increase the population diversity and expand the search range in the initialization and iteration jump phase based on the jump rate; crisscross search (CC) is adopted to promote the exploitation and/or exploration ability of MFO. The proposed algorithm’s performance is estimated by organizing a series of experiments; firstly, the CEC2017 benchmark set is adopted to evaluate the performance of GCMFO in tackling high-dimensional and multimodal problems. Secondly, GCMFO is applied to handle multilevel thresholding image segmentation problems. At last, GCMFO is integrated into kernel extreme learning machine classifier to deal with three medical diagnosis cases, including the appendicitis diagnosis, overweight statuses diagnosis, and thyroid cancer diagnosis. Experimental results and discussions show that the proposed approach outperforms the original MFO and other state-of-the-art algorithms on both convergence speed and accuracy. It also indicates that the presented GCMFO has a promising potential for application.

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method.

At present, in robot technology, remote control of robot is realized by wireless communication technology, and data anti-interference in wireless channel becomes a very important part. Any wireless communication system has an inherent multi-path propagation problem, which leads to the expansion of generated symbols on a time scale, resulting in symbol overlap and Inter-symbol Interference (ISI). ISI in the signal must be removed and the signal restores to its original state at the time of transmission or becomes as close to it as possible. Blind equalization is a popular equalization method for recovering transmitted symbols of superimposed noise without any pilot signal. In this work, we propose a concurrent modified constant modulus algorithm (MCMA) and the decision-directed scheme (DDS) with the Barzilai-Borwein (BB) method for the purpose of blind equalization of wireless communications systems (WCS). The BB method, which is two-step gradient method, has been widely employed to solve multidimensional unconstrained optimization problems. Considering the similarity of equalization process and optimization process, the proposed algorithm combines existing blind equalization algorithm and Barzilai-Borwein method, and concurrently operates a MCMA equalizer and a DD equalizer. After that, it modifies the DD equalizer's step size (SS) by the BB method. Theoretical investigation was involved and it demonstrated rapid convergence and improved equalization performance of the proposed algorithm compared with the original one. Additionally, the simulation results were consistent with the proposed technique.

Method for splitting the feasible region to increase the variability of continuous optimization test problems

The solution of optimization problems is essential for the design and control of technical systems. The optimization problem arising in practice has a high dimension, nonlinear criteria, and constraints. There are a lot of continuous optimization tasks for testing and research of optimization algorithms performance. These tasks have a convex range of acceptable values limited to a specified range for each parameter. The problem of generating test multidimensional continuous optimization tasks with nonlinear constraints and splitting the feasible region is considered. A method was proposed for splitting the feasible region by separate domains using the multidimensional grid of forbidden solutions. As a result, the problem acquires properties closer to optimizing technical systems with complex constraints. The method allows creating an unlimited number of test optimization problems, which can be used to research and develop optimization algorithms. The method is simple to implement, and the impact on the computational complexity of tasks is insignificant. Research has been carried out on four widely used continuous single-objective optimization test functions, with the Genetic algorithm and the Particle Swarm Optimization algorithm. It is shown that the proposed method has an influence on the process of solving multidimensional continuous optimization problems by population algorithms and on the dependence of the accuracy of the algorithm on its heuristic coefficients.

Importance sampling based direct maximum likelihood position determination of multiple emitters using finite measurements

The exact Direct Maximum Likelihood Position Determination (ML-DPD) of multiple emitters requires a multidimensional searching with exponential complexity. The subspace-based DPD technique and the filtering-based DPD technique are recently proposed to reduce the complexity by transforming the original high-dimensional optimization problem into several low-dimensional ones. However, these techniques approximate the exact ML solution only if the measurements are assumed infinite. In this paper, we model the received signals in the nonlinear regression form and resort to the multidimensional optimization framework, consisting of the Pincus’ theorem and the Importance Sampling (IS) technique, to approximate the exact ML solution using finite measurements. The proposed IS based ML DPD approach also reduces the complexity by decoupling the multidimensional optimization problem into several three-dimensional ones. Moreover, the new non-iterative ML DPD approach guarantees global optimality and does not suffer from the off-grid problems inherent to most DPD techniques. The numerical simulations show that the proposed ML DPD estimator acquires the exact multidimensional ML solution even using a narrow bandwidth or being at low Signal to Noise Ratio (SNR).