Multidimensional Optimization Problem Research Articles

Fast pupil tracking based on the study of a boundary-stepped image model and multidimensional optimization Hook-Jives method

A new fast method for pupil detection and eyetracking real time is being developed based on the study of a boundary-step model of a grayscale image by the Laplacian-Gaussian operator and finding a new proposed descriptor of accumulated differences (point identifier), which displays a measure of the equidistance of each point from the boundaries of some relative monotonous area (for example, the pupil of the eye). The operation of this descriptor is based on the assumption that the pupil in the frame is the most rounded monotonic region with a high brightness difference at the border, the pixels of the region should have an intensity less than a predetermined threshold (but the pupil may not be the darkest region in the image). Taking into account all of the above characteristics of the pupil, the descriptor allows achieving high detection accuracy of its center and size, in contrast to methods based on threshold image segmentation, based on the assumption of the pupil as the darkest area, morphological methods (recursive morphological erosion), correlation or methods that investigate only the boundary image model (Hough transform and its variations with two-dimensional and three-dimensional parameter spaces, the Starburst algorithm, Swirski, RANSAC, ElSe). The possibility of representing the pupil tracking problem as a multidimensional unconstrained optimization problem and its solution by the Hook-Jeeves non-gradient method, where the function expressing the descriptor is used as the objective function, is investigated. In this case, there is no need to calculate the descriptor for each point of the image (compiling a special accumulator function), which significantly speeds up the work of the method. The proposed descriptor and method were analyzed, and a software package was developed in Python 3 (visualization) and C ++ (tracking kernel) in the laboratory of the Physics and Mathematics Faculty of Kamchatka State University of Vitus Bering, which allows illustrating the work of the method and tracking the pupil in real time.

Robust design and evaluation of phase codes for radar performance optimization with a finite alphabet constraint

This letter considers the robust design of radar waveform with discrete phase codes under constant modulus constraint to enhance target detectability. To solve the resultant max-min non-convex optimization problem, a robust discrete phase coding algorithm via iterative technology (R-DPCA-IT) is developed which monotonically improves the worst-case SNR and has an upper bound ensuring to converge a finite value. At each iteration, the original multidimensional quadratic optimization problem is turned into multiple one-dimensional optimization problems solved globally via line search. Finally, the computational time and objective value of the proposed algorithm are assessed in comparison with the existing methods.

Как обмануть нейронную сеть? Синтез шума для уменьшения точности нейросетевойклассификации изображений

The study aims to develop an algorithm and then software to synthesise noise that could be used to attack deep learning neural networks designed to classify images. We present the results of our analysis of methods for conducting this type of attacks. The synthesis of attack noise is stated as a problem of multidimensional constrained optimization. The main features of the attack noise synthesis algorithm proposed are as follows: we employ the clip function to take constraints on noise into account; we use the top-1 and top-5 classification error ratings as attack noise efficiency criteria; we train our neural networks using backpropagation and Adam's gradient descent algorithm; stochastic gradient descent is employed to solve the optimisation problem indicated above; neural network training also makes use of the augmentation technique. The software was developed in Python using the Pytorch framework to dynamically differentiate the calculation graph and runs under Ubuntu 18.04 and CentOS 7. Our IDE was Visual Studio Code. We accelerated the computation via CUDA executed on a NVIDIA Titan XP GPU. The paper presents the results of a broad computational experiment in synthesising non-universal and universal attack noise types for eight deep neural networks. We show that the attack algorithm proposed is able to increase the neural network error by eight times

Joint Resource Allocation for Device-to-Device Communication Assisted Fog Computing

In this paper, joint resource management for device-to-device (D2D) communication assisted multi-tier fog computing is studied. In the considered system model, each subscribed mobile end user can choose to offload its computation task to either an edge server deployed at the base station via the cellular connection or one nearby third-party fog node via the direct D2D connection. After receiving offloading requests from all end users, the network operator determines the optimal management of the fog computing system, including both computation and communication resource allocations, according to its service agreements with end users, energy cost of edge-server processing and total expense in renting third-party fog nodes. With the objective of maximizing the network management profit, a joint multi-dimensional resource optimization problem, integrating link scheduling, channel assignment and power control, is formulated. An optimal solution algorithm is proposed based on the idea of branch-and-price for addressing this complicated mixed integer nonlinear programming problem. To facilitate the practical implementation in large-scale systems, a suboptimal greedy algorithm with significantly reduced computational complexity is also developed. Simulation results examine the efficiency of the proposed D2D-assisted fog computing framework, and demonstrate the superiority of the proposed resource allocation algorithm over the counterparts.

A Modified Sparrow Search Algorithm with Application in 3d Route Planning for UAV.

The unmanned aerial vehicle (UAV) route planning problem mainly centralizes on the process of calculating the best route between the departure point and target point as well as avoiding obstructions on route to avoid collisions within a given flight area. A highly efficient route planning approach is required for this complex high dimensional optimization problem. However, many algorithms are infeasible or have low efficiency, particularly in the complex three-dimensional (3d) flight environment. In this paper, a modified sparrow search algorithm named CASSA has been presented to deal with this problem. Firstly, the 3d task space model and the UAV route planning cost functions are established, and the problem of route planning is transformed into a multi-dimensional function optimization problem. Secondly, the chaotic strategy is introduced to enhance the diversity of the population of the algorithm, and an adaptive inertia weight is used to balance the convergence rate and exploration capabilities of the algorithm. Finally, the Cauchy–Gaussian mutation strategy is adopted to enhance the capability of the algorithm to get rid of stagnation. The results of simulation demonstrate that the routes generated by CASSA are preferable to the sparrow search algorithm (SSA), particle swarm optimization (PSO), artificial bee colony (ABC), and whale optimization algorithm (WOA) under the identical environment, which means that CASSA is more efficient for solving UAV route planning problem when taking all kinds of constraints into consideration.

Sparse Bayesian Inference-Based Direct Off-Grid Position Determination in Multipath Environments

The classical super-resolution Direct Position Determination (SR-DPD) algorithms fail to suppress the coherent Non-Line-of-Sight (NLOS) interference due to the lack of independent measurements. The existing Sparse Signal Reconstruction (SSR) based DPD approach suffers from the intractable complexity since it needs to solve a Second-Order Cone Programming (SOCP) problem. Besides, the Grid Quantization Error (GQE) exists in all above on-grid model based algorithms inherently. The proposed Sparse Bayesian Inference (SBI) based off-grid DPD algorithm is easy to implement as the Expectation-Maximization (EM) method is applied to decouple the multi-dimensional optimization problem. In addition, the GQE is also eliminated by introducing the Gradient Descent (GD) mechanism into the EM steps to update the grid point coordinates of interest iteratively.

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.

Implementation of APSO and Improved APSO on Non-Cascaded and Cascaded Short Term Hydrothermal Scheduling

Short-term hydrothermal scheduling (STHTS) is a highly non-linear, multi-model, non-convex, and multi-dimensional optimization problem that has been worked upon for about 5 decades. Many research articles have been published in solving different test cases of STHTS problem, while establishing the superiority of one type of optimization algorithm over the type, in finding the near global best solution of these complex problems. This paper presents the implementation of an improved version of a variant of the Particle Swarm Optimization algorithm (PSO), known as Accelerated Particle Swarm Optimization (APSO) on three benchmark test cases of STHTS problems. The adaptive and variable nature of the local and global search coefficients for the proposed APSO significantly improve its performance in obtaining the optimal solution for the STHTS test cases. Two of these cases are non-cascaded cases of STHTS problem (NCSTHTS) and one case is cascaded case of STHTS problem (CSTHTS). The results are compared with the results of the previous implementations of the other algorithms as presented in the literature. Due to the stochastic nature of the meta-heuristic algorithms, the parametric and non-parametric statistical tests have been implemented to establish the superiority of results of one type of algorithm over the results of the other type of algorithms.

Software-Defined Design Space Exploration for an Efficient DNN Accelerator Architecture

Deep neural networks (DNNs) have been shown to outperform conventional machine learning algorithms across a wide range of applications, e.g., image recognition, object detection, robotics, and natural language processing. However, the high computational complexity of DNNs often necessitates extremely fast and efficient hardware. The problem gets worse as the size of neural networks grows exponentially. As a result, customized hardware accelerators have been developed to accelerate DNN processing without sacrificing model accuracy. However, previous accelerator design studies have not fully considered the characteristics of the target applications, which may lead to sub-optimal architecture designs. On the other hand, new DNN models have been developed for better accuracy, but their compatibility with the underlying hardware accelerator is often overlooked. In this article, we propose an application-driven framework for architectural design space exploration of DNN accelerators. This framework is based on a hardware analytical model of individual DNN operations. It models the accelerator design task as a multi-dimensional optimization problem. We demonstrate that it can be efficaciously used in application-driven accelerator architecture design: we use the framework to optimize the accelerator configurations for eight representative DNNs and select the configuration with the highest geometric mean performance. The geometric mean performance improvement of the selected DNN configuration relative to the architectural configuration optimized only for each individual DNN ranges from 12.0 to 117.9 percent. Given a target DNN, the framework can generate efficient accelerator design solutions with optimized performance and area. Furthermore, we explore the opportunity to use the framework for accelerator configuration optimization under simultaneous diverse DNN applications. The framework is also capable of improving neural network models to best fit the underlying hardware resources. We demonstrate that it can be used to analyze the relationship between the operations of the target DNNs and the corresponding accelerator configurations, based on which the DNNs can be tuned for better processing efficiency on the given accelerator without sacrificing accuracy.

OABC: An Otsu-Artificial Bee Colony Multilevel Image Threshold Optimization for Liver Tumor Segmentation

Grey scale or color image conversion involves thresholding technique which can be either at single or multiple threshold levels. Resultant images have reduced pixel level classes. As level of thresholding required increases, the process becomes complex involving exhaustive search and thereby increasing computational resources and time complexity. Meta-heuristic optimization algorithms show promise to reduce time-complexity, especially the Artificial Bee Colony (ABC) algorithm mimicking honeybee foraging activities. It provides optimal results when sampling a large solution space. Since threshold-based image segmentation is a multidimensional discreet optimization problem, for fitness evaluation of threshold level candidates, Otsu’s thresholding method has been widely employed. In this paper, proposed is an Otsu-ABC multilevel image thresholding model for CT images using MATLAB for Liver tumor segmentation. The developed model is evaluated for increased dimensionality and computation time. It is also benchmarked against other commonly used algorithms. Results demonstrate that the proposed model is immune to dimensionality increase and outperforms all other models with regards to quality of images segmented and computation time proving that the model is ideal for optimizing multilevel image thresholding problems involving large thresholds for complex computer vision problems in medical diagnostics, biometrics, surveillance, satellite imagery and gaming.

Nodes Deployment Algorithm Based on Data Fusion and Evidence Theory in Wireless Sensor Networks

Wireless sensor networks have been widely researched and developed in recent years. The node deployment problem is a multi-dimensional nonlinear optimization problem with continuous discrete variables. In order to improve the coverage effect of wireless sensor networks, a network coverage algorithm based on evidence theory is proposed. The motion direction of the wireless sensor node is calculated. The wireless sensor node is moved to the area with low perception probability. Improve the network coverage effect. Reduce the moving distance of wireless sensor nodes. Extended the service time of wireless sensor network. The simulation results show that this algorithm can improve the coverage effect of the monitoring area and reduce the moving distance of nodes effectively.

Hybrid Niche Immune Genetic Algorithm for Fault Detection Coverage in Industry Wireless Sensor Network

The industry wireless sensor network (IWSN) technology, which is used to monitor industrial equipment, has attracted more and more attention in recent years. Sensor nodes in IWSN can spontaneously complete distributed networking and carry out monitoring tasks under random deployment conditions. Therefore, a self‐organized IWSN is particularly suitable for the fault detection and diagnosis of industrial equipment in complex environments. However, due to the detection, ability of a single sensor node is limited, and the monitoring distribution problem is a typical multidimensional discrete NP‐hard combinatorial stochastic optimization problem, which is challenging to solve for the traditional mathematical methods. With the purpose of improving the target monitoring capability and prolonging lifetime of IWSN, a novel hybrid niche immune genetic algorithm (HNIGA) for optimizing the target coverage model of fault detection is proposed. It uses the genetic operation to evolve antibody groups and applies niche technology to maintain the diversity of antibody groups. As a result, HNIGA can effectively reduce the failure rate of detection targets. To verify the performance of HNIGA, a series of simulations under different simulation conditions are carried out. Specifically, HNIGA is compared with genetic algorithm (GA) and simulated annealing (SA). Simulation results show that HNIGA has a faster convergence speed and more robust global search capability than the other two algorithms.

МАСШТАБИРУЕМОСТЬ БИОЭВРИСТИК ДЛЯ ЗАДАЧ МНОГОМЕРНОЙ ОПТИМИЗАЦИИ

A scalable bio-heuristic algorithm capable of solving multidimensional optimization problems is proposed. Special operators are used to support the diversity of the solution population, to expand the search area for solutions at the expense of less promising solutions. The efficiency of the proposed algorithm is evaluated on a set of multidimensional functions of Grivank, Rastrigin, Rosenbrock, and Schwefel. The indicators of the developed algorithm are com-pared with those of competing algorithms.

Direction of arrival estimation in the presence of model errors by signal subspace matching

We present a novel solution to the problem of direction-of-arrival estimation, aimed at coping with the critical problem of model errors. Unlike the existing approaches to this problem, the proposed solution copes with model errors implicitly, without any parameterization or statistical modeling of these errors. The solution is based on matching the error-contaminated model-based signal subspace to its noisy sampled-data-based counterpart, and is referred to as signal subspace matching (SSM) solution. The resulting multidimensional optimization problem amounts to finding the directions-of-arrival for which the angle between these two subspaces is minimal. To simplify the computational load involved in this multidimensional optimization problem, we derive an iterative solution involving only 1-dimensional optimization, which is inspired by the alternating projection (AP) solution to the deterministic maximum likelihood (DML) cost function. Simulation results demonstrating the performance are included. The results show the clear performance superiority of the SSM solution over the DML and MUSIC solutions, especially in the case of high modeling errors and in challenging scenarios involving low number of samples, low angular separation and highly correlated signals.

The Impact of Cost Information Sharing on Procurement Contract Design

In this paper, we provides contract design mechanisms and analysis for manufacturers to manage decentralized supply chain. Suppose the manufacturer’s final product consists of components, each produced by a different supplier, and the manufacturer first purchases components from suppliers, then assembles them into final product and meet demands aftermarket realization. While supply chain’s internal cooperation always benefits both, suppliers are often reluctant to proactively share their own production cost structure, otherwise manufacturers may depress purchase prices, which may reduce supplier’s profit. Manufacturers on the other hand, prefers to be informed of true cost information in order to gain greater revenues. We takes manufacturer’s perspective and design the optimal contract menu for suppliers, both to enable suppliers to disclose private cost information and to maximize the benefits. We start by modeling the original problem and find that the original problem is a complex multidimensional optimization problem. We then examine the nature of the original problem solving and devise the solution algorithm to arrive at the optimal contract menu. This algorithm reduces the complexity of the original question from o(2 n ) to o(n). We further investigate the influence mechanism of model parameters on the results and find that when market demand increases or the selling price of the final product increases, value of private information increases significantly. However, if market demand uncertainty increases, the value of information may increase or decrease for both sides.

A Genetic Algorithm Based on Auxiliary-Individual-Directed Crossover for Internet-of-Things Applications

In order to solve the large-scale, strong coupling, and nonlinear optimization problems in many Internet-of-Things (IoT) applications, such as intelligent infrastructure and smart city, this article proposes a real-coded genetic algorithm based on an auxiliary-individual-directed crossover operator (AIDX). AIDX is an alternative offspring framework of the directed crossover which uses auxiliary individual to reduce the search space of alternative offspring for the rapid optimization of multidimensional problems. In our solution AIDX, the parents-center distribution is adopted to reduce the risk of convergence to local optimization and enhance the stability of the algorithm. In addition, in order to increase the diversity of the population at the late stage of optimization, K-Bit-Swap (KBS) is used as a supplement for the exchange of genetic information among individuals in different dimensions. In the extensive experiments, 24 benchmarks with different dimensions are used to evaluate the performance of AIDX-GA. The results show that the proposed AIDX-GA has a significantly improved optimization effect on multidimensional optimization problems, and the stability of the algorithm is largely enhanced even when the global optimum is located near the boundary. AIDX-GA has also been evaluated in an industrial IoT case that identifies the resistance coefficients of a pipe network in the city infrastructure. The results show that the accuracy of AIDX-GA is high, and it has excellent universality and stability, which can be used to solve many IoT problems.

Optimal measurement area determination algorithm of articulated arm measuring machine based on improved FOA

The determination of the optimal measurement area of the articulated arm measuring machine belongs to the multi-dimensional function optimization problem under complex constraints. To realize high-precision measurement of low-precision articulated arm measuring machine, we analyze the working principle and error source of the measuring machine, and establish the optimization target model of the optimal measurement area in this paper. We propose a method for determining the optimal measurement area of an articulated arm measuring machine based on improved FOA. The basic FOA algorithm is improved, the historical optimal individual and population centroid information are added in the population iteration update process, and the fruit fly individuals in each iteration are directly used as the taste concentration judgment value, which increases cooperation and information sharing among fruit fly individuals, and improves the global optimization ability and stability of the algorithm. In the designated area of the measuring machine, we have carried out comparative experiments on the optimization results of improved FOA and basic FOA, ACO, PSO, AL-SC-FOA, LGMS-FOA, IPGS-FFO. Experimental results show that the improved FOA, ACO, PSO, and IPGS-FFO algorithms do not fall into local optimum, and the optimal measurement area determined by them is consistent with the optimization results of other algorithms, and is superior to other algorithms in convergence speed and stability, so it is more suitable for determining the optimal measurement area of articulated arm measuring machine.

Coverage optimization algorithm based on control nodes position in wireless sensor networks

SummaryCoverage is one of the basic problems that any wireless sensor network application must solve properly to achieve the expected quality of service. The communication distance of wireless sensor network nodes is limited, the initial energy is low, and many optimization objectives need to be considered in the deployment, which makes the network deployment optimization very complicated, and many problems are difficult. In essence, the deployment problem is a multidimensional nonlinear optimization problem with continuous discrete variables. In order to meet the needs of network monitoring, this article establishes a reasonable mathematical model according to the research objectives. By adjusting node position to obtain better network coverage effect, an optimization algorithm of monitoring area coverage based on control node position is proposed. By calculating the new location of nodes, more monitoring areas can be covered by the nodes. The simulation results show that the proposed algorithm can improve the coverage effect rapidly.

A Diagnostics of Conveyor Belt Splices

Damage detection in complex mechanical structures is important for cost-effective and safe operation. Conveyor belts with steel cords are used for bulk material transport in mining companies. Due to harsh environmental conditions, both covers and cords are subjected to damage. As lengths of conveyors may vary from dozens of meters to kilometers, a belt loop consists of many connected belt pieces. Thus, the condition of splices between belt pieces is also critical. For both steel cord damage/wear detection and splice condition evaluations the NDT techniques based on magnetic field measurement and variability analysis are used. To obtain appropriate resolution, multi-channel data are collected. Here we propose a pre-processing technique developed for signal synchronization for biased splices data. The biased splices mean a phase shift between signals from a multi-channel sensor due to the design technology of the splice. As the quality of the splice is related to the appropriate precision of splice production, splice evaluation is defined as a similarity analysis of each signal with respect to the estimated pattern. Due to the mentioned phase shift, signals should be "synchronized" first, before final analysis. In industrial conditions, many factors may influence the signal shape. Thus, the problem of automated synchronization by shifting the signals may be defined as a multidimensional optimization problem. Here, we proposed to use a genetic algorithm with an algorithmically simple cost function for that purpose. In this paper, the authors propose an automated procedure applied to real measurement data and final results. A multidimensional optimization has been compared to simple signal shifting according to several criteria, and GA-based results were the best.

Global and local optimization in identification of parabolic systems

Abstract The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder–Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.