Uncovering the direct causal relationships between decision variables and optimization objectives can significantly simplify the complexity of optimization problems. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) fail to address constrained multi-objective optimization from this perspective. To bridge this gap, this study introduces a novel algorithm, CI-CMOEA (Causal Intervention-based CMOEA), which leverages causal intervention techniques to enhance optimization performance. CI-CMOEA begins by constructing a causal relationship network that captures the interactions between decision variables and optimization objectives. Using this network, a genetic operator with a causal relationship mask is designed to group decision variables based on their causal impact on the objectives. By focusing genetic operations on key variables with significant causal influence, the algorithm effectively guides the evolutionary optimization process towards better solutions. To further improve performance, CI-CMOEA employs a dual-population collaboration mechanism. One population operates under relaxed epsilon constraints to explore the solution space, while the other disregards constraints to enhance convergence. Preliminary experiments on the LIR-CMOP test suite demonstrate that CI-CMOEA not only accurately identifies the causal relationships between decision variables and objectives but also outperforms eight state-of-the-art CMOEAs in terms of IGD, IGD+ and HV metrics, showcasing its superior optimization performance and reliability.

Accurate retinal vessel segmentation plays a critical role in the early detection and monitoring of ophthalmic diseases. In this work, we propose a novel retinal vessel segmentation method that integrates Neural Architecture Search (NAS) with a U-shaped encoder-decoder network, optimized using particle swarm optimization (PSO). The framework automates the design of scalable architectures by exploring an extensible search space built with lightweight construction modules, including 3 × 3 convolutions, batch normalization, attention modules, and residual connections. Experimental results on the DRIVE and CHASE_DB1 datasets demonstrate that the searched model achieves superior segmentation accuracy with the fewest parameters (only 0.04M) compared to existing methods. Furthermore, the model exhibits competitive performance on the crack bench-mark dataset CrackLS315, highlighting the strong generalization capability of the searched architecture. In conclusion, the proposed method achieves an optimal balance between segmentation accuracy and model complexity, demonstrating its potential for clinical applications.

To address slow convergence and formation maintenance challenges in swarm robotic entrapment tasks, a predictive entrapment control algorithm that combines gene regulatory network and sliding mode control (GRN-SMC) is proposed. First, to stabilize the target position information generated by the hierarchical GRN, a novel sorting rule is designed. Then, an artificial neural network (ANN) is employed to perform on-line prediction of the swarm robots’ kinematic states. These predicted values are then fed into a specifically designed sliding mode controller, which ultimately outputs the optimal control velocities for the swarm robots. Comparative simulation experiments with three state-of-the-art algorithms demonstrate that our method achieves significant improvements in tracking accuracy(error reduced by 82%), single-iteration execution time(reduced by 29%), and formation maintenance (formation integrity increased by 34%). Furthermore, physical robot experiments demonstrate that even in the presence of unknown external disturbances (such as ground slippage) and robot positioning errors (±0.1 m, ±5°), the proposed algorithm still exhibits excellent robustness.

Real-world production scenarios often involve multiobjective optimization problems with intricate constraints. Although there has been a growing interest in multiobjective problems with complex constraints, such as the vehicle routing problem with time windows, existing multiobjective evolutionary optimization techniques still face significant challenges, particularly when addressing the fragmented and narrow feasible regions that arise from these constraints. Our research introduces a refined framework tailored for complex constrained multiobjective evolutionary optimization. The methodology conducts an initial strong-weak analysis to categorize constraints and merges each strong constraint with all weak constraints to form subsets. Each subset, combined with the original objective functions, defines a subproblem. Independent optimization of the original problem and subproblems is carried out by utilizing multiple populations. Information acquired from the subproblems’ populations is transferred into the population of the original issue, thereby expediting the detection of the feasible region and simplifying the resolution of the original problem. The efficacy of our innovative algorithm, when benchmarked against traditional constrained multiobjective evolutionary algorithms across 72 test functions, has demonstrated superior convergence, diversity, and competitiveness.

In the field of drilling engineering, the design and optimization of well trajectories are crucial. This study focuses on optimizing key aspects such as the length of the well trajectory, drill string torque, the energy of the well-profile, and accuracy in reaching the target. This problem encompasses eleven complex nonlinear constraints and four conflicting objectives, presenting challenges for traditional mathematical programming methods. To tackle this problem, we introduce a novel constrained many-objective optimization algorithm, named PPS-NSGA-III. The proposed algorithm partitions the objective space into subspaces, using NSGA-III to find Pareto optimal solutions in each, enhancing diversity. The push-and-pull search framework is employed to overcome local optima in each subproblem, accelerating overall convergence. Through a comparative analysis with some evolutionary algorithms, PPS-NSGA-III has shown superior performance. It delivers more effective design solutions with lower risk, reduced cost, and a higher drilling encounter rate in the proposed well trajectory optimization model.

Compared with traditional synthetic wideband signals, synthetic ultrawideband (UWB) signals with higher range resolution can obtain more information for target identification. The stepped-frequency chirp signal (SFCS) based on dechirp processing can simultaneously achieve a UWB, a high data rate and a low sampling rate. In this paper, a synthetic UWB range profiling method for high-speed targets based on phase-derived velocity measurement (PDVM) is proposed. High-precision velocity compensation is key to synthetic UWB range profiling for high-speed targets. Thus, the PDVM based on the pulses at the same carrier frequency is adopted to obtain high-precision velocity measurement results. Then, based on PDVM results, the synthetic UWB range profiling method in the time domain is analyzed in detail, which mainly contains time shift, linear phase correction and constant phase correction. In the phase correction process, the compensation of intrapulse Doppler modulation, range migration and tracking gate movement is emphatically analyzed. In addition, to guide the implementation in radar systems, the phase hopping caused by parameter estimation error is theoretically derived. Finally, simulation results and raw data are presented to verify the performance of the proposed method.

In real-world applications, there are some constrained multi-objective problems where the evaluation of objectives is expensive and the evaluation of constraints is cheap. Currently, few studies have focused on solving expensive constrained multi-objective optimization problems (ECMOPs), and they usually assume that the constraints of ECMOPs are also expensive. In this paper, we propose a surrogate-ensemble assisted coevolutionary algorithm (SEACoEA) for ECMOPs with inexpensive constraint evaluation. First, a feasible sampling strategy is designed to initialize the population in the feasible regions. Next, two populations are set to optimize the original ECMOP and the problem without considering constraints, respectively. To improve the search efficiency, we redesigned the objective function of the surrogate-ensemble model. Finally, a new infill strategy is proposed to select candidate individuals from each population for real evaluation. Experimental results show that the proposed algorithm performs significantly better on most MW problems compared to several state-of-the-art algorithms.

The dynamic multi-objective optimization problems (DMOPs) have brought great challenges to the traditional evolutionary optimization algorithms because of their constantly changing Pareto set(PS) and Pareto front(PF). In order to track the change of PS and PF quickly and keep the diversity of population, prediction-based methods have shown great prospects. However, most of the current methods utilize linear models to predict the changing PS. When the PS between different environments has nonlinear relationship, this kind of method can not accurately predict the PS at a new environment. In this paper, a dynamic multi-objective evolutionary optimization algorithm based on long short-term memory network (LSTM) prediction is proposed. In this algorithm, The first step is to calculate the center point of the obtained PS. The center points at different time form a time series. Then the LSTM model is trained by using the time series as training samples. Moreover, the center of the new PS are predicted by the obtained model. Because LSTM can make full use of historical information and fit the nonlinear relationship between the PS, the prediction accuracy can be guaranteed. Finally, a population generation strategy is used to generate an initialized population with both convergence and diversity. The proposed algorithm is tested on DF benchmark function. Experiments results show that the proposed algorithm can effectively handle DMOPs and has shown its superiorityin comparison with state-of-the-art algorithms.

The micromotion features of a target contain unique structural information and motion information about the target, which can be used as an important basis for target classification and recognition. To achieve high-accuracy three-dimensional micromotion measurements in the clutter environment, a stationary clutter suppression method for three-dimensional micromotion measurements based on wideband radar amplitude and phase information is proposed in this paper. This method is capable of accurately measuring the trajectory of small amplitude micromotion with the high-accuracy phase-derived angle measurement (PDAM) and phase-derived range measurement (PDRM). However, the measurement accuracy of three-dimensional micromotion deteriorates sharply when clutter exists. Thus, the main challenge that we overcome is achieving high-accuracy clutter estimation based on wideband radar measurements. The clutter suppression method is proposed by utilizing wideband radar amplitude and phase of multiple range cells jointly. Finally, simulation and experiment are presented to validate the feasibility and effectiveness of the proposed method under stationary clutter conditions.

The phase-derived velocity measurement (PDVM) technique can achieve a high measurement accuracy at the phase level and thus has great application prospects in the field of micromotion feature extraction and target recognition. To achieve a PDVM with a low signal-to-noise ratio (SNR), a PDVM method based on the generalized Radon–Fourier transform (GRFT) is proposed in this article. The main challenges that we overcome are phase extraction and phase ambiguity resolving under the condition of a low SNR. By utilizing the GRFT to estimate the target motion parameters, the echo peak position can be reconstructed, and then the peak phase value can be extracted. In the meantime, the phase ambiguity integer can be resolved based on the rough velocity estimation results obtained by the GRFT, and the phase ambiguity resolving can be realized at a low SNR. In addition, to suppress the influence of noise on the extracted phase, a filter design method based on the target motion characteristics is proposed to further improve the accuracy of the PDVM. In the simulation, the performance of the proposed method under different motion models and different SNR conditions is analyzed, and the effectiveness of the proposed method under low-SNR conditions is verified. Compared with directly using the GRFT, the proposed method has the advantages of strong applicability to different motion models and low computational load.

Recently, many methods based on hand-designed convolutional neural networks (CNNs) have achieved promising results in automatic retinal vessel segmentation. However, these CNNs remain constrained in capturing retinal vessels in complex fundus images. To improve their segmentation performance, these CNNs tend to have many parameters, which may lead to overfitting and high computational complexity. Moreover, the manual design of competitive CNNs is time-consuming and requires extensive empirical knowledge. Herein, a novel automated design method, called Genetic U-Net, is proposed to generate a U-shaped CNN that can achieve better retinal vessel segmentation but with fewer architecture-based parameters, thereby addressing the above issues. First, we devised a condensed but flexible search space based on a U-shaped encoder-decoder. Then, we used an improved genetic algorithm to identify better-performing architectures in the search space and investigated the possibility of finding a superior network architecture with fewer parameters. The experimental results show that the architecture obtained using the proposed method offered a superior performance with less than 1% of the number of the original U-Net parameters in particular and with significantly fewer parameters than other state-of-the-art models. Furthermore, through in-depth investigation of the experimental results, several effective operations and patterns of networks to generate superior retinal vessel segmentations were identified. The codes of this work are available at https://github.com/96jhwei/Genetic-U-Net.

In this article, we propose a phase-derived velocity measurement (PDVM) method for high-speed spatial targets based on the stepped-frequency chirp signal (SFCS). This method is capable of accurately measuring the velocity of high-speed targets and yields root-mean-squared error values at the level of centimeters per second; therefore, it has great potential for measuring the micromotion of targets and is of significant importance for target recognition. The traditional phase-derived measurement method is not applicable for high-speed targets. The main challenge that we have solved is how to extract the echo phase from the high-resolution range profile, which is corrupted by range migration, intrapulse motion, and range straddling under high-speed target conditions. To guide the implementation of the proposed method in radar systems, constraint conditions for the compensation accuracy are thoroughly derived and systematically justified under different radar parameter settings. The simulation results are presented to validate the high accuracy of the method under various circumstances. In addition, the small-amplitude micromotion measurement capability of the proposed method is verified, and reconstruction of the target micromotion trajectory is demonstrated.

Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs-MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)-C-MOEA/DD and C-NSGA-III-are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

This paper proposes an improved$\epsilon$constrained handling method (IEpsilon) for solving constrained single-objective optimization problems (CSOPs). The IEpsilon method adaptively adjusts the value of$\epsilon$according to the proportion of feasible solutions in the current population, which has an ability to balance the search between feasible regions and infeasible regions during the evolutionary process. The proposed constrained handling method is embedded to the differential evolutionary algorithm LSHADE44 to solve CSOPs. Furthermore, a new mutation operator DE/randr1*/1 is proposed in the LSHADE44-IEpsilon. In this paper, twenty-eight CSOPs given by “Problem Definitions and Evaluation Criteria for the CEC 2017 Competition on Constrained Real-Parameter Optimization” are tested by the LSHADE44-IEpsilon and four other differential evolution algorithms CAL-SHADE, LSHADE44+IDE, LSHADE44 and UDE. The experimental results show that the LSHADE44-IEpsilon outperforms these compared algorithms, which indicates that the IEpsilon is an effective constraint-handling method to solve the CEC2017 benchmarks.

Automated optic disk (OD) detection plays an important role in developing a computer aided system for eye diseases. In this paper, we propose an algorithm for the OD detection based on structured learning. A classifier model is trained based on structured learning. Then, we use the model to achieve the edge map of OD. Thresholding is performed on the edge map, thus a binary image of the OD is obtained. Finally, circle Hough transform is carried out to approximate the boundary of OD by a circle. The proposed algorithm has been evaluated on three public datasets and obtained promising results. The results (an area overlap and Dices coefficients of 0.8605 and 0.9181, respectively, an accuracy of 0.9777, and a true positive and false positive fraction of 0.9183 and 0.0102) show that the proposed method is very competitive with the state-of-the-art methods and is a reliable tool for the segmentation of OD.

Solving constrained multi-objective optimization problems is a difficult task, it needs to simultaneously optimize multiple conflicting objectives and a number of constraints. This paper first reviews a number of popular constrained multi-objective evolutionary algorithms (CMOEAs) and twenty-three widely used constrained multi-objective optimization problems (CMOPs) (including CF1-10, CTP1-8, BNH, CONSTR, OSY, SRN and TNK problems). Then eight popular CMOEAs with simulated binary crossover (SBX) and differential evolution (DE) operators are selected to test their performance on the twenty-three CMOPs. The eight CMOEAs can be classified into domination-based CMOEAs (including ATM, IDEA, NSGA-II-CDP and SP) and decomposition-based CMOEAs (including CMOEA/D, MOEA/D-CDP, MOEA/D-SR and MOEA/D-IEpsilon). The comprehensive experimental results indicate that IDEA has the best performance in the domination-based CMOEAs and MOEA/D-IEpsilon has the best performance in the decomposition-based CMOEAs. Among the eight CMOEAs, MOEA/D-IEpsilon with both SBX and DE operators has the best performance on the twenty-three test problems.

Multi-objective evolutionary algorithms (MOEAs) have been widely used in solving multi-objective optimization problems. A great number of the-state-of-art MOEAs have been proposed. These MOEAs can be classified into the following categories: decomposition-based, domination-based, indicator-based, and probability-based methods. Among them, the first four categories belong to non-model based methods, while the fifth one is considered to be model-based method, in which machine learning techniques are often used to build the models. Recently, embedding machine learning mechanisms into MOEAs is becoming popular and promising. In this paper, a relatively thorough review on both traditional MOEAs and those equipped with machine learning mechanisms are made, with the aim of shedding light on the future development of this emerging research field.

This paper proposes a new constraint handling method named Angle-based Constrained Dominance Principle (ACDP). Unlike the original Constrained Dominance Principle (CDP), this approach adopts the angle information of the objective functions to enhance the population's diversity in the infeasible region. To be more specific, given two infeasible solutions, if the angle of the solutions is greater than a given threshold, they are considered to be non-dominated by each other. For a feasible solution and an infeasible solution, if the angle of the solutions is less than a given threshold, the feasible solution is better, otherwise they are non-dominated. To verify the proposed constraint handling approach ACDP, eight test problems CMOP1 to CMOP8 are introduced. The suggested algorithm MOEA/D-ACDP is compared with MOEA/D-CDP and NSGA-II-CDP on CMOP1 to CMOP8. The experimental results demonstrate that ACDP performs better than CDP in the framework of MOEA/D, and MOEA/D-ACDP is significantly better than NSGA-II-CDP, especially on the test instances with the very low ratio of feasible region against the whole objective space.