Evolutionary Optimization Method Research Articles

Evolutionary Optimization Methods for High-Dimensional Expensive Problems: A Survey

Evolutionary Optimization Methods for High-Dimensional Expensive Problems: A Survey

Topology optimization structure design of shape memory alloy with multiple constraints

As an emerging functional material, shape memory alloy (SMA) exhibits remarkable mechanical properties and finds diverse applications across industries. This paper presents a topology optimization framework based on the bi-directional evolutionary structural optimization (BESO) method for designing SMA structures, which maximizes structural stiffness under multiple constraints of specified volume fraction, displacement, and fundamental frequency. A phenomenological constitutive model is utilized to simulate the mechanical behavior of SMA accurately. The unit virtual load method is employed to determine sensitivities. Several optimized SMA beam structures and simply-supported cube structures are designed under different thermal-mechanical loads, and their displacement, mean compliance, and fundamental frequency are evaluated throughout the optimization process. The results demonstrate that the proposed framework successfully customizes the SMA topology structure with adjustable displacement and fundamental frequency, and the optimized schemes exhibit more considerable deformation and more uniform mechanical properties than their initial counterparts. The proposed framework has higher computational efficiency than the traditional SIMP-based SMA topology optimization design method.

An Eigenfrequency-Constrained Topology Optimization Method with Design Variable Reduction

The dynamic response of structures heavily relies on eigenfrequency, so the optimization of eigenfrequency is valuable in various working conditions. The bi-directional evolutionary structural optimization (BESO) method has been widely applied due to its ability to eliminate grayscale elements. Based upon BESO, this paper introduces a topology optimization method that incorporates eigenfrequency constraints and reduces the number of design variables. In this method, the optimization objective was to minimize compliance. The Lagrange multiplier was used to introduce eigenfrequency constraints, allowing for coordinated control of compliance and eigenfrequency. To prevent oscillation during the optimization process, the sensitivity was normalized. Additionally, to achieve faster convergence, the variables were reduced after meeting volume constraints. The numerical examples demonstrate the effectiveness of this method in increasing the eigenfrequency of the structure and avoiding resonance.

Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms.

Exploring the Explainable Aspects and Performance of a Learnable Evolutionary Multiobjective Optimization Method

Multiobjective optimization problems have multiple conflicting objective functions to be optimized simultaneously. The solutions to these problems are known as Pareto optimal solutions, which are mathematically incomparable. Thus, a decision maker must be employed to provide preferences to find the most preferred solution. However, decision makers often lack support in providing preferences and insights in exploring the solutions available. We explore the combination of learnable evolutionary models with interactive indicator-based evolutionary multiobjective optimization to create a learnable evolutionary multiobjective optimization method. Furthermore, we leverage interpretable machine learning to provide decision makers with potential insights about the problem being solved in the form of rule-based explanations. In fact, we show that a learnable evolutionary multiobjective optimization method can offer advantages in the search for solutions to a multiobjective optimization problem. We also provide an open source software framework for other researchers to implement and explore our ideas in their own works. Our work is a step toward establishing a new paradigm in the field on multiobjective optimization: explainable and learnable multiobjective optimization . We take the first steps toward this new research direction and provide other researchers and practitioners with necessary tools and ideas to further contribute to this field.

Machine learning-based design optimization of aperiodic multilayer coatings for enhanced solar reflection

Multilayered coatings are promising and successful for applications in semiconductors, optical mirrors, and energy harvesting technologies. Amongst these, optical mirrors are essential for passive radiative cooling. Building upon the multilayer radiative cooling systems observed in snails and drawing from previous research, this study showcases the efficacy of machine learning algorithms in optimizing and gaining insights into multilayer structures. Due to the constraint of low sky window emissivity in biologically found calcite shells, focusing on solar reflectance becomes crucial to maximize the biological phenomenon found in snails. The manual search of the periodic multilayer design space for calcite with air gaps points to the maximum solar reflectance of ∼89% at 170 nm layer thickness for 20 μm coating. To unlock the full potential of these multilayers, we then employ machine learning-based evolutionary optimization method - a genetic algorithm. The optimized aperiodic coating shows a significant enhancement of solar reflectance to ∼99.8% for a 20 μm coating. Interestingly, the same average layer thickness of 170 nm provides maximum solar reflectance in 20 μm periodic and aperiodic calcite multilayer. Investigation of the spectral reflectance shows that layer thickness is crucial in tuning the solar reflectance. For small coatings, wavelengths with higher solar intensity are prioritized. Increasing the coating thickness allows inclusion of thicker layers to reflect longer wavelengths, leading to increasing trend of average calcite layer thickness. Further work exploring radiative cooling materials shows that calcite and barium sulfate reflect sunlight significantly better than silicon dioxide due to their refractive index contrast. Our findings and insights using bio-inspired design can provide superior solar reflectance utilizing thin coatings with modern manufacturing technology.

Process Knowledge-Guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.

Plastic-limit probabilistic structural topology optimization of steel beams

This work presents a novel geometrically nonlinear analysis with imperfections reliability-based topology optimization (RBTO) approach, considering the volume fraction and geometric imperfections as random variables due to their crucial connections to the manufacturability of web openings in steel I-beams. The objective is achieved by controlling the plastic behavior through limit analysis, which imposes a limit on the plastic ultimate load multipliers. The suggested method is developed by imposing constraints related to the available material volume. The bi-directional evolutionary structural optimization (BESO) method is utilized to fulfill the objectives of this paper. The adequacy of the proposed technique is demonstrated by comparing the results of the algorithm with benchmark steel beams that have conventional web openings. Based on the numerical examples, it appears that the selected technique has the potential to increase the load capacity of steel beams while utilizing the same quantity of material within the design domain. Moreover, the improved beams also exhibit better performance in terms of stress levels. The results of this research suggest that the proposed technique enhances the load capacity of steel beams while maintaining the same quantity of material and improving their performance in terms of stress levels.

Maximum likelihood estimation for discrete latent variable models via evolutionary algorithms

We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.

Thefittest: evolutionary machine learning in Python

Thefittest is a new Python library specializing in evolutionary optimization methods and machine learning methods that use evolutionary optimization methods. Thefittest provides both classical evolutionary algorithms and efficient modifications of these algorithms that do not have implementations in the open access. Among the advantages of the library are the performance of the implemented methods, accessibility and ease of use. The paper discusses the motivation for developing and leading the project, describes the structure of the library with examples of use, and provides a comparison with other projects with a similar development goal. Thefittest is an open-source project published on GitHub and PyPi, developed using modern methods of code analysis and testing. At the moment of writing the paper, the latest version of the library is 0.2.3.

A Performance Indicator for Interactive Evolutionary Multiobjective Optimization Methods

In recent years, interactive evolutionary multiobjective optimization methods have been getting more and more attention. In these methods, a decision maker, who is a domain expert, is iteratively involved in the solution process and guides the solution process toward her/his desired region with preference information. However, there have not been many studies regarding the performance evaluation of interactive evolutionary methods. On the other hand, indicators have been developed for a priori methods, where the DM provides preference information before optimization. In the literature, some studies treat interactive evolutionary methods as a series of a priori steps when assessing and comparing them. In such settings, indicators designed for a priori methods can be utilized. In this paper, we propose a novel performance indicator for interactive evolutionary multiobjective optimization methods and show how it can assess the performance of these interactive methods as a whole process and not as a series of separate steps. In addition, we demonstrate the shortcomings of using indicators designed for a priori methods for comparing interactive evolutionary methods.

Topological Optimization of Bi-Directional Progressive Structures with Dynamic Stress Constraints under Aperiodic Load

The topology optimization of dynamic stress constraints is highly nonlinear and singular and has been little studied. Dynamic stress based on progressive structural optimization is only available by applying the modal iteration method, but due to the nonlinear limitations of the modal superposition method, there is an urgent need to develop a progressive structural optimization method based on dynamic stress sensitivity under direct integration. This method is for the dynamic stresses under non-periodic loading with iterative cycle updating variations. This article proposes a topological optimization method of continuum structures with stress constraints under an aperiodic load based on the Bi-directional Evolutionary Structural Optimization Method (BESO). First, the P-norm condensation function was used to obtain the global stress to approximate maximum stress. By introducing the Lagrange multiplier, the design goal was to increase the P-norm stress on the basis of the smallest volume. After that, based on the dynamic finite element theory, the sensitivity of each cell formula of the objective function and the constraint conditions of the design variables were strictly derived. Then, the performance evaluation index was put forward based on volume and stress, and the convergence criterion based on the performance evaluation index was defined. This method solves the topology optimization problem of stress constraints under a non-periodic load and the topology optimization problem of stress constraints under a periodic load, such as a simple harmonic load.

Statistical Evaluation of Sustainable Urban Planning: Integrating Renewable Energy Sources, Energy-Efficient Buildings, and Climate Resilience Measures

In the face of increasing climate-related challenges, sustainable urban energy networks must grapple with transmission congestion in deregulated power systems. This study introduces a novel statistical approach that synergizes two powerful methodologies for evaluating and managing urban energy networks: the integration of photovoltaic (PV) renewable energy sources and Gated Recurrent Unit (GRU)-based PV forecasting. By combining evolutionary optimization techniques with GRU forecasting, we aim to bolster the sustainability and reliability of urban energy networks while addressing climate change adaptation. In this study, we employ statistical methods, including generator sensitivity ratios and bus sensitivity ratios (BSR), to pinpoint optimal locations for PV power integration within urban networks. The Lion Optimization Algorithm (LOA), an evolutionary optimization method, is employed within a digital twin framework to optimize active power rescheduling values and congestion prices. The incorporation of GRU-based PV forecasting enhances the precision and resilience of our energy management approach. Through extensive simulations conducted on the New England 39-bus system, our findings reveal that the combination of the LOA method and GRU forecasting outperforms traditional optimization techniques such as the Ant Lion Optimizer (ALO) and Particle Swarm Optimization (PSO). This dual-optimization strategy leads to significantly reduced active power rescheduling values and congestion prices, underlining the potential of our statistical model to effectively manage congestion in transmission lines within sustainable urban energy networks. In the context of integrating renewable PV sources and adapting urban energy infrastructure to climate change impacts, the synergy of evolutionary optimization and GRU-based forecasting offers a robust pathway to enhance sustainability and reliability in urban energy networks.

Reinforcement layout design for deep beams based on bi-objective topology optimization

Determining an effective and efficient reinforcement layout for reinforced concrete deep beams is still a challenging problem. This paper proposes a bi-objective evolutionary structural topology optimization method for the reinforcement layout design. Based on a discrete model for steel bars, the optimization aims to achieve a uniform stress distribution of steel rebars while promoting the peak rebar stress. A lexicographic method is used to solve the bi-objective optimization. Two numerical examples are presented to demonstrate the proposed algorithm's feasibility, stability and universal applicability. It is shown the reinforcement stresses in both tension and compression zones are more uniformly distributed and, on average, closer to the yield strength than those of the single-objective optimization. Compared with the design based on the conventional strut-and-tie method, the deep beams optimized by the proposed method use less reinforcement steel, provide a higher ultimate load capacity, and, more interestingly, fail in a ductile failure mode.

Simultaneous estimation of five temporally regular land variables at seven spatial resolutions from seven satellite data using a multi-scale and multi-depth convolutional neural network

Various satellite sensors have provided a huge amount of observations of Earth's environment at variable spatial and temporal resolutions. Many global coarse-resolution land products have been generated from single-satellite data, but global temporally regular land products at fine spatial resolutions (say 10-30 m) are scarce because of infrequent observations. An ideal inversion framework can estimate multiple global continuous land variables at different spatial resolutions by combining all sources of satellite data. This paper proposes a new framework that can estimate five land variables simultaneously from the top-of-atmosphere (TOA) reflectance acquired by seven satellite sensors based on a multi-scale and multi-depth convolutional neural network (MSDCNN). This framework enables us to estimate temporally regular land variables at as fine as 10 m spatial resolution by transforming information from satellite data at coarser spatial resolutions. The estimated land variables include Leaf Area Index (LAI), Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), shortwave albedo, visible albedo, and spectral reflectance. Seven sensors that acquire data at different spatial resolutions, include Visible Infrared Imaging Radiometer Suite (VIIRS) (750 m), Moderate Resolution Imaging Spectroradiometer (MODIS) (500 m), Fengyun-3 (FY-3) Medium Resolution Spectral Imager (MERSI) (250 m), China-Brazil Earth Resources Satellite 04 (CBERS-04) Wide Field Imager (WFI) (73 m), Landsat 8 Operational Land Imager (OLI) (30 m), Gaofen-1 (GF-1) Wide-Field-of-View (16 m) and Sentinel 2 A/B Multispectral Imager (MSI) (10 m). This framework is mainly composed of four steps. First, a Shuffled Complex Evolution (SCE) optimization method is adopted to estimate these variables from VIIRS TOA reference. Second, a joint-output random forest regression (RF) method is used to link the satellite observations and the estimated values from step 1. Third, the six-type multi-resolution satellite observations are used to downscale the VIIRS TOA reflectance to six different spatial resolutions by using the MSDCNN. Finally, the downscaled six-resolution VIIRS TOA reflectance is fed into the multiple-variable RF model to estimate land variables. The framework was validated, and the results based on high-resolution reference maps from ImagineS network and time series shortwave albedo field values from Surface Radiation (SURFRAD) and Integrated Carbon Observation System (ICOS) network show that the retrieved variables had high validation accuracy, with root mean square error (RMSE) ranges of 0.361–0.489 (LAI), 0.023–0.120 (FAPAR), 0.013–0.026 (snow-free shortwave albedo), respectively. Comparison results of the retrieved multi-scale variables with the Sentinel 2 A/B (10 m), Landsat 8 (30 m), Global LAnd Surface Satellite (GLASS, 250 m, 500 m), MODIS (500 m), and VIIRS (750 m) products show that their values were close, with RMSE ranges of 0.107–0.273 (LAI), 0.015–0.027 (FAPAR), 0.003–0.007 (shortwave albedo), 0.001–0.007 (visible albedo), and 0.003–0.025 (spectral reflectance), respectively. The results of the direct validation as well as the product intercomparison show that this novel framework has the potential to be used in estimating global land variables at various spatial scales using a variety of satellite data sources.

Predicting the small strain shear modulus of sands and sand-fines binary mixtures using machine learning algorithms

This study aims to develop several novel machine learning (ML) evolutionary algorithms for the prediction of small strain shear modulus (Gmax) of clean sands and sand-fines binary mixtures. To this end, five key features of isotropic confining pressure (p), void ratio (e), uniformity coefficient (Cu), particle shape descriptor (ρ), and non-plastic fines content (FC) are adopted as the inputs to artificial neural network (ANN) models as well as genetic programming (GP) algorithm so as to render the maximum shear modulus of granular soils as the output. Accordingly, a comprehensive dataset containing 1055 Gmax data points is exploited to develop ML simulations. The validity of ML-based models in estimating the Gmax of clean sands and sand-silt mixtures is rigorously examined through various statistical indices and measurement criteria. The results show that a novel ML model utilizing ANN-Levenberg Marquardt (LM) in conjunction with an evolutionary optimization method named Success History-based Adaptive Differential Evolution with Linear population size reduction (LSHADE) is capable of predicting Gmax data with a very high precision rendering R2 values of 0.9833, 0.9841, 0.9802, and 0.9835 for the whole, training, validation, and test datasets, respectively. Meanwhile, using the well-established GP algorithm, a new practical model is proposed to predict the Gmax of clean sands and sand-fines mixtures containing non-cohesive silt inclusion with R2 values of 0.9323, 0.9351, and 0.9312 for the whole, training, and test datasets, respectively. Finally, the proposed models of ANN-LSHADE-LM and GP are shown to be appreciably superior, in terms of accuracy, to all commonly used empirical correlations in the literature for Gmax estimation.

Evolutionary auto-design for aircraft engine cycle

Traditional engine cycle innovation is limited by human experiences, imagination, and currently available engine component performance expectations. Thus, the engine cycle innovation process is quite slow for the past 90 years. In this work, we propose a mixed variable multi-objective evolutionary optimization method for automatic engine cycle design. In the first, a simulation toolkit is developed for performance evaluation of potentially viable engine cycle solutions. Then, the engine cycle solutions are mixed encoded by the pins and the parameters of different engine components. The new engine cycle solutions are generated through the mutation operator. Finally, we construct two optimization objectives to drive the optimization process. Through the experimental research, new engine cycle solutions are discovered that exceed the performance of known turbojet and turbofan engines.

Multi‐objective optimal power flow using grasshopper optimization algorithm

SummaryThis paper introduces grasshopper optimization algorithm to efficiently prove its superiority in the optimal power flow problem. To demonstrate the efficiency of the proposed algorithm, it is implemented on the standard IEEE 30‐bus, IEEE 57‐bus, and IEEE 118‐bus test systems with different objectives that reveal presentation indices of the power system. Twelve different cases, in single and multi‐objective optimization space, are considered on different curves of fuel cost, environmental pollution emission, voltage profile, and active power loss. The simulation results obtained from grasshopper optimization algorithm techniques are compared to other new evolutionary optimization methods surfaced in the current state‐of‐the‐art literature. It is revealed that the proposed approach secures better consequence over the other newly originated popular optimization techniques and reflects its improved quality solutions and faster convergence speed. The results obtained in this work demonstrate that the grasshopper optimization algorithm method can successfully be applied to solve the non‐linear problems connected to power systems.

Practical application of multi-material topology optimization to performance-based architectural design of an iconic building

With the rapid development of architectural design methods and structural analysis techniques, structural performance-based design approaches have become increasingly important in architectural design. Among these approaches, topology optimization is a significant design method. However, most existing topology optimization research and related applications are based on single-material topology optimization techniques, which have limitations when applied to the design of complex and challenging structures. Building upon our previously proposed multi-material bi-directional evolutionary structural optimization (multi-material BESO) method, this paper presents the approaches for achieving diverse and competitive structural designs and then presents a practical application of the multi-material BESO method to the structural design of the core structure of a long-cantilevered building project called “Xiong’an Wings”. After an evolutionary design process based on the multi-material BESO method, an efficient frame with lower overall material costs, better static and dynamic performance compared to the initial design by experienced engineers is achieved. As the first practical application of the multi-material BESO method to a large-scale architectural design, the example of the “Xiong’an Wings” building demonstrates the tremendous prospects for the application of multi-material topology optimization technology to the generative design of innovative and efficient building structures.

Learning-Based Cuckoo Search Algorithm to Schedule a Flexible Job Shop With Sequencing Flexibility.

This work considers an extended version of flexible job-shop problem from a postprinting or semiconductor manufacturing environment, which needs a directed acyclic graph rather than a linear order to describe the precedences among operations. To obtain its reliable and high-quality schedule in a reasonable time, a learning-based cuckoo search (LCS) algorithm is presented. In it, cuckoo search is selected as an optimizer. To produce promising solutions in a high-dimensional solution space, a sparse autoencoder is introduced to compress a high-dimensional solution into an informative low-dimensional one. It extends the application area of autoencoder-embedded evolutionary optimization methods into combinational optimization by developing an improved one-hot encoding method. Then, in order to reveal the linkages among decision variables and enhance the explore ability of the proposed method, a factorization machine (FM) is used, for the first time, to capture the relevant and complementary features of population. Hence, a parallel framework involving three co-evolved subpopulations is constructed. The first one is an autoencoder embedded subpopulation, the second one is assisted by an FM, and the last one undergoes a regular iteration process. To balance the exploration and exploitation of the proposed framework and avoid unnecessary computation, a reinforcement learning algorithm is used to adaptively adjust the proportion of subpopulations and tune parameters of each subpopulation iteratively. Numerical simulations with benchmarks are performed to compare it with CPLEX, some classical heuristics, and several recently developed methods. The results shows that it well outperforms them.