Constraint-handling techniques and genetic operators are two crucial components in constrained multi-objective evolutionary algorithms (CMOEAs). Recent research in most of CMOEAs has primarily focused on adaptive designs of these components to address various constrained multi-objective optimization problems (CMOPs). However, the evolutionary process of solving a CMOP can involve various characteristics, such as continuity, discreteness, degeneracy, or some combination thereof, necessitating the tailored selection of constraint-handling techniques and genetic operators across different generations. This study conceptualizes these selections as a temporal sequence of constrained handling selection, where the time means the generation number. We argue that discovering the systematic patterns within the sequence based on the historical data of applying different selections significantly improves the performance of CMOEAs in finding Pareto optimal solutions. Based on this conceptualization, we propose a CMOEA with a deep reinforcement learning model for solving CMOPs. Specifically, the deep reinforcement learning model dynamically refines the selection of constraint-handling techniques and genetic operators for upcoming generations by learning from the performance of previous selections, thereby enhancing the predictive accuracy for subsequent selections. Experiments are conducted to validate the performance of the proposed algorithm against nine CMOEAs on thirty-seven benchmark problems and an unmanned aerial vehicle path planning problem. Experimental results show that the proposed algorithm substantially outperforms the compared algorithms regarding the obtained Pareto optimal solutions. Additionally, the results verify that discovering the systematic patterns within the sequence for CMOEAs has a positive impact on solving CMOPs in terms of objective optimization and constraint satisfaction.

Dispersed computing has emerged as a promising paradigm that leverages underutilized resources from massive Internet of Things devices (IoTDs) to enhance the computing capacity at the network edge. However, existing works about the dispersed computing overlook the heterogeneous computing environment with parallel and serial computations and task reliability requirements for the hardware-constrained IoTDs, and they lack multi-objective optimization approaches to optimize the task offloading. To address the challenges, we propose a comprehensive scheme to achieve a delay-aware and economic-aware dispersed computing paradigm by using a multi-objective optimization approach. Particularly, we consider parallel processing at an edge server and serial processing at the lightweight IoTDs, and leverage the task redundancy to satisfy the task reliability requirements on the IoTD side. We further formulate a constrained multi-objective optimization problem (CMOP) aiming at jointly optimizing the task assignment, bandwidth allocation, and CPU frequency allocation to simultaneously minimize the total delay cost and the total charge cost of the tasks. To address the CMOP, we propose an improved constrained multi-objective evolutionary algorithm that employs a dual-population cooperative mechanism between two populations and a repairing constraint-handling technique. The dual-population cooperative mechanism can balance convergence toward Pareto optimality and solution diversity maintenance. The repairing constraint-handling technique is designed to guide solutions toward feasible regions, achieving efficient exploration of complex constrained search spaces. Simulation results demonstrate the superiority of our algorithm in seeking the better-converged and better-distributed Pareto optimal solutions to well address the tradeoffs between the two objectives.

Cooperative perception constitutes a critical technology to enhance situational awareness of vehicular users (VUs) by fusing multi-source observation data. Existing approaches employ either vehicles or road infrastructure as fusion platforms. However, vehicle-based approaches suffer from severe occlusions that compromise perception reliability, while infrastructure-based approaches are constrained by fixed coverage ranges that restrict spatial perception, thereby failing to achieve both reliable and comprehensive perception simultaneously. To overcome these limitations, we propose an uncrewed aerial vehicle (UAV)-enabled cooperative perception system where a UAV operates in a cyclic process: it adjusts its position to respond to VU requests, collects observation data, and returns the compressed fusion results to the VUs. In each cycle, we jointly optimize decisions regarding UAV trajectory, request response, data collection, compression degree of the fusion results, and resource allocation to balance fusion reliability and service latency, subject to UAV kinematics, task assignment, resource allocation, and latency constraints. We formulate this optimization problem as a dynamic constrained multi-objective optimization problem featuring cascaded dependencies where the request response, data collection, and resource allocation should be determined sequentially due to the inherent logic of cooperative perception. To solve this problem, we design an evolutionary algorithm based on a cascaded dependency generation strategy in which decision variables are generated according to their dependency order. Experimental results demonstrate the superior solution performance of our algorithm over four baseline algorithms. This study advances cooperative perception for vehicular networks by providing a UAV-enabled solution ensuring reliable fusion and timely service under dynamic traffic conditions.

As a privacy-preserving solution, federated learning (FL) demonstrates great potential in distributed model training, but limited bandwidth, particularly in near-field communication (NFC)-based systems, emerges as a key bottleneck by restricting the number of participating clients. To address this challenge, over-the-air FL leverages the superposition property of wireless multiple-access channels, enabling faster model training and accommodating more clients, even in bandwidth-constrained scenarios like NFC. However, due to its analog-integrated nature, the FL performance is also affected by other factors, such as channel noise. These motivate us to consider how the selected client set and channel noise affect FL performance. To explore this concern, in this article, we consider an over-the-air FL system with analog gradient aggregation and analyze the impact of the selected client set and channel noise on FL training performance. The theoretical analysis effectively shows the importance of the clients’ number and the power scaling factor to the FL training performance. Based on the theoretical analysis, we transform the global optimization problem into the client selection problem and propose a dynamic client selection scheme to optimize the training performance under the aggregation error constraint. Experimental results demonstrate that our proposed scheme can boost FL by speeding up the convergence of the global model (at least 35%) and saving energy consumption.

Both dual-population and two-phase strategies are effective for utilizing infeasible solution information and significantly enhancing the ability of algorithms to solve constrained multi-objective optimization problems. However, most existing algorithms tend to underperform when facing problems with complex constraints. To address these issues, a constrained multi-objective evolutionary algorithm named DPTPEA, which combines dual-population and two-phase strategies, is proposed in this paper. DPTPEA employs two collaborative populations (the exploitive population and the tractive population) and divides the evolutionary process of the tractive population into two phases (Phase 1 and Phase 2). In Phase 1, the tractive population ignores constraints and drags the exploitive population across the infeasible region by sharing offspring information. In Phase 2, the tractive population adopts the epsilon-constrained method to converge toward the constrained Pareto front and to guide the exploitive population exploiting different feasible regions. Moreover, a dynamic cooperation strategy, a boundary point direction sampling strategy, and a dynamic environmental selection are proposed to improve the exploration ability of tractive population for solving complex problems. Comprehensive experiments on three popular test suites demonstrate that DPTPEA outperforms seven state-of-the-art algorithms on most test problems.

In recent years, many constrained multi-objective evolutionary algorithms have been proposed to address com-plex constrained multi-objective optimization problems and have shown significant performance. However, when facing challenging constrained multi-objective optimization problem, some algorithms struggle to explore all feasible regions. To address this issue, this paper proposes a feasibility tracking strategy. By setting an expansion value and controlling constraint relaxation, adaptive adjustment of the reference vectors simulates an ex-panded narrow feasible region. After the preliminary exploration of the feasible region, a new set of reference vectors is generated to ensure the existence of feasible regions in the direction of the new reference vectors, thereby increasing the density of individuals within the feasible region. Experimental results on a series of benchmark problems demonstrate that the proposed algorithm is quite effective compared to other state-of-the-art constrained multi-objective evolutionary algorithms.

An unmanned aerial vehicle (UAV)-enabled intelligent transportation system utilizes a set of UAVs to collect and process surveillance data for transportation management. Subsequently, the processing results of the UAVs are transmitted to a control center that makes a centralized transportation management decision based on the fusion of all processing results. When performing the monitoring tasks, the UAVs can access to an edge server for offloading. To reduce the energy consumption and improve the fusion performance, the control center schedules the UAVs to perform the tasks in an energy-efficient manner while synchronizing the completion time of the UAVs. As a result, the control center studies a constrained multi-objective optimization problem (CMOP), in which two objectives, i.e., the total energy consumption of the UAVs and total completion time difference among the UAVs, are simultaneously considered. To tackle the CMOP, we develop an improved constrained multi-objective evolutionary algorithm. Particularly, we design an improved genetic operator and repairing constraint-handling technique to improve the overall performance of the proposed algorithm in seeking Pareto optimal solutions for the CMOP. Numerical results demonstrate that compared with the baseline algorithms, the proposed algorithm has great advantages in finding better solutions with the enhanced diversity and convergence for the CMOP.

Software defect prediction technology aids the reliability assurance team in identifying defect-prone code and assists the team in reasonably allocating limited testing resources. Recently, researchers assumed that the topological associations among code fragments could be harnessed to construct defect prediction models. Nevertheless, existing graph-based methods only concentrate on features of single-view association, which fail to fully capture the rich information hidden in the code. In addition, software defects may involve multiple code fragments simultaneously, but traditional binary graph structures are insufficient for representing these multivariate associations. To address these two challenges, this article proposes a multiview hypergraph representation learning approach (MVHR-DP) to amplify the potency of code features in defect prediction. MVHR-DP initiates by creating hypergraph structures for each code view, which are then amalgamated into a comprehensive fusion hypergraph. Following this, a hypergraph neural network is established to extract code features from multiple views and intricate associations, thereby enhancing the comprehensiveness of representation in the modeling data. Empirical study shows that the prediction model utilizing features generated by MVHR-DP exhibits superior area under the curve (AUC), F-measure, and matthews correlation coefficient (MCC) results compared to baseline approaches across within-project, cross-version, and cross-project prediction tasks.

To provide a dependency-aware application, multiple unmanned aerial vehicles (UAVs) are employed to serve a ground user with a set of interdependent tasks. This leads to a new computing paradigm called as multi-UAV-enabled aerial edge computing (MU-AEC). For the large-scale application of MU-AEC, both the task-centric objective and UAV-centric objective should be simultaneously considered. Thus, we focus on the joint interdependent task scheduling and energy balancing for MU-AEC by using a multiobjective optimization approach, which enables a decision maker to identify the optimal solutions corresponding to the best feasible tradeoffs between the two objectives. A constrained multiobjective optimization problem involving two objectives: 1) the makespan minimization of all tasks and 2) energy balancing among different UAVs, is formulated. In the solution methodology, we propose a constrained decomposition-based multiobjective evolution algorithm. To quickly seek more superior solutions, a local search mechanism by utilizing the objective information, and an improved genetic operator are proposed for remarkable performance improvements. Finally, numerical results demonstrate that compared with the baseline algorithms, our algorithm achieves both advantages in increasing the convergence and diversity of the solutions.

When solving constrained multiobjective optimization problems (CMOPs), the most commonly used way of measuring constraint violation is to calculate the sum of all constraint violations of a solution as its distance to feasibility. However, this kind of constraint violation measure may not reflect the distance of an infeasible solution from feasibility for some problems, for example, when an infeasible solution closer to a feasible region does not have a smaller constraint violation than the one farther away from a feasible region. Unfortunately, no set of artificial benchmark problems focusing on this area exists. To remedy this issue, a set of CMOPs with deceptive constraints is introduced in this article. It is the first attempt to consider CMOPs with deceptive constraints (DCMOPs). Based on our previous work, which designed a set of directed weight vectors to solve CMOPs, this article proposes a cooperative framework with an improved version of directed weight vectors to solve DCMOPs. Specifically, the cooperative framework consists of two switchable phases. The first phase uses two subpopulations-one to explore feasible regions and the other to explore the entire space. The two subpopulations provide useful information about the optimal direction of objective improvement to each other. The second phase aims mainly at finding Pareto-optimal solutions. Then an infeasibility utilization strategy is used to improve the objective function values. The two phases are switchable based on the information found to date at any time in the evolutionary process. The experimental results show that this method significantly outperforms the algorithms with which it is compared on most of the DCMOPs, in terms of reliability and stability in finding a set of well-distributed optimal solutions.

Despite the effectiveness of the decomposition-based multi-objective evolutional algorithm (MOEA/D-M2M) in solving continuous multi-objective optimization problems (MOPs), its performance in addressing 0/1 multi-objective knapsack problems (MOKPs) has not been fully explored. In this paper, we use MOEA/D-M2M with an improved greedy repair strategy to solve MOKPs. It first decomposes an MOKP into a number of simple optimization subproblems and solves them in a collaborative way. Each subproblem has its own subpopulation, and then an improved greedy strategy is introduced to improve the performance of the proposed algorithm on MOKPs. Therein, a weight vector chosen randomly from a corresponding subpopulation is utilized to repair infeasible individuals or improve feasible individuals to have a better fitness, which improves the convergence of the population. Experimental studies on a set of test instances indicate that the MOEA/D-M2M with the improved greedy strategy is superior to MOGLS and MOEA/D in terms of finding better approximations to the Pareto front.

This paper proposes two constraint-handling techniques based on multiobjective optimization with biased dynamic weights for constrained optimization problems (COPs). Transforming a COP into an unconstrained biobjective optimization, two popular strategies based on decomposition, i.e. Tchebycheff approach (TEA) and weighted sum approach (WSA) are used in this paper respectively. In order to keep a good balance between convergence and diversity of the population, this paper uses the weights, which are designed with bias and change dynamically as the generation increases, to select different individuals with smaller objective values and lower degree of constraint violations. Furthermore, 13 benchmark test functions are used to investigate the effectiveness of TEA and WSA. Experimental results demonstrate that TEA not only works better than WSA, but also is superior to the compared algorithms, i.e. MDPE, GDE and SR in terms of reliability and stabilization of converging to a global solution.

In this paper, we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problems (CMOPs), named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. Moreover, a novel constraint handling scheme based on the boundary search and archive is proposed. Each subproblem has one archive, including a subpopulation and a temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation, while the temporary register consists of those individuals ever found before. To improve the efficiency of the algorithm, the boundary search method is designed. This method makes the feasible individuals with a higher probability to perform genetic operator with the infeasible individuals. Especially, when the constraints are active at the Pareto solutions, it can play its leading role. Compared with two algorithms, i.e. CMOEA/D-DE-CDP and Gary’s algorithm, on 18 CMOPs, the results show the effectiveness of the proposed constraint handling scheme.

This paper proposes an improved version of the single objective optimization evolutionary algorithm based on Covariance Matrix Learning and Searching Preference (CMLSP), named ICMLSP. ICMLSP uses the same way with CMLSP to generate high quality solutions by sampling a multivariate Gauss distribution, which uses the best solutions found so far as its mean value. However, unlike the previous one, ICMLSP uses different covariance matrix learning philosophy, that is, the principal component analysis (PCA) method is used to estimate the covariance matrix. Furthermore, ICMLSP tends to use smaller population size than CMLSP to achieve a faster search. In order to get enough information for a reliable estimation, a new cumulation strategy is designed in ICMLSP. Solutions are selected from an archive set which stores the best λ individuals in present population and last t(t >= 1) populations to estimate the covariance matrix. A new adaptive rule, which makes use of the history successful information to generate different searching step from two different Cauchy distributions, is designed for ICMLSP to balance global exploration and local exploitation. Finally, the performance of the ICMLSP has been tested on 15 noiseless optimization problems designed for the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization. The results are reported at the end of this paper.