High-dimensional Optimization Problems Research Articles

Modeling Approach of Cloud 4D Printing Service Composition Optimization Based on Non-Dominated Sorting Genetic Algorithm III

The manufacturing industry is currently experiencing a paradigm shift from traditional centralized systems to distributed, personalized, and cloud-based intelligent manufacturing ecosystems. The advent of 4-dimensional (4D) printing technology introduces dynamic characteristics to manufacturing design and functionality, necessitating the effective management of these emergent 4D printing services. This study aims to bridge the gap between the static nature of existing cloud manufacturing services and the dynamic requirements imposed by 4D printing technology. We propose a comprehensive multiobjective optimization model for cloud-based 4D printing service portfolios, incorporating the intricate complexities of 4D printing services and assessing the efficacy of the Non-Dominated Sorting Genetic Algorithm III (NSGA III) in optimizing these service portfolios to meet dynamic demands. In this research, the NSGA III algorithm is employed to develop a multiobjective optimization framework for 4D printing service portfolios, addressing critical issues such as service cost, time, quality, adaptability, and overall service optimization amidst fluctuating demand and service availability. The findings indicate that the NSGA III algorithm demonstrates superior performance in terms of generational distance (GD) and inverted generational distance (IGD), particularly excelling in convergence and diversity for high-dimensional optimization problems when compared to the comparison algorithms. The study concludes that the NSGA III algorithm exhibits significant potential in optimizing the orchestration of cloud-based 4D printing service portfolios, underscoring its effectiveness in managing the complexities associated with these services. This research provides valuable insights for the advancement of intelligent cloud-based 4D printing systems, paving the way for future developments in this field.

Revolutionizing optimization: An innovative nutcracker optimizer for single and multi-objective problems

Nutcracker Optimization Algorithm (NOA) is a recently proposed meta-heuristic algorithm inspired by foraging and storing behavior of nutcracker birds. NOA demonstrates strong performance across various test sets and optimization problems. However, it faces challenges in effectively balancing exploration and exploitation, particularly in high-dimensional and complex applications. In this paper, an improved variant of NOA based on Bernoulli map strategy and seasonal behavior strategy, called INOA, is proposed. Firstly, the Bernoulli map strategy enhances the quality of the initial population during the initialization process. Secondly, the seasonal behavior strategy is employed to balance the exploration and exploitation of NOA, enabling it to effectively handle high-dimensional problems by improving convergence and exploration capabilities. Additionally, this paper extends INOA to a multi-objective version called MONOA, enabling the algorithm to solve multi-objective problems. The proposed algorithm, INOA, undergoes evaluation using 30 classical benchmark problems, CEC-2014, CEC-2017, CEC-2019 test suites, and two real-world engineering design problems. INOA’s performance is compared with three categories of optimization methods: (1) recently-developed algorithms, i.e., NOA, BWO, DBO, RIME, MGO, HBA, and SO, (2) highly-cited algorithms, i.e., SMA, MPA, GWO, and (3) high-performing optimizers and winners of CEC competition, i.e., CJADE, L-SHADE-RSP, L-SHADE, and EBOwithCMAR. The proposed algorithm, MONOA, undergoes evaluation using well-known ZDT and DTLZ suites, as well as six constrained and engineering design problems. MONOA’s performance is compared with some state-of-the-art approaches such as MOPSO, NSSO, MOGOA, MOSMA, and MOMGA. Five performance indicators are employed for comparison purposes. Experimental results and comparisons affirm the efficacy of INOA in solving complex and higher-dimensional optimization problems. Similarly, the findings underscore the effectiveness of MONOA in solving diverse multi-objective problems with distinct characteristics.

Arctic tern-optimized weighted feature regression system for predicting bridge scour depth

This paper presents a pioneering artificial intelligence (AI) solution – the Arctic Tern-Optimized Weighted Feature Least Squares Support Vector Regression (ATO-WFLSSVR) system to aid civil engineers in accurately predicting scour depth at bridges. This prediction system amalgamates the strengths of hybrid models by uniting a metaheuristic optimization algorithm with weighted features and least squares support vector regression (WFLSSVR). The metaheuristic algorithm concurrently optimizes all hyperparameters of constituent WFLSSVR models, resulting in a highly effective system. Validation involves a comprehensive assessment using two case studies, which include datasets of scour depths across various complexities and pier foundation types. Comparative analyses against single AI models, conventional ensemble models, hybrid techniques, and empirical methods demonstrate that ATO-WFLSSVR's reliability outperforms others in performance evaluation metrics. Specifically, for the field dataset, ATO-WFLSSVR achieves MAPE and R values of 20.92% and 0.9435, respectively, and for scour depth data at complex pier foundations, it records MAPE and R values of 6.49% and 0.9384, respectively. The automated predictive analytics underscore the robustness, efficiency, and stability of ATO-WFLSSVR compared to existing methods. This study's notable contributions include the development of an innovative optimization algorithm named Arctic Terns Optimizer (ATO), proficiency in solving high-dimensional optimization problems, and the creation of a user-friendly graphical interface system, a promising tool for civil engineers to estimate scour depth at bridges. Further testing and evaluation of ATO-WFLSSVR across diverse datasets encompassing more complex scenarios are recommended. The data and source code for this study are currently accessible at https://www.researchgate.net/profile/Jui-Sheng-Chou/publications.

A rhinopithecus swarm optimization algorithm for complex optimization problem

This paper introduces a novel meta-heuristic algorithm named Rhinopithecus Swarm Optimization (RSO) to address optimization problems, particularly those involving high dimensions. The proposed algorithm is inspired by the social behaviors of different groups within the rhinopithecus swarm. RSO categorizes the swarm into mature, adolescent, and infancy individuals. Due to this division of labor, each category of individuals employs unique search methods, including vertical migration, concerted search, and mimicry. To evaluate the effectiveness of RSO, we conducted experiments using the CEC2017 test set and three constrained engineering problems. Each function in the test set was independently executed 36 times. Additionally, we used the Wilcoxon signed-rank test and the Friedman test to analyze the performance of RSO compared to eight well-known optimization algorithms: Dung Beetle Optimizer (DBO), Beluga Whale Optimization (BWO), Salp Swarm Algorithm (SSA), African Vultures Optimization Algorithm (AVOA), Whale Optimization Algorithm (WOA), Atomic Retrospective Learning Bare Bone Particle Swarm Optimization (ARBBPSO), Artificial Gorilla Troops Optimizer (GTO), and Harris Hawks Optimization (HHO). The results indicate that RSO exhibited outstanding performance on the CEC2017 test set for both 30 and 100 dimension. Moreover, RSO ranked first in both dimensions, surpassing the mean rank of the second-ranked algorithms by 7.69% and 42.85%, respectively. Across the three classical engineering design problems, RSO consistently achieves the best results. Overall, it can be concluded that RSO is particularly effective for solving high-dimensional optimization problems.

Integrating Artificial Intelligence Techniques with Computational Mathematics for Solving Complex Problems

Using Artificial Intelligence (AI) methods along with computational mathematics is changing the way that hard problems are solved in many areas. This combination of fields uses the best parts of AI, like machine learning, neural networks, and natural language processing, to make computational mathematics, which is mostly about numbers, algorithms, and statistics, more powerful. Researchers can solve difficult problems more quickly, accurately, and on a larger scale by building AI methods into computer systems. Machine learning systems, for example, can find the best answers to differential equations by guessing what will happen and finding trends in very big datasets that would be hard to process any other way. In addition, neural networks help by modeling nonlinear systems and estimating difficult functions. This makes their answers more reliable when standard methods fail. Also, AI-driven optimization methods like genetic algorithms and simulated annealing are very useful for solving high-dimensional optimization problems that come up in economics, engineering, and physics. Putting these technologies together makes it easier to create adaptable, smart systems that can learn and change in real time. This improves the way decisions are made and predictive analytics are used. AI and computer mathematics also work well together to make models more accurate in areas that need them, like biological engineering, climate modeling, and financial forecasting. This combined method not only speeds up the computing process, but it also creates new study and growth opportunities by letting people look into problems that were previously impossible to solve. AI is getting better all the time, and combining it with computational mathematics could completely change how problems are solved, leading to huge finds and progress in many fields of science and industry.

A scalable adaptive sampling approach for surrogate modeling of rigid pavements using machine learning

Rigid pavement design is a high-dimensional optimization problem, involving several variables and design considerations. The existing machine learning (ML) design models are either low-dimensional or less accurate than computational simulations. Surrogate modeling is a powerful tool for approximating the results of high-fidelity computational simulations, which is commonly used to approximate the results of these simulations by sampling their solutions to train models. However, conventional and adaptive sampling methods face the challenge of “curse of dimensionality”, due to the exponential increase in required sample size and computations with the number of variables. To overcome this, we propose a scalable adaptive sampling (SAS) method that uses random samples for testing the model's performance but generates new training samples as a subset of a full factorial design of experiments (DoE). The factorial level increases with each iteration, allowing the algorithm to sample training data at a progressively finer scale, and updating the ML models each time adaptively. The proposed method was tested on several 2D benchmark examples, as well as practical pavement design problems. Our results demonstrate that the proposed technique can develop accurate surrogate models for both low- and high-dimensional inference spaces. For a 4D inference space, the surrogate models derived from the proposed method had an order of magnitude lower error than those derived from “one-shot” conventional sampling with the same sample size. For a 6D inference space, the sample size required by the proposed method was only 5 % of that required by conventional sampling for comparable performance.

Alternating minimization for generalized rank-1 matrix sensing: sharp predictions from a random initialization

Abstract We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study the convergence properties of a natural alternating update rule for this non-convex optimization problem starting from a random initialization. We show sharp convergence guarantees for a sample-split version of the algorithm by deriving a deterministic one-step recursion that is accurate even in high-dimensional problems. Notably, while the infinite-sample population update is uninformative and suggests exact recovery in a single step, the algorithm—and our deterministic one-step prediction—converges geometrically fast from a random initialization. Our sharp, non-asymptotic analysis also exposes several other fine-grained properties of this problem, including how the nonlinearity and noise level affect convergence behaviour. On a technical level, our results are enabled by showing that the empirical error recursion can be predicted by our deterministic one-step updates within fluctuations of the order $n^{-1/2}$ when each iteration is run with $n$ observations. Our technique leverages leave-one-out tools originating in the literature on high-dimensional $M$-estimation and provides an avenue for sharply analyzing complex iterative algorithms from a random initialization in other high-dimensional optimization problems with random data.

A sequence decomposition genetic algorithm for petrophysical inversion with spatial correlation

Predicting petrophysical properties based on seismic attributes is essential for accurate subsurface characterization. Typically, a forward model is first established to relate the petrophysical properties to geophysical measurements, and then the petrophysical properties are inverted from the actual measurements. Imposing prior constraints of the spatial relationship is also desirable to regularize the ill-posed inverse problem. However, petrophysical inversion involving spatial correlation presents a high-dimensional optimization problem with multiple local extrema. This problem can be challenging to solve, particularly when discrete variables (such as lithofacies) and continuous variables (such as porosity and fluid saturation) are considered together. Therefore, we develop a global optimization algorithm that uses the Markov chain decomposition and a genetic algorithm for a joint discrete-continuous petrophysical inversion with spatial correlation. The innovation of this algorithm is to spatially decouple the sequence optimization problem into multiple low-dimensional subproblems and overcome the initial value dependence to converge to the global optimal solution. Furthermore, an approximation operation is introduced to expedite the optimization algorithm. Numerical experiments show that after algorithmic acceleration, the spatially correlated inversion requires the same computational time as a simple spatially uncorrelated inversion and achieves significantly better accuracy than the latter. Finally, we apply the method to a case study in East China, wherein the lithofacies, clay content, porosity, and water saturation are inferred from the data of the wave velocities and density. The inversion results around the wells generally match the well-logging data, verifying the feasibility of the new method.

Taking another step: A simple approach to high-dimensional Bayesian optimization

Scaling Bayesian optimization to high-dimensional problems is a meaningful but challenging task. Most of current approaches assume only a few variables are effective to the objective function or the objective function is additively separable, therefore are not suitable when the problem violates these assumptions. In this work, we propose a simple and efficient approach to extend Bayesian optimization to high dimensions. The proposed approach does not make these two assumptions. In each iteration, after locating a candidate point by the global Gaussian process model, we train a local Gaussian process model around the candidate point and locate a new point using the local model. Instead of evaluating the solution located by the global model, we evaluate the solution located by the local model. This simple taking-another-step approach is shown to be able to improve Bayesian optimization's performance significantly on high-dimensional optimization problems. The proposed algorithm also shows competitive performance when compared with four high-dimensional Bayesian optimization algorithms and four surrogate-assisted evolutionary algorithms.

A Sampling Strategy for High-Dimensional, Simulation-Based Transportation Optimization Problems

When tackling high-dimensional, continuous simulation-based optimization (SO) problems, it is important to balance exploration and exploitation. Most past SO research focuses on the enhancement of exploitation techniques. The exploration technique of an SO algorithm is often defined as a general-purpose sampling distribution, such as the uniform distribution, which is inefficient at searching high-dimensional spaces. This work is motivated by the formulation of exploration techniques that are suitable for large-scale transportation network problems and high-dimensional optimization problems. We formulate a sampling mechanism that combines inverse cumulative distribution function sampling with problem-specific structural information of the underlying transportation problem. The proposed sampling distribution assigns greater sampling probability to points with better expected performance as defined by an analytical network model. Validation experiments on a toy network illustrate that the proposed sampling distribution has important commonalities with the underlying and typically unknown true sampling distribution of the simulator. We study a high-dimensional traffic signal control case study of Midtown Manhattan in New York City. The results show that the use of the proposed sampling mechanism as part of an SO framework can help to efficiently identify solutions with good performance. Using the analytical information for exploration, regardless of whether it is used for exploitation, outperforms benchmarks that do not use it, including standard Bayesian optimization. Using the analytical information for exploration only yields solutions with similar performance than when the information is used for exploitation only, reducing the total compute times by 65%. This paper sheds light on the importance of developing suitable exploration techniques to enhance both the scalability and the compute efficiency of general-purpose SO algorithms. Funding: T. Tay thanks the Agency for Science, Technology and Research (A*STAR) Singapore for funding his work. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0110 .

An improved golden jackal optimization algorithm for combined economic emission dispatch problems

In this research paper, a new improved golden jackal optimization (IGJO) algorithm is applied to address the combined economic emission dispatch (CEED) problem, along with various thermal generator constraints such as valve point loading (VPL) effect, generator limits (GL) in power system. The hunting behavior of the golden jackals is mimicked in the golden jackal optimization (GJO) algorithm. The main aim of the CEED problem is to find the best optimal generation scheduling while minimizing both fuel cost and emission besides meeting the different power system constraints. The original GJO algorithm faces challenges when dealing with high-dimensional optimization problems, as it tends to get trapped in local optima. To address this issue the opposition-based learning (OBL) method was adopted in this GJO algorithm to obtain the global optimal solution and ensure enhanced performance in finding the solution for the CEED problems. To assess the competitiveness of the IGJO algorithm, it is used for various CEED test problems available in the literature, and results are contrasted with other recent heuristic optimization algorithms. Simulation results show that the proposed IGJO performs more effectively than the other compared algorithms in terms of solution quality, and robustness.

An enhanced sparrow search swarm optimizer via multi-strategies for high-dimensional optimization problems

With the development of science and technology, high-dimensional global optimization problems have become increasingly prevalent for scientific research and engineering, such as gene recognition, vehicle routing, job scheduling, and network topology. These problems are typically characterized by enormous and complex search spaces and numerous local minima, making it challenging to find the global optimal solution with limited computing resources. This paper introduces an enhanced sparrow search swarm optimizer (ESSSO) based on a bio-mimetic method. The ESSSO employs an adaptive sinusoidal walk strategy based on the von Mises distribution, a learning strategy utilizing roulette wheel selection, a two-stage evolution strategy, and a selection mutation strategy to address these issues. The proposed sinusoidal walk strategy, grounded in the von Mises distribution, supports a balanced evolutionary search. This mechanism disperses the individuals in a swarm in various directions based on a circular normal distribution. It then leads the search and adaptively adjusts their step sizes according to the size of the search domain during each generation of evolution. The learning strategy, based on roulette wheel selection, enhances the diversity of the population and improves the global search capability of the algorithm during the initial iterations. The two-stage evolution strategy involves a sine-learning mechanism based on the von Mises distribution and an adaptive mutation mechanism. The former is designed to boost the convergence speed of ESSSO, while the latter prevents ESSSO from getting trapped in a local optimum. Additionally, the selection mutation strategy further enhances convergence speed while maintaining population diversity. These strategies promote exploration in the early stages of evolution and exploitation in the later stages, enabling a well-balanced search for optimal solutions. We conducted comprehensive experiments two standard benchmark sets (i.e., CEC2010 and CEC2013), antenna array optimization, feature selection, and four engineering design problems. The results indicate that ESSSO outperforms ten comparison algorithms, especially in scenarios with smaller population sizes. This confirms its effectiveness in high-dimensional global optimization tasks and demonstrates that it can achieve better results with less computational resource consumption.

Optimal annuitisation, housing and reverse mortgage in retirement in the presence of a means-tested public pension

AbstractIn this paper we develop a model to find optimal decisions in retirement with respect to the consumption, risky asset allocation, access to annuities, reverse mortgage and the option to scale housing in the presence of a means-tested public pension. To solve the corresponding high-dimensional optimal stochastic control problem, we use the Least-Squares Monte Carlo simulation method. The model is applied in the context of the Australian retirement system. Few retirees in Australia utilise financial products in retirement, such as annuities or reverse mortgages. Since the government-provided means-tested Age Pension in Australia is an indirect annuity stream which is typically higher than the consumption floor, it can be argued that this could be the reason why many Australians do not annuitise. In addition, in Australia where assets allocated to the family home are not included in the means tests of Age Pension, the incentive to over-allocate wealth into housing assets is high. This raises the question whether a retiree is really better off over-allocating into the family home, while accessing home equity later on either via downsizing housing or by taking out a reverse mortgage. Our findings confirm that means-tested pension crowds out voluntary annuitisation in retirement, and that annuitisation is optimal sooner rather than later once retired. We find that it is never optimal to downscale housing when the means-tested pension and a reverse mortgage are available; only when there is no other way to access equity then downsizing is the only option.

Handling the balance of operators in evolutionary algorithms through a weighted Hill Climbing approach

Evolutionary Algorithms (EAs) are a well-known domain within Artificial Intelligence. EAs have demonstrated their ability to tackle intricate optimization problems using evolutionary theory principles. However, balancing the dual exploration and exploitation processes remains a crucial concern. This paper introduces the Balanced Hill Climbing Weight Algorithm with Diversity (BHWEAD), an innovative approach that combines elements from classic Genetic Algorithm and Differential Evolution. BHWEAD uniquely employs the Hill Climbing local search to guide the influence of its operators, ensuring an optimal interplay between exploration and exploitation. Additionally, it incorporates a diversity control mechanism, resetting specific solutions to prevent premature convergence to suboptimal solutions. The main contribution of the BHWEAD is the mechanism that permits the balance of the exploration and exploitation stages; also, the incorporation of Hill Climbing permits a proper balance of the influence of the operators. Notice that the proposal can escape from suboptimal solutions using a diversity-based strategy. Tested against the CEC2017 benchmark functions in both 50 and 100 dimensions, BHWEAD outperformed 12 notable EAs, underscoring its potential for high-dimensional optimization problems. Besides, the proposed BHWEAD has also been tested over seven engineering problems, and the comparisons include some memetic algorithms., The paper provides additional insights into the algorithm’s design, conducts a comparative analysis, and identifies potential areas for improvement.

A novel hippo swarm optimization: for solving high-dimensional problems and engineering design problems

Abstract In recent years, scholars have developed and enhanced optimization algorithms to tackle high-dimensional optimization and engineering challenges. The primary challenge of high-dimensional optimization lies in striking a balance between exploring a wide search space and focusing on specific regions. Meanwhile, engineering design problems are intricate and come with various constraints. This research introduces a novel approach called Hippo Swarm Optimization (HSO), inspired by the behavior of hippos, designed to address high-dimensional optimization problems and real-world engineering challenges. HSO encompasses four distinct search strategies based on the behavior of hippos in different scenarios: starvation search, alpha search, margination, and competition. To assess the effectiveness of HSO, we conducted experiments using the CEC2017 test set, featuring the highest dimensional problems, CEC2022 and four constrained engineering problems. In parallel, we employed 14 established optimization algorithms as a control group. The experimental outcomes reveal that HSO outperforms the 14 well-known optimization algorithms, achieving first average ranking out of them in CEC2017 and CEC2022. Across the four classical engineering design problems, HSO consistently delivers the best results. These results substantiate HSO as a highly effective optimization algorithm for both high-dimensional optimization and engineering challenges.

Study on the constraint handling method for high-dimensional optimization of cascade reservoirs

Multicomplex constraints often need to be considered in the optimal operation of cascade reservoirs with high-dimensional decision variables, making it difficult for traditional optimization methods and modern intelligent algorithms to solve such problems. Therefore, this study proposes a constraint handling method combining a penalty function nested DPSA-POA and an intelligent algorithm, to determine the optimal flood control operation of cascade reservoirs in the middle reaches of the Ganjiang River, a problem with decision variables of up to 2196 dimensions. The results indicate that the constraint handling method proposed in this paper can solve high-dimensional optimization problems in three modes: continuous nesting (Mode 1), optimization with intelligence after obtaining a feasible solution (Mode 2), and optimization with the DPSA-POA after obtaining a feasible solution (Mode 3). Of the three modes, Mode 2 has the highest accuracy, but its calculation time is approximately 10 h. Although the accuracy of Mode 3 is slightly worse, can only achieve 98%–99% of Mode 2, its calculation time is only approximately 1–3 h. The comprehensive performance of Mode 1 is poor, the convergence accuracy can only reach 97% of Mode 2, which corresponds to a calculation time of approximately 4–6 h. The existing superiority of feasibility (SF), stochastic ranking (SR), penalty function (PF), ε-constraint (EC) and adaptive ε-constraint (Adaptive EC) methods cannot converge to a feasible solution stably, and the accuracy of the results of these methods under the condition of obtaining a feasible solution is significantly lower than that of Mode 2 and Mode 3, reaching only 95%.

Fireworks algorithm with elitism-based selection strategy and optimal particle guidance mechanism

With the increasing complexity and difficulty of numerical optimization problems in the real world, many efficient meta-heuristic optimization methods have been proposed to solve these problems. An improved Fireworks Algorithm (FWA) with elitism-based selection and optimal particle guidance strategies (EO-FWA) was proposed to address the limitations of the traditional FWA in terms of optimization accuracy and convergence speed, which not only improves the efficiency of the searching agent but also accelerates its convergence speed. In addition, by adopting boundary-based mapping rules, EO-FWA eliminates the randomness of traditional modulo operation mapping rules, which improves its stability and reliability. Twelve benchmark functions in CEC-BC-2022 are used to test the performance of EO-FWA, and the welded beam design problem is optimized at the end. The results show that EO-FWA exhibits stronger competitiveness than other algorithms in dealing with high-dimensional optimization problems and engineering optimization problem, and it can balance exploitation and exploration effectively so as to prevent the algorithm from falling into local optimal solutions.

An Improved Cuckoo Search Algorithm for Maximizing the Coverage Range of Wireless Sensor Networks

The issue of increasing the range covered by a wireless sensor network with restricted sensors is addressed utilizing improved CS employing the PSO algorithm and opposition-based learning (ICS-PSO-OBL). At first, the iteration is carried out by updating the old solution dimension by dimension to achieve independent updating across the dimensions in the high-dimensional optimization problem. The PSO operator is then incorporated to lessen the preference random walk stage's imbalance between exploration and exploitation ability. Exceptional individuals are selected from the population using OBL to boost the chance of finding the optimal solution based on the fitness value. The ICS-PSO-OBL is used to maximize coverage in WSN by converting regional monitoring into point monitoring utilizing the discretization method in WSN. In the experiments, the ICS-PSO-OBL with the standard CS and three CS variants (MACS, ICS-2, and ICS) are utilized to execute the simulation experiment under different numbers of nodes (20 and 30, respectively). The experimental results reveal that the optimized coverage of ICS-PSO-OBL is 18.36%, 7.894%, 15%, and 9.02% higher than that of standard CS, MACS, ICS-2, and ICS when the number of nodes is 20. Moreover, it is 16.94%, 9.61%, 12.27%, and 7.75% higher when the quantity of nodes is 30, the convergence speed of ICS-PSO-OBL, and the distribution of nodes is superior to others.

Enhancing security for physical layer communication in RIS-aided MIMO-NOMA systems in the presence of an eavesdropper

This paper investigates the potential of leveraging a reconfigurable intelligent surface (RIS) in the multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) wireless communication systems. In fact, NOMA improves spectral efficiency (SE) through power domain utilization, and RIS enhances the system performance by manipulating the propagation environment. In this paper, we investigate the physical layer security (PLS) of a RIS-aided MIMO-NOMA system serving two users in the presence of an eavesdropper (EV), where the channel state information (CSI) of the EV is unknown for the BS. To address the security challenge, we utilize secrecy outage probability (SOP) and minimize it by optimizing the RIS’s phase shift matrix, the beamforming vector, and the power allocation coefficients. Due to the non-convexity of the main optimization problem, we decompose the initial problem into three subproblems, and then, we propose an iterative approach to determine the unknown parameters alternately. The first subproblem involves obtaining the optimal beamforming vector and phase shift matrix using the semidefinite relaxation (SDR) method, which introduces high complexity. As an alternative, another algorithm is proposed based on the duality of the optimization problem, offering lower complexity and better accuracy for high-dimensional optimization problems. In this algorithm, the successive convex approximation (SCA) technique is employed to achieve the optimum phase shift matrix, and the stochastic gradient (SG) approach is used to determine the beamforming vector. Furthermore, the paper establishes the optimal values of power allocation coefficients by minimizing the difference between the SOPs of the two users. Finally, the simulation results demonstrate that the proposed power allocation coefficients scheme significantly enhances system performance compared to the existing fixed power allocation coefficients scheme.

An improved optimization method combining particle swarm optimization and dimension reduction kriging surrogate model for high-dimensional optimization problems

An improved optimization method is proposed which combines the particle swarm optimization (PSO) algorithm with the dimension reduction kriging surrogate model (DK), namely PSO + DK. In this method, a surrogate model is dynamically constructed and updated between the lower dimensional principal components and the response, instead of between the high-dimensional design variables and the response as in traditional methods. The key point of DK is that the principal components analysis (PCA) is integrated with the active learning kriging surrogate model (AK). Since PCA can reduce the dimension effectively, DK makes surrogate model construction possible for complex high-dimensional optimization problems. Numerical examples and four classical engineering problems are presented to validate the effectiveness of the proposed method. The results show that the proposed method can decrease the computational cost significantly while guaranteeing the precision compared with PSO and PSO + AK for high-dimensional optimization problems.