Search Results (129)

As the number of feature dimensions increases, the decision-making space exhibits extensive and discrete characteristics, which poses a severe challenge to multi-objective (MO) evolutionary algorithms when searching for the optimal feature subset. Many existing algorithms face the difficulty of slow convergence speed and may fall into local optimal solutions. This study proposes AF-NSGA-II (an adaptive filtering-nondominated sorting genetic algorithm II), an improved MO evolutionary algorithm for high-dimensional feature selection, in which a novel sparse generation scheme for the solution set and an innovative adaptive crossover mechanism are introduced. This sparse initialization strategy, based on three distinct filter feature selection methods, produces initial solutions closer to the optimal Pareto solution set, which is beneficial for convergence. The adaptive crossover mechanism dynamically selects between geometric crossover operators (fostering convergence) and non-geometric crossover operators (enhancing diversity) based on parent similarity, effectively balancing both aspects and helping the algorithm to escape local optima. The algorithm is compared against six renowned multi-objective evolutionary algorithms across ten complex and publicly available datasets. The comparison results demonstrate the superiority of AF-NSGA-II over other algorithms, as well as its effectiveness in identifying the optimal feature subset. Full article

The exponential growth of the Internet of Things (IoT) has made it increasingly vulnerable to cyberattacks, where malicious manipulation of network and sensor data can lead to incorrect data classification. IoT data are inherently heterogeneous, comprising sensor readings, network flow records, and device metadata that differ significantly in scale and structure. This diversity motivates transforming tabular IoT data into image-based representations to facilitate the recognition of intrusion patterns and the analysis of spatial correlations. Many deep learning models offer robust detection performance, including CNNs, LSTMs, CNN–LSTM hybrids, and Transformer-based networks, but many of these architectures are computationally intensive and require significant training resources. To address this challenge, this study introduces an evolutionary-driven framework that mathematically formalizes the transformation of tabular IoT data into image-encoded matrices and optimizes feature selection through metaheuristic algorithms. Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Variable Neighborhood Search (VNS) are employed to identify optimal feature subsets for Random Forest (RF) and Extreme Gradient Boosting (XGBoost) classifiers. The approach enhances discrimination by optimizing multi-objective criteria, including accuracy and sparsity, while maintaining low computational complexity suitable for edge deployment. Experimental results on benchmark IoT intrusion datasets demonstrate that VNS-XGBoost configurations performed better on the IDS2017 and IDS2018 benchmarks, achieving accuracies up to 0.99997 and a significant reduction in Type II errors (212 and 6 in tabular form, reduced to 4 and 1 using image-encoded representations). These results confirm that integrating evolutionary optimization with image-based feature modeling enables accurate, efficient, and robust intrusion detection across large-scale IoT systems. Full article

In recent years, many constrained multi-objective evolutionary algorithms (CMOEAs) have primarily emphasized feasible solutions, overlooking the useful information contained in infeasible ones. This tendency effectively prioritizes feasibility over objective quality, often leading to the premature removal of infeasible solutions with strong convergence or diversity, thereby reducing performance on constrained multi-objective optimization problems (CMOPs) with complex or irregular feasible regions. To overcome these limitations, this paper introduces a weak constraint–Pareto dominance relation that integrates feasibility with objective performance, thereby preventing the premature elimination of infeasible solutions that may offer strong convergence or diversity. Moreover, an angle distance-based diversity maintenance strategy is proposed to preserve population diversity while ensuring solution feasibility. By combining these two mechanisms, we design the CMOEA-WA algorithm. Extensive experiments on benchmark and real-world problems confirm that the proposed method consistently outperforms state-of-the-art CMOEAs, achieving a more effective balance among feasibility, convergence, and diversity. Full article

Laser engraving may be used in a variety of industries, from medicine to defense, and it has many uses that require high-quality precision production. However, in practice, operators have to adjust the laser settings manually, which can result in wasted material and poor color quality and even decrease productivity. Current optimization approaches mostly concentrate on single objectives, making it impossible to co-optimize engraving quality and production efficiency simultaneously. In this paper, an approach based on a multi-objective genetic algorithm, a combination of NSGA-II, SPEA2, and MOEA/D, is proposed to automatically establish the relationship between CMYK color attributes, which are extracted from images of engravings, and laser parameters (power, speed, and frequency). Anodized aluminum 6061 was laser-processed using an SPI 30W fiber laser. While the proposed framework is general, the experimental validation in this study was specifically constrained to this material. The results also indicate that MOEA/D converges in a short time and becomes relatively stable after 20 generations. NSGA-II results in solutions that are more diverse, and SPEA2 offers a good trade-off between the speed of convergence and solution size. This approach resulted in optimization in terms of both a decrease in material used and color matching between manual operations, with the average CMYK improvement being up to 28%. Our results indicate that multi-objective evolutionary optimization is feasible for the optimization of efficiency and quality in laser cutting. Full article

Bayesian optimization (BO) struggles with data scarcity and poor scalability in high-dimensional many-objective optimization problems. To address this, we propose Co-Evolutionary GAN–Bayesian Optimization (CoEGAN-BO), a novel framework that synergizes generative adversarial networks (GANs) with Bayesian co-evolutionary search for data-driven optimization. The GAN module generates synthetic samples conditioned on promising regions identified by BO, while a co-evolutionary mechanism maintains two interacting populations: one explores the GAN’s latent space for diversity, and the other exploits BO’s probabilistic model for convergence. A bi-stage infilling strategy further enhances efficiency: early iterations prioritize exploration via $L_p$-norm-based candidate selection, later switching to a max–min distance criterion for Pareto refinement. Experiments on expensive multi/many-objective benchmarks show that CoEGAN-BO outperforms four state-of-the-art surrogate-assisted algorithms, achieving superior convergence and diversity under limited evaluation budgets. Full article

Optimization has always been viewed as a central component of many electrical engineering techniques, where it involves designing a complex system with various constraints and competing objectives. The method described in this work proposes a hybrid quantum–classical evolutionary optimization algorithm targeting high-frequency electromagnetic problems. A genetic algorithm with a quantum selection operator that applies high selection pressure while preserving selection diversity is introduced. This change means that stagnation can be reduced without compromising the speed of convergence. This was used on both real quantum hardware as well as quantum simulators. The results demonstrate that the performance of the real quantum devices was deteriorated by the noise in these devices and that simulators would be a useful option. We provide a description of the operation of the proposed evolutionary optimization method with mathematical benchmarks and electromagnetic design problems that show that it outperforms conventional evolutionary algorithms in terms of convergence behavior and robustness. Full article

The Dynamic Multi-objective Optimization Problem (DMOP) is one of the common problem types in academia and industry. The Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is an effective way for solving DMOPs. Despite the existence of many research works proposing a variety of DMOEAs, the demand for efficient solutions to DMOPs in drastically changing scenarios is still not well met. To this end, this paper is oriented towards DMOEA and innovatively proposes to explore the correlation between different points of the optimal frontier (PF) to improve the accuracy of predicting new PFs for new environments, which is the first attempt, to our best knowledge. Specifically, when the DMOP environment changes, this paper first constructs a spatio-temporal correlation model between various key points of the PF based on the linear regression algorithm; then, based on the constructed model, predicts a new location for each key point in the new environment; subsequently, constructs a sub-population by introducing the Gaussian noise into the predicted location to improve the generalization ability; and then, utilizes the idea of NSGA-II-B to construct another sub-population to further improve the population diversity; finally, combining the previous two sub-populations, re-initializing a new population to adapt to the new environment through a random replacement strategy. The proposed method was evaluated by experiments on the CEC 2018 test suite, and the experimental results show that the proposed method can obtain the optimal MIGD value on six DMOPs and the optimal MHVD value on five DMOPs, compared with six recent research results. Full article

As the number of objectives increases, the comprehensive processing performance of multi-objective optimization problems significantly declines. To address this challenge, this paper proposes an Angle-based dual-association Evolutionary Algorithm for Many-Objective Optimization (MOEA-AD). The algorithm enhances the exploration capability of unknown regions by associating empty subspaces with the solutions of the highest fitness through an angle-based bi-association strategy. Additionally, a novel quality assessment scheme is designed to evaluate the convergence and diversity of solutions, introducing dynamic penalty coefficients to balance the relationship between the two. Adaptive hierarchical sorting of solutions is performed based on the global diversity distribution to ensure the selection of optimal solutions. The performance of MOEA-AD is validated on several classic benchmark problems (with up to 20 objectives) and compared with five state-of-the-art multi-objective evolutionary algorithms. Experimental results demonstrate that the algorithm exhibits significant advantages in both convergence and diversity. Full article

In everyday scenarios, there are many challenges involving multi-objective optimization. As the count of objective functions rises to four or beyond, the problem’s complexity intensifies considerably, often making it challenging for traditional algorithms to arrive at satisfactory solutions. The non-dominated sorting evolutionary reference point-based (NSGA-III) and the grid-based evolutionary algorithms (GrEA) are two prevalent algorithms for many-objective optimization. These two algorithms preserve population diversity by employing reference point and grid mechanisms, respectively. However, they still have limitations when addressing many-objective optimization problems. Due to the uniform distribution of reference points, the reference point-based methods do not obtain good performance on problems with an irregular Pareto front, while grid-based methods do not achieve good results on problems with a regular Pareto front because of the uneven partition of grids. To address the limitations of reference point-based algorithms and grid-based approaches in tackling both regular and irregular problems, a reference point- and grid-based evolutionary algorithm with entropy is proposed for many-objective optimization, denoted as RGEA, which aims to solve both regular and irregular many-objective optimization problems. Entropy is introduced to measure the shape of the Pareto front of a many-objective optimization problem. In RGEA, a parameter $\alpha$ is introduced to determine the interval for calculating the entropy value. By comparing the current entropy value with the maximum entropy value, the reference point-based method or the grid-based method can be determined. In order to verify the performance of the proposed algorithm, a comprehensive experiment was designed on some popular test suites with 3-to-10 objectives. In addition, RGEA was compared against six algorithms without adaptive technology and six algorithms with adaptive technology. A great number of experimental results were obtained showing that RGEA can obtain good results. Full article

The construction of artificial islands is a complex engineering challenge requiring precise scheduling to optimize resource utilization, manage costs, ensure safety, and minimize environmental impacts in dynamic marine settings. In this paper, we present a multi-objective artificial island construction scheduling optimization model. This model considers many crucial factors that influence artificial island construction from 5 aspects: construction time, construction cost, project quality, resource utilization efficiency, and environmental impact. To optimize the proposed model, we propose an algorithm called Multi-objective Cooperative Differential Evolution (MOCDE). MOCDE integrates Cooperative Co-evolutionary Algorithms, and Differential Evolution to efficiently obtain the optimal schedules. To explore the performance of this model and the algorithm, extensive experiments are conducted based on real-world project data. Comparing MOCDE with established algorithms, results indicate that MOCDE improvements over previous SOTA models, achieving a reduction of 0.56% in Total Time, a decrease of 0.43% in Total Cost, and an enhancement of 7.38% in Total Quality. Besides, it also could adhere to ensure the environmental requirements. Full article

With the rapid development of radio technology and its widespread application in the military field, the electromagnetic environment in which radar communication operates is becoming increasingly complex. Among them, human radio interference makes radar countermeasures increasingly fierce. This requires radar systems to have strong capabilities in resisting electronic interference, anti-radiation missiles, and radar detection. However, array antennas are one of the effective means to solve these problems. In recent years, array antennas have been extensively utilized in various fields, including radar, sonar, and wireless communication. Many evolutionary algorithms have been employed to optimize the size and phase of array elements, as well as adjust the spacing between them, to achieve the desired antenna pattern. The main objective is to enhance useful signals while suppressing interference signals. In this paper, we introduce the dandelion optimization (DO) algorithm, a newly developed swarm intelligence optimization algorithm that simulates the growth and reproduction of natural dandelions. To address the issues of low precision and slow convergence of the DO algorithm, we propose an improved version called the chaos exchange nonlinear dandelion optimization (CENDO) algorithm. The CENDO algorithm aims to optimize the spacing of antenna array elements in order to achieve a low sidelobe level (SLL) and deep nulls antenna pattern. In order to test the performance of the CENDO algorithm in solving the problem of comprehensive optimization of non-equidistant antenna array patterns, five experimental simulation examples are conducted. In Experiment Simulation Example 1, Experiment Simulation Example 2, and Experiment Simulation Example 3, the optimization objective is to reduce the SLL of non-equidistant arrays. The CENDO algorithm is compared with DO, particle swarm optimization (PSO), the quadratic penalty function method (QPM), based on hybrid particle swarm optimization and the gravity search algorithm (PSOGSA), the whale optimization algorithm (WOA), the grasshopper optimization algorithm (GOA), the sparrow search algorithm (SSA), the multi-objective sparrow search optimization algorithm (MSSA), the runner-root algorithm (RRA), and the cat swarm optimization (CSO) algorithms. In the three examples above, the SLLs obtained using the CENDO algorithm optimization are all the lowest. The above three examples all demonstrate that the improved CENDO algorithm performs better in reducing the SLL of non-equidistant antenna arrays. In Experiment Simulation Example 4 and In Experiment Simulation Example 5, the optimization objective is to reduce the SLL of a non-uniform array and generate some deep nulls in a specified direction. The CENDO algorithm is compared with the DO algorithm, PSO algorithm, CSO algorithm, pelican optimization algorithm (POA), and grey wolf optimizer (GWO) algorithm. In the two examples above, optimizing the antenna array using the CENDO algorithm not only results in the lowest SLL but also in the deepest zeros. The above examples both demonstrate that the improved CENDO algorithm has better optimization performance in simultaneously reducing the SLL of non-equidistant antenna arrays and reducing the null depth problem. In summary, the simulation results of five experiments show that the CENDO algorithm has better optimization ability in the comprehensive optimization problem of non-equidistant antenna array patterns than all the algorithms compared above. Therefore, it can be regarded as a strong candidate to solve problems in the field of electromagnetism. Full article

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss). Full article

Many real-world expensive industrial and engineering multi-objective optimization problems (MOPs) are driven by historical, experimental, or simulation data. In such scenarios, due to the expensive cost and time required, we are only left with a small amount of labeled data to perform the optimization. These offline data-driven MOPs are usually solved by multi-objective evolutionary algorithms (MOEAs) with the help of surrogate models constructed from offline historical data. The key challenge in developing these data-driven MOEAs is that they have to replace multiple conflicting fitness functions by approximating these objective functions, which may produce cumulative approximation errors and misguide the search. In order to build a reliable surrogate model from a small amount of multi-output offline data and solve the DDMOPs, we have proposed an adaptive model selection method with a reliable individual-based model management-driven MOEA. The proposed algorithm dynamically selects between DNN and XGBoost by comparing their k-fold cross-validation MAE error, which can capture the true generalization ability of the surrogates on unseen data. Then, the selected surrogate is updated with a reliable individual selection strategy, where the individual who is closest, both in the decision and objective space, to the most preferred solution among labeled offline data is chosen. As a result, these two strategies guide the underlying MOEA to the Pareto optimal solutions. The empirical results of the ZDT and DTLZ benchmark test suite validate the use of the three state-of-the-art offline DDMOEAs, showing that our algorithm is able to achieve highly competitive results in terms of convergence and diversity for 2–3 objectives. Finally, our algorithm is applied to an offline data-driven multi-objective problem—transonic airfoil (RAE 2822) shape optimization—to validate its efficiency on real-world DDMOPs. Full article

Network dismantling is an important question that has attracted much attention from many different research areas, including the disruption of criminal organizations, the maintenance of stability in sensor networks, and so on. However, almost all current algorithms focus on unsigned networks, and few studies explore the problem of signed network dismantling due to its complexity and lack of data. Importantly, there is a lack of an effective quality function to assess the performance of signed network dismantling, which seriously restricts its deeper applications. To address these questions, in this paper, we design a new objective function and further propose an effective algorithm named as DSEDR, which aims to search for the best dismantling strategy based on evolutionary deep reinforcement learning. Especially, since the evolutionary computation is able to solve global optimization and the deep reinforcement learning can speed up the network computation, we integrate it for the signed network dismantling efficiently. To verify the performance of DSEDR, we apply it to a series of representative artificial and real network data and compare the efficiency with some popular baseline methods. Based on the experimental results, DSEDR has superior performance to all other methods in both efficiency and interpretability. Full article

Large-scale high-dimensional many-objective optimization problems (LaMaOPs) are prevalent in fields such as autonomous driving, cloud resource scheduling, and smart grids. LaMaOPs involve a large number of decision variables and multiple conflicting objectives that need to be optimized simultaneously. The challenges posed by the curse of dimensionality due to the vast number of decision variables, and the conflict between convergence and diversity caused by the numerous objective variables, make traditional optimization methods inadequate. To address these issues, this paper proposes a two-population cooperative evolutionary algorithm based on large-scale decision variable analysis (DVA-TPCEA). This algorithm integrates quantitative analysis methods for decision variables to deeply examine their impact on each objective and introduces a contribution-based objective detection method. Additionally, a dual-population cooperative evolution mechanism is employed, with targeted optimization strategies designed for convergence and diversity populations, achieving synergistic and complementary optimization between the two populations. To validate the algorithm’s effectiveness in practical applications, a large-scale container resource scheduling strategy based on the DVA-TPCEA algorithm is also proposed. The experimental results indicate that the proposed algorithm demonstrates significant advantages in both general datasets DTLZ, WFG, and LSMOP, and practical models. Full article