High-dimensional Optimization Problems Research Articles

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.

Performance Analysis of Immune Plasma Algorithm with Different Donor-Receiver Configurations

Immune Plasma Algorithm (IPA) is a novel meta-heuristic algorithm inspired by immune plasma transfer treatment. Many meta-heuristic algorithms are used for solving complex optimization problems, but their performance is mostly inspected on problems with 30 dimensions. Nowadays we are dealing with far more complex systems that require solving high-dimensional optimization problems with over 50 dimensions whereas performance of meta-heuristic algorithms for high-dimensional problems is mostly unexamined. So to overcome this problem, in this study, performance of IPA on solving high-dimensional problems is investigated. In this case, it is used to solve five well-known benchmark optimization problems with 100 dimensions. In this work, Immune Plasma Algorithm (IPA) is used for solving Sphere, Quartic, Rastrigin, Ackley and Griewank functions. It is compared with some other state-of-the-art meta-heuristic algorithms. Experimental results demonstrate that IPA outperforms these algorithms in finding best objective values, and has best standard deviation, and best mean value for most of the tested optimization problems.

Objective-sensitive principal component analysis for high-dimensional inverse problems

We introduce a novel approach of data-driven dimensionality reduction for solving high-dimensional optimization problems, including history matching. Objective-Sensitive parameterization of the argument accounts for the corresponding change of objective function value. The result is achieved via an extension of the conventional loss function, which only quantifies approximation error over realizations. This paper contains three instances of such an approach based on Principal Component Analysis (PCA). Gradient-Sensitive PCA (GS-PCA) exploits a linear approximation of the objective function. Two other approaches solve the problem approximately within the framework of stationary perturbation theory (SPT). All the algorithms are verified and tested with a synthetic reservoir model. The results demonstrate improvements in parameterization quality regarding the reveal of the unconstrained objective function minimum. Also, we provide possible extensions and analyze the overall applicability of the Objective-Sensitive approach, which can be combined with modern parameterization techniques beyond PCA.

A robust, multi-solution framework for well placement and control optimization

Field development and control optimization aim to maximize the economic profit of oil and gas production while considering several sources of uncertainty. This results in a high-dimensional optimization problem with a computationally demanding and uncertain objective function based on the simulated reservoir model. The limitations of many current robust optimization methods are: 1) it is single-level optimization (e.g. optimization of well locations/placement only; or of well production/injection control variables only) that ignores interference between the control variables from different levels; and 2) they provide a single optimal solution, whereas operational problems often add unexpected constraints likely to reduce that optimal, inflexible solution to a sub-optimal scenario. This paper presents a robust, multi-solution framework based on sequential iterative optimization of control variables at multiple levels using the Simultaneous Perturbation Stochastic Approximation (SPSA) optimization algorithm. A systematic realization selection process, tailored to the objective of the subsequent optimization stage, is used to select a small representative ensemble of reservoir model realizations to be used for calculating the expected objective value. The estimated gradients are calculated using a 1:1 ratio mapping ensemble of control variables perturbations at each iteration onto the ensemble of selected reservoir model realizations to reduce the computational cost. An ensemble of close-to-optimum solutions is then chosen from each level (e.g. from the well placement optimization level) and transferred to the next level of optimization (e.g. where the control settings are optimized), and this loop continues until no significant improvement is observed in the expected objective value. Fit-for-purpose clustering techniques are developed to systematically select an ensemble of solutions, with maximum differences in control variables but close-to-optimum objective values, at each optimization level. The proposed framework has been tested on a benchmark case study (Brugge field). Multiple solutions are obtained with different well locations and control settings but close-to-optimum objective values. We show that suboptimal solutions from an early optimization level can approach and even outdo the optimal one at the next level(s). Results demonstrate the advantage of the developed framework in more efficient exploration of the search space and providing the much-needed operational flexibility to field operators.

An improved firefly algorithm with dynamic self-adaptive adjustment.

The firefly algorithm (FA) is proposed as a heuristic algorithm, inspired by natural phenomena. The FA has attracted a lot of attention due to its effectiveness in dealing with various global optimization problems. However, it could easily fall into a local optimal value or suffer from low accuracy when solving high-dimensional optimization problems. To improve the performance of the FA, this paper adds the self-adaptive logarithmic inertia weight to the updating formula of the FA, and proposes the introduction of a minimum attractiveness of a firefly, which greatly improves the convergence speed and balances the global exploration and local exploitation capabilities of FA. Additionally, a step-size decreasing factor is introduced to dynamically adjust the random step-size term. When the dimension of a search is high, the random step-size becomes very small. This strategy enables the FA to explore solution more accurately. This improved FA (LWFA) was evaluated with ten benchmark test functions under different dimensions (D = 10, 30, and 100) and with standard IEEE CEC 2010 benchmark functions. Simulation results show that the performance of improved FA is superior comparing to the standard FA and other algorithms, i.e., particle swarm optimization, the cuckoo search algorithm, the flower pollination algorithm, the sine cosine algorithm, and other modified FA. The LWFA also has high performance and optimal efficiency for a number of optimization problems.

An enhanced whale optimization algorithm for large scale optimization problems

Whale optimization algorithm was developed based on the prey-catching characteristics of the humpback whales. Due to its simple structure and efficiency, the researchers employed the algorithm to address numerous disciplines’ numerous problems. The profound analysis of the whale optimization algorithm discloses that the algorithm suffers from low exploration ability, lesser accuracy, and early convergence. Additionally, performance of the whale optimization algorithm and most of its variants in high-dimensional optimization problems is not satisfactory. This study proposes a new variant with several modifications to the basic whale optimization algorithm to solve high-dimensional problems. A unique selection parameter is introduced in the whale optimization algorithm to balance the algorithm’s global and local search phase. The co-efficient vectors A and C are modified and used effectively to explore and exploit the search region better. In the exploration phase, random movement is allowed to reduce the computational burden of the algorithm. An inertia weight is introduced in the exploitation phase for exhaustive search nearby the best solution. The proposed algorithm evaluates twenty-five benchmark functions using dimensions 100, 500, 1000, and 2000 and compared the results with the whale optimization algorithm and its variants. The estimated outcomes are also compared with seven basic metaheuristic algorithms. Finally, statistical analysis, complexity analysis, and convergence analysis are performed to establish the algorithm’s efficacy. All the test result suggests better performance of the proposed algorithm on higher-dimensional problems.

Design of Biopharmaceutical Formulations Accelerated by Machine Learning.

In addition to activity, successful biological drugs must exhibit a series of suitable developability properties, which depend on both protein sequence and buffer composition. In the context of this high-dimensional optimization problem, advanced algorithms from the domain of machine learning are highly beneficial in complementing analytical screening and rational design. Here, we propose a Bayesian optimization algorithm to accelerate the design of biopharmaceutical formulations. We demonstrate the power of this approach by identifying the formulation that optimizes the thermal stability of three tandem single-chain Fv variants within 25 experiments, a number which is less than one-third of the experiments that would be required by a classical DoE method and several orders of magnitude smaller compared to detailed experimental analysis of full combinatorial space. We further show the advantage of this method over conventional approaches to efficiently transfer historical information as prior knowledge for the development of new biologics or when new buffer agents are available. Moreover, we highlight the benefit of our technique in engineering multiple biophysical properties by simultaneously optimizing both thermal and interface stabilities. This optimization minimizes the amount of surfactant in the formulation, which is important to decrease the risks associated with corresponding degradation processes. Overall, this method can provide high speed of converging to optimal conditions, the ability to transfer prior knowledge, and the identification of new nonlinear combinations of excipients. We envision that these features can lead to a considerable acceleration in formulation design and to parallelization of operations during drug development.