Metaheuristics in large-scale global continues optimization: A survey

Optimization of fungal secondary metabolites production via response surface methodology coupled with multi-parameter optimized artificial neural network model

Filamentous fungi's secondary metabolites (SMs) possess significant application owing to their distinct structure and diverse bioactivities, yet their restricted yield levels often hinder further research and application. The study developed a response surface methodology-artificial neural network (RSM-ANN) strategy with multi-parameter optimizations of the ANN model to optimize medium for the production of two high-value fungal SMs, echinocandin E and paraherquamide A. Multi-parameter optimization of the ANN model was achieved through stratifying experimental data, fully adjusting neural network internals, and evaluating metaheuristic algorithms for optimal initial weights and biases. Experimental validation of models revealed that ANN-genetic algorithm models outperformed traditional RSM models in terms of determination coefficients, accuracy, and mean squared errors. ANN models showed outstanding robustness across a variety of fungal species, mediums, and experimental designs (Central Composite Design or Box-Behnken Design). This work refines the RSM-ANN optimization technique to increase fungal SM production efficiency, enabling industrial-scale production and applications.

The optimum sizing of zero-emission water-cooled VCR cycle based on exergo-economic-environmental assessment criteria by triple-objective MPSO

Renewable energies are interesting as an alternative and sustainable resource for air conditioning applications. But initial investment cost of equipment, whose employed for converting the renewable energy into usable shape and also for air conditioning duty, are significant. Therefore, determining the optimum sizing has high priority. In current study, water cooled vapor compression refrigeration cycle powered by wind energy and storage tank is proposed, simulated and optimized. To contribute the total effective aspects in system optimum size, the thermo-economic-environmental criteria is defined. By the help of databank of parametric analysis, the optimum design variables are determined by employing the GA optimization algorithm. In the following, an intelligence neural network is developed to learn the reliable correlation between the inputs and outputs data. Finally, the optimum size of each subsystem is determined by using triple-objective MPSO. Based on detailed economic analysis, the system payback period is estimated about 450 days which is 41% less than the conventional system. The daily COP and exergy efficiency of the whole system has improved up to 98% and 40%, after substituting the optimum design variable parameters. Triple-objective MPSO results show that, the ice storage tank should be selected 22% smaller than the initial amount.

Reptile Search Algorithm Considering Different Flight Heights to Solve Engineering Optimization Design Problems

The reptile search algorithm is an effective optimization method based on the natural laws of the biological world. By restoring and simulating the hunting process of reptiles, good optimization results can be achieved. However, due to the limitations of natural laws, it is easy to fall into local optima during the exploration phase. Inspired by the different search fields of biological organisms with varying flight heights, this paper proposes a reptile search algorithm considering different flight heights. In the exploration phase, introducing the different flight altitude abilities of two animals, the northern goshawk and the African vulture, enables reptiles to have better search horizons, improve their global search ability, and reduce the probability of falling into local optima during the exploration phase. A novel dynamic factor (DF) is proposed in the exploitation phase to improve the algorithm's convergence speed and optimization accuracy. To verify the effectiveness of the proposed algorithm, the test results were compared with ten state-of-the-art (SOTA) algorithms on thirty-three famous test functions. The experimental results show that the proposed algorithm has good performance. In addition, the proposed algorithm and ten SOTA algorithms were applied to three micromachine practical engineering problems, and the experimental results show that the proposed algorithm has good problem-solving ability.

An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges

As the world moves towards industrialization, optimization problems become more challenging to solve in a reasonable time. More than 500 new metaheuristic algorithms (MAs) have been developed to date, with over 350 of them appearing in the last decade. The literature has grown significantly in recent years and should be thoroughly reviewed. In this study, approximately 540 MAs are tracked, and statistical information is also provided. Due to the proliferation of MAs in recent years, the issue of substantial similarities between algorithms with different names has become widespread. This raises an essential question: can an optimization technique be called 'novel' if its search properties are modified or almost equal to existing methods? Many recent MAs are said to be based on 'novel ideas', so they are discussed. Furthermore, this study categorizes MAs based on the number of control parameters, which is a new taxonomy in the field. MAs have been extensively employed in various fields as powerful optimization tools, and some of their real-world applications are demonstrated. A few limitations and open challenges have been identified, which may lead to a new direction for MAs in the future. Although researchers have reported many excellent results in several research papers, review articles, and monographs during the last decade, many unexplored places are still waiting to be discovered. This study will assist newcomers in understanding some of the major domains of metaheuristics and their real-world applications. We anticipate this resource will also be useful to our research community.

SUFEMO: A superpixel based fuzzy image segmentation method for COVID-19 radiological image elucidation

COVID-19 causes an ongoing worldwide pandemic situation. The non-discovery of specialized drugs and/or any other kind of medicines makes the situation worse. Early diagnosis of this disease will be certainly helpful to start the treatment early and also to bring down the dire spread of this highly infectious virus. This article describes the proposed novel unsupervised segmentation method to segment the radiological image samples of the chest area that are accumulated from the COVID-19 infected patients. The proposed approach is helpful for physicians, medical technologists, and other related experts in the quick and early diagnosis of COVID-19 infection. The proposed approach will be the SUFEMO (SUperpixel based Fuzzy Electromagnetism-like Optimization). This approach is developed depending on some well-known theories like the Electromagnetism-like optimization algorithm, the type-2 fuzzy logic, and the superpixels. The proposed approach brings down the processing burden that is required to deal with a considerably large amount of spatial information by assimilating the notion of the superpixel. In this work, the EMO approach is modified by utilizing the type 2 fuzzy framework. The EMO approach updates the cluster centers without using the cluster center updation equation. This approach is independent of the choice of the initial cluster centers. To decrease the related computational overhead of handling a lot of spatial data, a novel superpixel-based approach is proposed in which the noise-sensitiveness of the watershed-based superpixel formation approach is dealt with by computing the nearby minima from the gradient image. Also, to take advantage of the superpixels, the fuzzy objective function is modified. The proposed approach was evaluated using both qualitatively and quantitatively using 310 chest CT scan images that are gathered from various sources. Four standard cluster validity indices are taken into consideration to quantify the results. It is observed that the proposed approach gives better performance compared to some of the state-of-the-art approaches in terms of both qualitative and quantitative outcomes. On average, the proposed approach attains Davies-Bouldin index value of 1.812008792, Xie-Beni index value of 1.683281, Dunn index value 2.588595748, and β index value 3.142069236 for 5 clusters. Apart from this, the proposed approach is also found to be superior with regard to the rate of convergence. Rigorous experiments prove the effectiveness of the proposed approach and establish the real-life applicability of the proposed method for the initial filtering of the COVID-19 patients.

Trust-Tech Source-Point Method for Systematically Computing Multiple Local Optimal Solutions: Theory and Method

In this article, a Trust-Tech source-point method is proposed to systematically compute multiple local optimal solutions (LOSs) for continuous unconstrained nonlinear optimization problems. This proposed method consists of four stages. Stage I finds one LOS (in which existing effective optimizers can be applied), stage II is the stage of escaping an LOS while stage III is the stage for entering the stability region (SR) of another stable equilibrium point (SEP) (i.e., another LOS). Stage IV computes other SEPs (i.e., LOSs) in corresponding SRs. A theoretical foundation for both stages II and III is developed, and these theoretical results are quite general on their own. The proposed method is numerically evaluated to compute multiple LOSs. For instance, a total of 5085 LOSs have been computed by the proposed Trust-Tech source point method on a 50-D test function. In addition, the proposed method can find the global optimal solutions of several test functions with 50 dimensions and 100 dimensions.

An Improved Sea Lion Optimization for Workload Elasticity Prediction with Neural Networks

The work in this paper presents a study into nature-inspired optimization applied to workload elasticity prediction using neural networks. Currently, the trend is for proactive decision support in increasing or decreasing the available resource in cloud computing. The aim is to avoid overprovision leading to resource waste and to avoid resource under-provisioning. The combination of optimization and neural networks has potential for the performance, accuracy, and stability of the prediction solution. In this context, we initially proposed an improved variant of sea lion optimization (ISLO) to boost the efficiency of the original in solving optimization problems. The designed optimization results are validated against eight well-known metaheuristic algorithms on 20 benchmark functions of CEC’2014 and CEC’2015. After that, improved sea lion optimization (ISLO) is used to train a hybrid neural network. Finally, the trained neural model is used for resource auto-scaling based on workload prediction with 4 real and public datasets. The experiments show that our neural network model provides improved results in comparison with other models, especially in comparison with neural networks trained using the original sea lion optimization. The proposed ISLO proved efficiency and improvement in solving problems ranging from global optimization with swarm intelligence to the prediction of workload elasticity.

An Optimal WSN Node Coverage Based on Enhanced Archimedes Optimization Algorithm

Node coverage is one of the crucial metrics for wireless sensor networks’ (WSNs’) quality of service, directly affecting the target monitoring area’s monitoring capacity. Pursuit of the optimal node coverage encounters increasing difficulties because of the limited computational power of individual nodes, the scale of the network, and the operating environment’s complexity and constant change. This paper proposes a solution to the optimal node coverage of unbalanced WSN distribution during random deployment based on an enhanced Archimedes optimization algorithm (EAOA). The best findings for network coverage from several sub-areas are combined using the EAOA. In order to address the shortcomings of the original Archimedes optimization algorithm (AOA) in handling complicated scenarios, we suggest an EAOA based on the AOA by adapting its equations with reverse learning and multidirection techniques. The obtained results from testing the benchmark function and the optimal WSN node coverage of the EAOA are compared with the other algorithms in the literature. The results show that the EAOA algorithm performs effectively, increasing the feasible range and convergence speed.

An Improved Pity Beetle Algorithm for Solving Constrained Engineering Design Problems

To cope with increasingly complex models of engineering design problems and to obtain more accurate design solutions, this paper proposed an improved population-based, bio-inspired optimization algorithm, called the pity beetle algorithm based on pheromone dispersion model (PBA-PDM). PBA-PDM enables a local and global search for optimization problems through the pheromone release mechanisms in female beetles and the interaction relationship between male beetles. The experimental results compared with other state-of-the-art metaheuristic optimization algorithms show that PBA-PDM has an ideal performance when dealing with both classical test functions and CEC2017 benchmark test functions. Then, the PBA-PDM is applied in dealing with real-world constrained engineering design problems to verify the effectiveness and applicability. The above experimental results show that the PBA-PDM proposed in this paper is an effective and efficient algorithm for solving real-world optimization problems.

Contribution-Based Cooperative Co-Evolution for Nonseparable Large-Scale Problems With Overlapping Subcomponents

Cooperative co-evolutionary algorithms have addressed many large-scale problems successfully, but the nonseparable large-scale problems with overlapping subcomponents are still a serious difficulty that has not been conquered yet. First, the existence of shared variables makes the problem hard to be decomposed. Second, existing cooperative co-evolutionary frameworks usually cannot maintain the two crucial factors: high cooperation frequency and effective computing resource allocation, simultaneously when optimizing the overlapping subcomponents. Aiming at these two issues, this article proposes a new contribution-based cooperative co-evolutionary algorithm to decompose and optimize nonseparable large-scale problems with overlapping subcomponents effectively and efficiently: 1) a contribution-based decomposition method is proposed to assign the shared variables. Among all the subcomponents containing a shared variable, the one that contributes the most to the entire problem will include the shared variable and 2) to achieve the two crucial factors at the same time, a new contribution-based optimization framework is designed to award the important subcomponents based on the round-robin structure. Experimental studies show that the proposed algorithm performs significantly better than the state-of-the-art algorithms due to the effective grouping structure generated by the proposed decomposition method and the fast optimizing speed provided by the new optimization framework.

Research on Coverage Optimization in a WSN Based on an Improved COOT Bird Algorithm

To address the problems of uneven distribution and low coverage of wireless sensor network (WSN) nodes in random deployment, a node coverage optimization strategy with an improved COOT bird algorithm (COOTCLCO) is proposed. Firstly, the chaotic tent map is used to initialize the population, increase the diversity of the population, and lay the foundation for the global search for the optimal solutions. Secondly, the Lévy flight strategy is used to perturb the individual positions to improve the search range of the population. Thirdly, Cauchy mutation and an opposition-based learning strategy are fused to perturb the optimal solutions to generate new solutions and enhance the ability of the algorithm to jump out of the local optimum. Finally, the COOTCLCO algorithm is applied to WSN coverage optimization problems. Simulation results show that COOTCLCO has a faster convergence speed and better search accuracy than several other typical algorithms on 23 benchmark test functions; meanwhile, the coverage rate of the COOTCLCO algorithm is increased by 9.654%, 13.888%, 6.188%, 5.39%, 1.31%, and 2.012% compared to particle swarm optimization (PSO), butterfly optimization algorithm (BOA), seagull optimization algorithm (SOA), whale optimization algorithm (WOA), Harris hawks optimization (HHO), and bald eagle search (BES), respectively. This means that in terms of coverage optimization effect, COOTCLCO can obtain a higher coverage rate compared to these algorithms. The experimental results demonstrate that COOTCLCO can effectively improve the coverage rate of sensor nodes and improve the distribution of nodes in WSN coverage optimization problems.

Elite Directed Particle Swarm Optimization with Historical Information for High-Dimensional Problems

High-dimensional optimization problems are ubiquitous in every field nowadays, which seriously challenge the optimization ability of existing optimizers. To solve this kind of optimization problems effectively, this paper proposes an elite-directed particle swarm optimization (EDPSO) with historical information to explore and exploit the high-dimensional solution space efficiently. Specifically, in EDPSO, the swarm is first separated into two exclusive sets based on the Pareto principle (80-20 rule), namely the elite set containing the top best 20% of particles and the non-elite set consisting of the remaining 80% of particles. Then, the non-elite set is further separated into two layers with the same size from the best to the worst. As a result, the swarm is divided into three layers. Subsequently, particles in the third layer learn from those in the first two layers, while particles in the second layer learn from those in the first layer, on the condition that particles in the first layer remain unchanged. In this way, the learning effectiveness and the learning diversity of particles could be largely promoted. To further enhance the learning diversity of particles, we maintain an additional archive to store obsolete elites, and use the predominant elites in the archive along with particles in the first two layers to direct the update of particles in the third layer. With these two mechanisms, the proposed EDPSO is expected to compromise search intensification and diversification well at the swarm level and the particle level, to explore and exploit the solution space. Extensive experiments are conducted on the widely used CEC’2010 and CEC’2013 high-dimensional benchmark problem sets to validate the effectiveness of the proposed EDPSO. Compared with several state-of-the-art large-scale algorithms, EDPSO is demonstrated to achieve highly competitive or even much better performance in tackling high-dimensional problems.

An improved weighted optimization approach for large-scale global optimization

It is a great challenge for ordinary evolutionary algorithms (EAs) to tackle large-scale global optimization (LSGO) problems which involve over hundreds or thousands of decision variables. In this paper, we propose an improved weighted optimization approach (LSWOA) for helping solve LSGO problems. Thanks to the dimensionality reduction of weighted optimization, LSWOA can optimize transformed problems quickly and share the optimal weights with the population, thereby accelerating the overall convergence. First, we concentrate on the theoretical investigation of weighted optimization. A series of theoretical analyses are provided to illustrate the search behavior of weighted optimization, and the equivalent form of the transformed problem is presented to show the relationship between the original problem and the transformed one. Then the factors that affect problem transformation and how they take affect are figured out. Finally, based on our theoretical investigation, we modify the way of utilizing weighted optimization in LSGO. A weight-sharing strategy and a candidate solution inheriting strategy are designed, along with a better allocation of computational resources. These modifications help take full advantage of weighted optimization and save computational resources. The extensive experimental results on CEC’2010 and CEC’2013 verify the effectiveness and scalability of the proposed LSWOA.

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.

An Adaptive Stochastic Dominant Learning Swarm Optimizer for High-Dimensional Optimization

High-dimensional problems are ubiquitous in many fields, yet still remain challenging to be solved. To tackle such problems with high effectiveness and efficiency, this article proposes a simple yet efficient stochastic dominant learning swarm optimizer. Particularly, this optimizer not only compromises swarm diversity and convergence speed properly, but also consumes as little computing time and space as possible to locate the optima. In this optimizer, a particle is updated only when its two exemplars randomly selected from the current swarm are its dominators. In this way, each particle has an implicit probability to directly enter the next generation, making it possible to maintain high swarm diversity. Since each updated particle only learns from its dominators, good convergence is likely to be achieved. To alleviate the sensitivity of this optimizer to newly introduced parameters, an adaptive parameter adjustment strategy is further designed based on the evolutionary information of particles at the individual level. Finally, extensive experiments on two high dimensional benchmark sets substantiate that the devised optimizer achieves competitive or even better performance in terms of solution quality, convergence speed, scalability, and computational cost, compared to several state-of-the-art methods. In particular, experimental results show that the proposed optimizer performs excellently on partially separable problems, especially partially separable multimodal problems, which are very common in real-world applications. In addition, the application to feature selection problems further demonstrates the effectiveness of this optimizer in tackling real-world problems.

Dimensional Learning Strategy-Based Grey Wolf Optimizer for Solving the Global Optimization Problem

Grey wolf optimizer (GWO) is an up-to-date nature-inspired optimization algorithm which has been used for solving many of the real-world applications since it was proposed. In the standard GWO, individuals are guided by the three dominant wolves alpha, beta, and delta in the leading hierarchy of the swarm. These three wolves provide their information about the potential locations of the global optimum in the search space. This learning mechanism is easy to implement. However, when the three wolves are in conflicting directions, an individual may not obtain better knowledge to update its position. To improve the utilization of the population knowledge, in this paper, we proposed a grey wolf optimizer based on the dimensional learning strategy (DLGWO). In the DLGWO, the three dominant wolves construct an exemplar wolf through the dimensional learning strategy (DLS) to guide the grey wolves in the swarm. Thereafter, to reinforce the exploration ability of the algorithm, the Levy flight is also utilized in the proposed method. 23 classic benchmark functions and engineering problems are used to test the effectiveness of the proposed method against the standard GWO, variants of the GWO, and other metaheuristic algorithms. The experimental results show that the proposed DLGWO has good performance in solving the global optimization problems.

Multithreshold Image Segmentation Technique Using Remora Optimization Algorithm for Diabetic Retinopathy Detection from Fundus Images

One of the most common complications of diabetes mellitus is diabetic retinopathy (DR), which produces lesions on the retina. A novel framework for DR detection and classification was proposed in this study. The proposed work includes four stages: pre-processing, segmentation, feature extraction, and classification. Initially, the image pre-processing is performed and after that, the Multi threshold-based Remora Optimization (MTRO) algorithm performs the vessel segmentation. The feature extraction and classification process are done by using a Region-based Convolution Neural Network (R-CNN) with Wild Geese Algorithm (WGA). Finally, the proposed R-CNN with WGA effectively classifies the different stages of DR including Non-DR, Proliferative DR, Severe, Moderate DR, Mild DR. The experimental images were collected from the DRIVE database, and the proposed framework exhibited superior DR detection performance. Compared to other existing methods like fully convolutional deep neural network (FCDNN), genetic-search feature selection (GSFS), Convolutional Neural Networks (CNN), and deep learning (DL) techniques, the proposed R-CNN with WGA provided 95.42% accuracy, 93.10% specificity, 93.20% sensitivity, and 98.28% F-score results.

AntTrust: An Ant-Inspired Trust Management System for Peer-to-Peer Networks

In P2P networks, self-organizing anonymous peers share different resources without a central entity controlling their interactions. Peers can join and leave the network at any time, which opens the door to malicious attacks that can damage the network. Therefore, trust management systems that can ensure trustworthy interactions between peers are gaining prominence. This paper proposes AntTrust, a trust management system inspired by the ant colony. Unlike other ant-inspired algorithms, which usually adopt a problem-independent approach, AntTrust follows a problem-dependent (problem-specific) heuristic to find a trustworthy peer in a reasonable time. It locates a trustworthy file provider based on four consecutive trust factors: current trust, recommendation, feedback, and collective trust. Three rival trust management paradigms, namely, EigenTrust, Trust Network Analysis with Subjective Logic (TNA-SL), and Trust Ant Colony System (TACS), were tested to benchmark the performance of AntTrust. The experimental results demonstrate that AntTrust is capable of providing a higher and more stable success rate at a low running time regardless of the percentage of malicious peers in the network.

A novel three layer particle swarm optimization for feature selection

Feature selection (FS) is a vital data preprocessing task which aims at selecting a small subset of features while maintaining a high level of classification accuracy. FS is a challenging optimization problem due to the large search space and the existence of local optimal solutions. Particle swarm optimization (PSO) is a promising technique in selecting optimal feature subset due to its rapid convergence speed and global search ability. But PSO suffers from stagnation or premature convergence in complex FS problems. In this paper, a novel three layer PSO (TLPSO) is proposed for solving FS problem. In the TLPSO, the particles in the swarm are divided into three layers according to their evolution status and particles in different layers are treated differently to fully investigate their potential. Instead of learning from those historical best positions, the TLPSO uses a random learning exemplar selection strategy to enrich the searching behavior of the swarm and enhance the population diversity. Further, a local search operator based on the Gaussian distribution is performed on the elite particles to improve the exploitation ability. Therefore, TLPSO is able to keep a balance between population diversity and convergence speed. Extensive comparisons with seven state-of-the-art meta-heuristic based FS methods are conducted on 18 datasets. The experimental results demonstrate the competitive and reliable performance of TLPSO in terms of improving the classification accuracy and reducing the number of features.

Bio-inspired computation for big data fusion, storage, processing, learning and visualization: state of the art and future directions

This overview gravitates on research achievements that have recently emerged from the confluence between Big Data technologies and bio-inspired computation. A manifold of reasons can be identified for the profitable synergy between these two paradigms, all rooted on the adaptability, intelligence and robustness that biologically inspired principles can provide to technologies aimed to manage, retrieve, fuse and process Big Data efficiently. We delve into this research field by first analyzing in depth the existing literature, with a focus on advances reported in the last few years. This prior literature analysis is complemented by an identification of the new trends and open challenges in Big Data that remain unsolved to date, and that can be effectively addressed by bio-inspired algorithms. As a second contribution, this work elaborates on how bio-inspired algorithms need to be adapted for their use in a Big Data context, in which data fusion becomes crucial as a previous step to allow processing and mining several and potentially heterogeneous data sources. This analysis allows exploring and comparing the scope and efficiency of existing approaches across different problems and domains, with the purpose of identifying new potential applications and research niches. Finally, this survey highlights open issues that remain unsolved to date in this research avenue, alongside a prescription of recommendations for future research.

Large-Scale Evolution Strategy Based on Search Direction Adaptation

The covariance matrix adaptation evolution strategy (CMA-ES) is a powerful evolutionary algorithm for single-objective real-valued optimization. However, the time and space complexity may preclude its use in high-dimensional decision space. Recent studies suggest that putting sparse or low-rank constraints on the structure of the covariance matrix can improve the efficiency of CMA-ES in handling large-scale problems. Following this idea, this paper proposes a search direction adaptation evolution strategy (SDA-ES) which achieves linear time and space complexity. SDA-ES models the covariance matrix with an identity matrix and multiple search directions, and uses a heuristic to update the search directions in a way similar to the principal component analysis. We also generalize the traditional 1/5th success rule to adapt the mutation strength which exhibits the derandomization property. Numerical comparisons with nine state-of-the-art algorithms are carried out on 31 test problems. The experimental results have shown that SDA-ES is invariant under search-space rotational transformations, and is scalable with respect to the number of variables. It also achieves competitive performance on generic black-box problems, demonstrating its effectiveness in keeping a good tradeoff between solution quality and computational efficiency.

Structural Optimization in Civil Engineering: A Literature Review

Since tremendous resources are consumed in the architecture, engineering, and construction (AEC) industry, the sustainability and efficiency in this field have received increasing concern in the past few decades. With the advent and development of computational tools and information technologies, structural optimization based on mathematical computation has become one of the most commonly used methods for the sustainable and efficient design in the field of civil engineering. However, despite the wide attention of researchers, there has not been a critical review of the recent research progresses on structural optimization yet. Therefore, the main objective of this paper is to comprehensively review the previous research on structural optimization, provide a thorough analysis on the optimization objectives and their temporal and spatial trends, optimization process, and summarize the current research limitations and recommendations of future work. The paper first introduces the significance of sustainability and efficiency in the AEC industry as well as the background of this review work. Then, relevant articles are retrieved and selected, followed by a statistical analysis of the selected articles. Thereafter, the selected articles are analyzed regarding the optimization objectives and their temporal and spatial trends. The four major steps in the structural optimization process, including structural analysis and modelling, formulation of optimization problems, optimization techniques, and computational tools and design platforms, are also reviewed and discussed in detail based on the collected articles. Finally, research gaps of the current works and potential directions of future works are proposed. This paper critically reviews the achievements and limitations of the current research on structural optimization, which provide guidelines for future research on structural optimization in the field of civil engineering.