High-dimensional Optimization Problems Research Articles

A velocity-based butterfly optimization algorithm for high-dimensional optimization and feature selection

Throughout the last decade, high-dimensional function optimization problems have received substantial research interest in the field of intelligence computation. Butterfly optimization algorithm is a new meta-heuristic technique that has been proven to be more competitive than other optimization methods on low- dimensional problems. The basic butterfly optimization algorithm and its variants are not used to solve high-dimensional problems. Therefore, this paper develops an improved version of butterfly optimization algorithm to deal with the high- dimensional optimization problems. Inspired by particle swarm optimization, a modified position updated equation is designed by introducing velocity item and memory item in the local search phase to guide the search for candidate individuals. Moreover, a novel refraction-based learning strategy is introduced into butterfly optimization algorithm to effectively enhance diversity and exploration. The effectiveness of the proposed algorithm is tested on 40 benchmark problems with 100, 1000, 10,000 dimensions. The statistical results show that our algorithm has better performance than the basic butterfly optimization algorithm, its variants, and other population-based approaches to deal with the high-dimensional optimization problems. Finally, the high-dimensional feature selection and fault identification of wind turbine problems are solved and the comparisons show that the proposed algorithm outperforms better than most methods in terms of classification accuracy and number of the optimal feature subset.

Machine learning with knowledge constraints for process optimization of open-air perovskite solar cell manufacturing

Machine learning with knowledge constraints for process optimization of open-air perovskite solar cell manufacturing

An Improved particle swarm optimization based on lévy flight and simulated annealing for high dimensional optimization problem

Particle swarm optimization (PSO) is a simple metaheuristic method to implement with robust performance. PSO is regarded as one of the numerous researchers' most well-studied algorithms. However, two of its most fundamental problems remain unresolved. PSO converges onto the local optimum for high-dimensional optimization problems, and it has slow convergence speeds. This paper introduces a new variant of a particle swarm optimization algorithm utilizing Lévy flight-McCulloch, and fast simulated annealing (PSOLFS). The proposed algorithm uses two strategies to address high-dimensional problems: hybrid PSO to define the global search area and fast simulated annealing to refine the visited search region. In this paper, PSOLFS is designed based on a balance between exploration and exploitation. We evaluated the algorithm on 16 benchmark functions for 500 and 1,000 dimension experiments. On 500 dimensions, the algorithm obtains the optimal value on 14 out of 16 functions. On 1,000 dimensions, the algorithm obtains the optimal value on eight benchmark functions and is close to optimal on four others. We also compared PSOLFS with another five PSO variants regarding convergence accuracy and speed. The results demonstrated higher accuracy and faster convergence speed than other PSO variants. Moreover, the results of the Wilcoxon test show a significant difference between PSOLFS and the other PSO variants. Our experiments' findings show that the proposed method enhances the standard PSO by avoiding the local optimum and improving the convergence speed.

A Dimension Group-Based Comprehensive Elite Learning Swarm Optimizer for Large-Scale Optimization

High-dimensional optimization problems are more and more common in the era of big data and the Internet of things (IoT), which seriously challenge the optimization performance of existing optimizers. To solve these kinds of problems effectively, this paper devises a dimension group-based comprehensive elite learning swarm optimizer (DGCELSO) by integrating valuable evolutionary information in different elite particles in the swarm to guide the updating of inferior ones. Specifically, the swarm is first separated into two exclusive sets, namely the elite set (ES) containing the top best individuals, and the non-elite set (NES), consisting of the remaining individuals. Then, the dimensions of each particle in NES are randomly divided into several groups with equal sizes. Subsequently, each dimension group of each non-elite particle is guided by two different elites randomly selected from ES. In this way, each non-elite particle in NES is comprehensively guided by multiple elite particles in ES. Therefore, not only could high diversity be maintained, but fast convergence is also likely guaranteed. To alleviate the sensitivity of DGCELSO to the associated parameters, we further devise dynamic adjustment strategies to change the parameter settings during the evolution. With the above mechanisms, DGCELSO is expected to explore and exploit the solution space properly to find the optimum solutions for optimization problems. Extensive experiments conducted on two commonly used large-scale benchmark problem sets demonstrate that DGCELSO achieves highly competitive or even much better performance than several state-of-the-art large-scale optimizers.

Research on Forecast of Macroeconomic Indicators Based on Multiobjective Optimization

In recent years, with China’s economic development entering a new normal, the total scale and complexity of economic development have increased unprecedentedly, and the requirements of government management and regulation of the economy are getting higher and higher. Traditional management concepts, methods, and tools are difficult to meet the needs of the new situation. Therefore, using computer science and technology to fully consider the correlation between various industries and explore new laws of economic operation under the new normal can provide new technical support for promoting the precision of government governance. In previous studies, Most of them take statistics and econometrics as the theoretical basis of macroeconomic decision-making research. This study is based on the analysis of the relationship between the macroeconomic indicators, the establishment of forecasting models to predict the trend of the macroeconomic indicators, and according to the relationship between various economic indicators to build a multiobjective optimization problem, through the multiobjective optimization algorithm to obtain optimal data for the government decision-making basis. In the research process, we focus on solving the problem of prediction overfitting caused by small samples of economic index data and high feature dimension of samples and how to balance the convergence and diversity of solution set in high-dimensional multiobjective optimization problems. In view of the above problems, we propose two economic index forecasting models to solve a variety of fitting problems. On the premise of optimizing space decomposition, an adaptive generation strategy based on inflection point and center point is proposed, and an adaptive solution set selection strategy based on included angle, inflection point, and strong dominance relationship is proposed to balance the convergence and diversity of the multiobjective optimization algorithm.

A dynamic stochastic search algorithm for high-dimensional optimization problems and its application to feature selection

As the number of dimensions of an optimization problem increases, the process of deriving the solution becomes more complicated and difficult. Metaheuristic algorithms are effective methods for solving many optimization problems, whereas most of these algorithms perform poorly on high-dimensional problems. In this paper, a novel metaheuristic algorithm called Dynamic Stochastic Search (DSS) is proposed for high-dimensional optimization problems. To effectively execute the exploration (diversification) and exploitation (intensification) processes of DSS, a dynamic stochastic search process is designed by defining a stochastic search control factor, a search process based on the Gaussian distribution, two shrink modes inspired by the Whale Optimization Algorithm, and a balance mechanism derived from the Bat Algorithm. The proposed algorithm has the following advantages: no specific control parameters other than the population size and the maximum number of iterations, a simple structure, and less computational effort in the implementation. Analyzing the computational complexity of DSS demonstrates its simplicity. To evaluate the performance of DSS, twenty 300-dimensional and 3000-dimensional classical benchmark functions as well as thirty 100-dimensional CEC2014 benchmark functions are utilized. The statistical results prove the effectiveness and feasibility of DSS for high-dimensional optimization problems because it shows better convergence performance and higher efficiency than various advanced optimization algorithms. Moreover, the superiority of DSS in solving high-dimensional real-world optimization problems is validated by applying it to feature selection for ten real-world benchmark classification datasets from the UCI machine learning repository.

Common defects in diamond lattices as instances of the general T ⊗ (e+t2) Jahn-Teller effect

Finding the ground-state configuration of point defects in semiconductors is in general a high-dimensional optimization problem. However, their adiabatic potential energy surfaces (APES) can be described with few effective coordinates by exploiting symmetry arguments within the Jahn-Teller (JT) theoretical framework. In this paper, we propose a general framework, that combines group theory and ab initio calculations, to build a full picture of common defects in diamond lattices (vacancies and substitutional impurities) as instances of the general T $\ensuremath{\bigotimes}\phantom{\rule{4pt}{0ex}}(e+{t}_{2})$ APES. Starting from the original tetrahedral symmetry, we consider all possible JT symmetries and we numerically investigate the shape of the APES by targeting the minimum energy path between equivalent JT distortions taking as examples the vacancy (V) and the metallic impurities Pd, Pt, and Au in crystalline silicon.

A Multipopulation Dynamic Adaptive Coevolutionary Strategy for Large-Scale Complex Optimization Problems.

In this paper, a multipopulation dynamic adaptive coevolutionary strategy is proposed for large-scale optimization problems, which can dynamically and adaptively adjust the connection between population particles according to the optimization problem characteristics. Based on analysis of the network evolution characteristics of collaborative search between particles, a dynamic adaptive evolutionary network (DAEN) model with multiple interconnection couplings is established in this algorithm. In the model, the swarm type is divided according to the judgment threshold of particle types, and the dynamic evolution of collaborative topology in the evolutionary process is adaptively completed according to the coupling connection strength between different particle types, which enhances the algorithm’s global and local searching capability and optimization accuracy. Based on that, the evolution rules of the particle swarm dynamic cooperative search network were established, the search algorithm was designed, and the adaptive coevolution between particles in different optimization environments was achieved. Simulation results revealed that the proposed algorithm exhibited a high optimization accuracy and converging rate for high-dimensional and large-scale complex optimization problems.

Adaptive backtracking search optimization algorithm with a dual-learning strategy for dynamic economic dispatch with valve-point effects

Dynamic economic dispatch with valve-point effect (DED_vpe) is a dynamic nonlinear high-dimensional optimization problem with non-smooth and non-convex characteristics. Meta-heuristic methods have become the mainstream for solving the DED_vpe problem. However, most of these methods only focus on minimizing the generation costs and ignore the algorithmic robustness. In this paper, an adaptive backtracking search optimization algorithm with a dual-learning strategy (DABSA) is proposed for solving the DED_vpe problem. In DABSA, a dual-learning strategy (DL) based on the current and historical optimal individuals is developed to update each individual. This updating strategy helps DABSA improve solution accuracy and overcome premature convergence. In addition, an adaptive parameter control mechanism (APC), which can automatically adjust parameter ‘mixrate’ value according to the current iteration number, is presented. To handle the system constraints, a ‘repair + penalty’ constraints-handling approach is employed to lead non-feasible solutions towards the feasible region quickly. The performance of DABSA is assessed by testing on four DED problems containing 5, 10 and 30 units. The experimental results show that DABSA is very competitive compared with reported representative methods in yielding low fuel costs along with high robustness.

Transmit-Receive Beamforming for Distributed Phased-MIMO Radar System

Distributed phased Multiple-Input Multiple-Output (phased-MIMO) radar system consisting of separated subarrays possesses a high angle resolution but with sharing high sidelobes. This paper therefore focuses on the design of a virtual low-sidelobe beampattern in distributed phased-MIMO radar. An iterative framework with respect to subarray layout and receive weighting coefficients is proposed to minimize beampattern Peak Sidelobe Level (PSL) accounting for practical position constraints as well as the mainlobe level restriction. In each iteration, an efficient cyclic optimization algorithm based on the Coordinate Descent (CD) framework is developed to seek for the subarray layout through splitting high dimensional layout optimization problem into multiple one-dimensional optimization problems, and the SemiDefinite Relaxation (SDR) technique and rank one approximation are explored to design weighting coefficients. Numerical simulations are provided to assess the performance of the proposed algorithms in term of the achieved beampattern under different constraints and parameter settings.

Wavefront shaping with a Hadamard basis for scattering soil imaging.

Soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.

Differential evolution-assisted salp swarm algorithm with chaotic structure for real-world problems.

There is a new nature-inspired algorithm called salp swarm algorithm (SSA), due to its simple framework, it has been widely used in many fields. But when handling some complicated optimization problems, especially the multimodal and high-dimensional optimization problems, SSA will probably have difficulties in convergence performance or dropping into the local optimum. To mitigate these problems, this paper presents a chaotic SSA with differential evolution (CDESSA). In the proposed framework, chaotic initialization and differential evolution are introduced to enrich the convergence speed and accuracy of SSA. Chaotic initialization is utilized to produce a better initial population aim at locating a better global optimal. At the same time, differential evolution is used to build up the search capability of each agent and improve the sense of balance of global search and intensification of SSA. These mechanisms collaborate to boost SSA in accelerating convergence activity. Finally, a series of experiments are carried out to test the performance of CDESSA. Firstly, IEEE CEC2014 competition fuctions are adopted to evaluate the ability of CDESSA in working out the real-parameter optimization problems. The proposed CDESSA is adopted to deal with feature selection (FS) problems, then five constrained engineering optimization problems are also adopted to evaluate the property of CDESSA in dealing with real engineering scenarios. Experimental results reveal that the proposed CDESSA method performs significantly better than the original SSA and other compared methods.

Hierarchical Multi-Objective Optimization of Automobile Seat Frame Based on Grey Fuzzy Logic System

In development of the automobile industry, lightweight and safety performance are contradictory, yet they are of great significance.The optimization process of auto parts is a high-dimensional optimization problem which has a variety of regulations limits and safety tests at the same time. In order to address this issue, hierarchical multi-objective optimization of a passenger car seat frame is carried out in this research. Different from previous researches, in this paper, all car seat frame parts are listed as the optimization objects and are given different optimized attributes. Meanwhile, in order to achieve the goal of effectively reducing the sample sizes of the design of experiments, hierarchical optimization is proposed, and the optimization process is divided into three stages. In each stage, components with different optimized attributes are introduced into various safety tests and then conducting design of experiments. On the other hand, through adopting the grey fuzzy logic system to assign the appropriate optimized grade, the optimization process is simplified and the errors caused by the manual selection or unified optimization levels are avoided. The proposed method is considered to be an universal approach to solve the lightweight optimization of the auto parts. Design parameters of the car seat frame before and after the hierarchical multi-objective optimization are compared, it illustrated that total mass and material cost of the seat frame are reduced by 2.3kg (28.5%) and ¥ 13.8 (32.4%) respectively. Moreover, various comparisons are carried out to verify the validity of the optimization method proposed in this paper. In conclusion, the proposed method is quite promising yet with less sample points associated, is an effective mean to solve the multi-objective optimization problems of automobile component.

Global Aerodynamic Topology Optimization using Dimensionality Reduction Methods

In recent years, topology optimizations have attracted attention as advanced optimization methods with higher degree of freedom to represent various topologies. These methods can automatically propose innovative/optimal topologies. Therefore, the topology optimization can be an efficient tool to extract innovative design insights. In general, the topology optimizations become high-dimensional optimization problems. This increases the possibility to represent optimal topologies, while requires a large number of performance evaluations to solve the optimization problems. In this study, we investigate the introduction of dimensionality reduction methods that can replace a high-dimensional design space with a low-dimensional design space in order to reduce the computational cost to solve the topology optimization problems. Proper orthogonal decomposition and active subspace method are considered as the dimensionality reduction methods in this study. As a result, it is confirmed that the computational cost can be reduced by using the dimensionality reduction methods.

Distributed Model Predictive Coordinated Control for Combined Heat and Power Load of an Integrated Energy System

Due to the strong coupling and multiple constraints of combined heat and power (CHP) generation in an integrated energy system (IES), the model predictive control (MPC) is widely adopted as the lower layer coordination controller. However, with the upgrade of capacity and the expansion of scale, centralized MPC (CMPC) is no longer capable of dealing with heavy-data, high dimensional IES optimization problem. To address this concern, distributed MPC (DMPC) is applied to coordinate the energy supply of CHP-IES. In view of the characteristics of CHP-IES, DMPC should be endowed with the capability of offset-free tracking and disturbance rejection. Hence, the disturbance augmentation method and the modification of objective function have been applied to facilitate each DMPC controller with the required abilities. Through simulation comparison with CMPC on the same theoretical model, the performance of modified cooperative DMPC (CDMPC) is on par with CMPC, while the computational burden is drastically relieved.

Машинное обучение с подкреплением для решения задач математического программирования

This paper discusses modern approaches to finding rational solutions in problems of mixed integer linear programming, both generated with random data and from real practice. The main emphasis is on how to implement the process of finding a solution to discrete optimization problems using the concept of reinforcement learning; what techniques can be applied to improve the speed and quality of work. Three main variants of the algorithm were developed using the Ray library API, as well as the environment - the Gym library. The results of the developed solver are compared with the OR-Tools library. The best model can be used as a solver for high-dimensional optimization problems, in addition, this concept is applicable to other combinatorial problems with a change in the environment code and the intelligent agent algorithm.

An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Recent years witness a great deal of interest in artificial intelligence (AI) tools in the area of optimization. AI has developed a large number of tools to solve the most difficult search-and-optimization problems in computer science and operations research. Indeed, metaheuristic-based algorithms are a sub-field of AI. This study presents the use of the metaheuristic algorithm, that is, water cycle algorithm (WCA), in the transportation problem. A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull distribution. Since the parameters are stochastic, the corresponding constraints are probabilistic. They are converted into deterministic constraints using the stochastic programming approach. In this study, we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization problems. WCA is influenced by the water cycle process of how streams and rivers flow toward the sea (optimal solution). WCA is applied to the stochastic transportation problem, and obtained results are compared with that of the new metaheuristic optimization algorithm, namely the neural network algorithm which is inspired by the biological nervous system. It is concluded that WCA presents better results when compared with the neural network algorithm.

Algorithm-Driven Advances for Scientific CT Instruments: From model-based to deep learning-based approaches

Multi-scale 3D characterization is widely used by materials scientists to further their understanding of the relationships between microscopic structure and macroscopic function. Scientific computed tomography (CT) instruments are one of the most popular choices for 3D non-destructive characterization of materials at length scales ranging from the angstrom-scale to the micron-scale. These instruments typically have a source of radiation that interacts with the sample to be studied and a detector assembly to capture the result of this interaction. A collection of such high-resolution measurements are made by re-orienting the sample which is mounted on a specially designed stage/holder after which reconstruction algorithms are used to produce the final 3D volume of interest. The end goal of scientific CT scans include determining the morphology,chemical composition or dynamic behavior of materials when subjected to external stimuli. In this article, we will present an overview of recent advances in reconstruction algorithms that have enabled significant improvements in the performance of scientific CT instruments - enabling faster, more accurate and novel imaging capabilities. In the first part, we will focus on model-based image reconstruction algorithms that formulate the inversion as solving a high-dimensional optimization problem involving a data-fidelity term and a regularization term. In the last part of the article, we will present an overview of recent approaches using deep-learning based algorithms for improving scientific CT instruments.

A Dual Biogeography-Based Optimization Algorithm for Solving High-Dimensional Global Optimization Problems and Engineering Design Problems

Biogeography-based optimization (BBO) cannot effectively solve high-dimensional global optimization problems due to its single migration mechanism and random mutation operator. To overcome these limitations, this paper propose a dual BBO based on sine cosine algorithm (SCA) and dynamic hybrid mutation, named SCBBO. Firstly, the Latin hypercube sampling method is innovatively used to improve the initial population ergodicity. Secondly, a nonlinear transformation parameter and a inertia weight adjustment factor are designed into the position update formula of SCA to make SCBBO suitable for high dimensional environments. Then, a dynamic hybrid mutation operator is designed by combining Laplacian and Gaussian mutation, which helps the algorithm to escape from local optima and balance the exploration and exploitation. Finally, the dual learning strategy is integrated, so the convergence accuracy is further improved by generating dual individuals. Meanwhile, A sequence convergence model is established to prove the algorithm can converge to the global optimal solution with probability 1. Compared with other state-of-the-art evolutionary algorithms, SCBBO effectively improves the optimization accuracy and convergence speed for high-dimensional optimization problems. To further show the superiority of SCBBO, the performance is compared on 1000, 2000, 5000 and 10000 dimensions, respectively. The comparsions show that SCBBO’s optimization results on these dimensions are basically the same. SCBBO also applied to engineering design problems, and the simulation results demonstrate that the proposed method is also effective on constrained optimization problems.

A Multimodal Improved Particle Swarm Optimization for High Dimensional Problems in Electromagnetic Devices

Particle Swarm Optimization (PSO) is a member of the swarm intelligence-based on a metaheuristic approach which is inspired by the natural deeds of bird flocking and fish schooling. In comparison to other traditional methods, the model of PSO is widely recognized as a simple algorithm and easy to implement. However, the traditional PSO’s have two primary issues: premature convergence and loss of diversity. These problems arise at the latter stages of the evolution process when dealing with high-dimensional, complex and electromagnetic inverse problems. To address these types of issues in the PSO approach, we proposed an Improved PSO (IPSO) which employs a dynamic control parameter as well as an adaptive mutation mechanism. The main proposal of the novel adaptive mutation operator is to prevent the diversity loss of the optimization process while the dynamic factor comprises the balance between exploration and exploitation in the search domain. The experimental outcomes achieved by solving complicated and extremely high-dimensional optimization problems were also validated on superconducting magnetic energy storage devices (SMES). According to numerical and experimental analysis, the IPSO delivers a better optimal solution than the other solutions described, particularly in the early computational evaluation of the generation.