Large-scale multi-objective optimization problems (LSMOPs) face computational challenges due to high-dimensional search spaces and variable correlations. Existing algorithms often struggle to balance convergence, diversity, and efficiency in high-dimensional scenarios. We propose ATSPCA, a two-stage adaptive algorithm employing PCA-guided perturbation. The first stage uses PCA-based dynamic variable screening to identify key decision variable groups, applying adaptive Gaussian perturbation to guide optimization. The second stage enhances convergence and diversity through an improved competitive swarm optimizer (CSO) and reference pointbased environmental selection. An adaptive transition mechanism bridges the two stages. Tested on LSMOP and WFG benchmarks against state-of-the-art large-scale multi-objective evolutionary algorithms(LSMOEAs), ATSPCA demonstrates superior performance.
This study addresses the Container Stowage Planning Problem (CSPP) from a perspective of vessel-yard collaboration. A bi-level multi-objective evolutionary algorithm based on NSGA-II is proposed, in which the upper-level assigns the containers to bays and the lower-level decides specific position for each container. The algorithm employs adaptive evolutionary strategies to enhance diversity. The result of extensive experiments demonstrates the superiority of the proposed method and practical value for real-world scale CSPP in container terminal.
Community detection in social networks plays a vital role in understanding structural influence and optimizing promotional strategies. This study proposes a capacity-constrained community detection problem (CCDP) model to identify the most influential community under practical limitations of promotion opportunities. Given the NP-hard nature of the problem, an efficient memetic algorithm is developed. Extensive experiments demonstrate its superiority over CPLEX and several heuristic and community detection approaches. Further analysis on convergence, parameter sensitivity, and crossover operator provides deeper insights into the algorithm’s performance.
The successful manipulation of a robotic arm is crucial in industry, in surgical fields, or in space exploration. Many previous studies on evolutionary or genetic algorithms successfully determined effective configurations of arm joints in order to reach a specific target. Nevertheless, most existing methods face challenges in obstacle avoidance, as it might be required to find an extremely specific and not direct result to surpass a certain obstacle, causing local maxima to be found. This paper proposes the use of a known path-finding method such as the A* Search algorithm establish an optimized route for the arm to extend over, before the evolutionary algorithm is applied to determine the configurations of arm joints. Specifically, the process starts with a predefined scenario containing both the target, the starting point and a set of obstacles. The A* algorithm is then used to map a route, which is divided into a set of targets that the robotic arm must follow to reach its final destination. The evaluation function used in this project ensures that proximity to obstacles negatively affects individual fitness. The experimental findings show that this strategy is able to find a way around local maxima quickly and outperform previous purely evolutionary approaches in both 2D and 3D simulated environments.
In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have been extensively utilized to address expensive optimization problems. However, it becomes a great challenge how to train the surrogate using the dynamic data distributed across multiple clients due to privacy and security concerns. To address this issue, this paper proposes a meta-learning-based federated surrogate-assisted evolutionary algorithm for dynamic expensive optimization problems. The proposed algorithm utilizes a gradient-based meta-training algorithm to extract the experiences of historical optimization environments as the initial surrogate parameters in the new environment and then utilizes limited data samples for fine-tuning to achieve fast surrogate adaptation in the new environment. In addition, we utilize differential privacy techniques to add artificial noise to the parameters of the global and local surrogates to protect the private information of clients. Experimental results on a set of dynamic optimization benchmark problems with different settings show that the proposed federated surrogate-assisted evolutionary algorithm can achieve superior optimization performance while protecting data privacy.
Sequential recommendation (SR) aims to predict users’ next-item preferences by analyzing their historical interaction sequences. Most existing SR models primarily focus on user preferences for a single objective of item relevance; they often overlook users’ personalized preferences for diversified item attributes. Although recent studies have attempted to address this limitation, efficiently resolving the inherent accuracy-diversity trade-off remains an open challenge. Drawing inspirations from multiobjective optimization and evolutionary multitasking, this paper proposes a multiobjective clustering-guided multitasking framework (MCGM-SR) that reconciles the two competing objectives in sequential recommendation. To enable knowledge transfer across homologous preference patterns, a user-level multiobjective clustering mechanism is introduced to group users with similar behavioral trajectories into objective-oriented clusters. Within each cluster, a multiobjective multitasking algorithm facilitates synergistic optimization across tasks to improve convergence efficiency. Extensive experiments on two real-world public datasets demonstrate that MCGM-SR achieves significant improvements in both accuracy and diversity metrics, compared to state-of-the-art sequential models and their diversified baselines. Further ablation studies reveal that the proposed clustering method significantly enhances optimization performance by effectively facilitating knowledge transfer.
Electric vehicles (EVs) are increasingly utilized in logistics and distribution to expedite achieving carbon peaking and neutrality goals, drawing considerable attention to the Electric Vehicle Routing Problem (EVRP). This study investigates the Multi-Depot Half-Open Time-Dependent Electric Vehicle Routing Problem (MDHOTDEVRP) and aims to improve coordination and distribution efficiency among logistics depots. This problem involves multiple depots, with EVs allowed to return to the nearest depot after completing their distribution tasks. We propose a hybrid method to solve the MDHOTDEVRP by integrating granular ball (GB) computing with the Ant Colony Optimization (ACO) algorithm. Firstly, enhanced k-means clustering is utilized to allocate customers to EVs. Then, customers within each cluster are subdivided into multiple GBs, with the paths of these GBs being scheduled. Finally, the ACO algorithm establishes routes within each GB. Experimental results indicate that the proposed GB-ACO algorithm efficiently allocates charging stations and plans distribution routes in scenarios with clustered distributions.
Existing metaheuristic algorithms often struggle to balance diversity, convergence, and stability when solving complex, high-dimensional multiobjective optimization problems due to their sensitivity to parameter settings. To address this issue, we propose CMOPSO/DR, an adaptive co-competitive multiobjective PSO algorithm incorporating dimensionality reduction. First, the denoising adversarial autoencoder (DAAE) network is automatically determined to construct a compressed coordinate system (CCS) to accelerate convergence. Second, simulated binary crossover (SBX) is used to enhance both the diversity and stability of the algorithm. Finally, the co-competitive strategy of coupling CCS and SBX is developed to respond to various optimization demands at different optimization stages adaptively. The experimental results show that CMOPSO/DR performs better than other advanced optimization algorithms on various benchmark and real-world problems, and it achieves efficient acquisition of high-quality optimal solutions, demonstrating its obvious improvements in theory and application.
Code smells signal poor software design that can prevent maintainability and scalability. Identifying code smells is difficult because of the large volume of code, considerable detection expenses, and the substantial effort needed for manual tagging. Although current techniques perform well in within-project situations, they frequently struggle to adapt to cross-project environments that have varying data distributions. In this paper, we introduce CLADES (Cross-project Learning and Adaptation for Detection of Code Smells), a hybrid evolutionary approach consisting of three main modules: Initialization, Evolution, and Adaptation. The first module generates an initial population of decision tree detectors using labeled within-project data and evaluates their quality through fitness functions based on structural code metrics. The evolution module applies genetic operators (selection, crossover, and mutation) to create new offspring solutions. To handle cross-project scenarios, the adaptation module employs a clustering-based instance selection technique that identifies representative instances from new projects, which are added to the dataset and used to repair the decision trees through simulated annealing. These locally refined decision trees are then evolved using a genetic algorithm, thus enabling continuous adaptation to new project instances. The resulting optimized decision tree detectors are then employed to predict labels for the new unlabeled project instances. We assess CLADES across five open-source projects and we show that it has a better performance with respect to baseline techniques in terms of weighted F1-score and AUC-PR metrics. These results emphasize its capacity to effectively adjust to different project environments, facilitating precise and scalable detection of code smells while minimizing the need for manual review, contributing to more robust and maintainable software systems.
As the dimensionality of the decision space in multi-objective optimization problems increases, the decision space expands exponentially, presenting significant challenges to the search efficiency of traditional multi-objective evolutionary algorithms in large-scale multi-objective optimization problems. To quickly locate promising search regions in the vast decision space, this paper proposes utilizing denoising diffusion probabilistic models to generate promising solutions, based on which a novel elite-guided large-scale multi-objective evolutionary algorithm is introduced. Specifically, in our proposed method, the population is divided into elite and poor solutions, with each poor solution paired with an elite solution. The elite solutions serve as generation targets, and their paired poor solutions act as conditions during the training of the generative model. Our approach allows the model to not only capture the distribution of elite solutions but also effectively model the evolutionary trajectory from poor solutions to elite solutions. The entire population is used as conditions, and the trained generative model generates ideal positions, which are then updated to produce offspring solutions. Experimental results on large-scale multi-objective benchmark functions demonstrate that the proposed algorithm outperforms four state-of-the-art large-scale multi-objective evolutionary algorithms.
This paper investigates heuristic initialisation for shortest path search on multi-objective multigraphs using genetic algorithms. An initialised solution comprises a node path and an edge path. The state-of-the-art initialisation method encodes node paths into random-key node priority sequences and assigns random values to represent the indices of traversed parallel edges, where the node priority is a combination of hop count and a random value. However, this method has three limitations. (i) Hop counts are computed using Dijkstra’s algorithm, incurring non-negligible computational cost. (ii) The upper bound of the random values added to hop counts is defined by a hyperparameter, requiring tedious parameter tuning. (iii) Heuristic information about edges is ignored, despite its potential to improve solution quality. To address these issues, this paper first eliminates the randomisation hyperparameter and constrains randomness to the range [0, 1). Second, a heuristic edge initialisation method is proposed. Finally, to reduce the computational burden of Dijkstra’s algorithm, a learning-based node priority generation method is devised using neural networks trained on node embeddings. Experiments on benchmark multi-objective multigraphs show that (i) combining hop counts with randomness in [0, 1) and heuristic edge initialisation outperforms the state-of-the-art method, and (ii) with limited training data, the learning-based node priorities surpass entirely random node priorities and are comparable to state-of-the-art performance, highlighting their potential in large-scale and dynamic scenarios.
Learning to optimize (L2O) is a paradigm designed to train a learnable optimizer that can quickly infer optimal solutions with less computation. While supervised learning (SL) and reinforcement learning (RL) are prevalent, SL needs to obtain optimal solutions of training instances beforehand and RL heavily relies on the meticulous design of rewards. More importantly, both paradigms struggle with good generalization across new problem instances. Therefore, this paper pioneers a novel learning framework, named evolutionary multitasking-based unsupervised learning (EMTUL), eliminating dependency on optimal labels and complicated rewards, and maintaining diversified parameter vectors to improve generalization. Taking the traveling salesman problem (TSP) as a case study, a lightweight learnable optimizer named tour generator (TrGen) is devised. During training, each instance is treated as a task, and an EMT algorithm is employed to train the TrGen on multiple tasks simultaneously. Upon termination of the algorithm, an epoch ends, and a set of candidate parameter vectors is preserved for the subsequent epoch based on distribution diversity and generalization performance. This approach gradually directs the training process towards diversified search regions beneficial for generalization. Following training, the set of candidate parameter vectors serves as a knowledge reserve. When encountering new instances, the learnable optimizer can either directly infer optimal solutions via the knowledge reserve or fine-tune its parameters to accommodate the specifics of each new instance. The main benefits of the EMTUL are: 1) it directly uses the objective function as the loss function, dispensing the necessity of optimal solutions and differentiable loss or reward function; 2) it maintains a set of elite parameter vectors to efficiently handle new instances. Finally, experimental results demonstrate that TrGen, with few model parameters and trained under EMTUL, effectively identifies global or local optima for new instances of varying scales, even with relatively few training instances.
Neural Architecture Search (NAS) has emerged as a promising approach to automating the discovery of optimal neural network architectures. However, the computational cost of evaluating candidate architectures through full training presents a significant barrier to efficient search. While surrogate models can accelerate this process by predicting network performance, they struggle to accurately model the vast architecture search space when working with limited training data. To mitigate this challenge, we propose a Multi-Task, Multi-Surrogate Assisted Evolutionary NAS framework (MT-MSAENAS) that combines multiple surrogate models to enhance search efficiency. To fully exploit the limited training data, MT-MSAENAS constructs both strong and weak surrogate predictors, a global model (strong) that captures overall search space patterns and a local model (weak) that specializes in promising regions. Based on the two surrogate model, MT-MSAENAS employs evolutionary multi-tasking optimization by treating the strong and weak model-assisted search as two related optimization tasks to facilitate knowledge transfer between these models and improve the search efficiency. Experiments on the NAS-Bench101 and NAS-Bench201 search spaces show that the proposed algorithm outperforms state-of-the-art methods in architecture search.
This paper presents a learning-assisted evolutionary algorithm for energy-efficient dynamic task scheduling, simultaneously tackling processor allocation, task sequencing, and frequency determination. Specifically, it integrates deep reinforcement learning with a delayed reward update mechanism to guide the selection of appropriate search operators of evolutionary algorithm. An optimal computing budget allocation is further introduced into its training phase to balance model accuracy and computational overhead. Additionally, an long short-term memory autoencoder compresses high-dimensional solutions into low-dimensional representations, facilitating efficient offspring generation. A dual-subpopulation co-evolution framework then evolves solutions in both the compressed and original search spaces. Theoretical analysis confirms the effectiveness of the delayed reward mechanism and validates the algorithm’s complexity. Numerical experiments demonstrate that our proposed method outperforms several recently developed algorithms in finding high-quality schedules within a reasonable time.
Constrained multi-objective optimization problems (CMOPs) are challenging due to conflicting objectives and numerous constraints. In recent years, dual-population constrained multi-objective evolutionary algorithms (DP-CMOEAs) have been shown impressive performance in solving CMOPs, in which the main population searches for the constrained Pareto front (CPF), while the auxiliary population focuses on locating the unconstrained Pareto front (UPF) and providing valuable information to the main population. However, for existing DP-CMOEAs, the way of utilizing the auxiliary population is either under-utilized or over-utilized, leaving room for further performance improvement. To tackle this, this paper proposes a novel DP-CMOEA based on alternative evolution and degeneration. The proposed algorithm utilizes the auxiliary population by alternating between evolutionary and degradation stages based on its state. In the third stage, the auxiliary population ceases to evolve, thus avoiding unnecessary computational resource waste. Experimental results on three benchmark suites and three real-world problems show that the proposed algorithm outperforms seven state-of-the-art constrained multi-objective evolutionary algorithms (CMOEAs) in terms of both convergence and diversity.
Fluence map optimization problem (FMOP) refers to the optimization of the intensity of radiation beams, which is a crucial part of intensity-modulated radiation therapy (IMRT). The FMOP is often considered as a multi-objective optimization problem due to the numerous treatment objectives that need to be met. This paper formulates FMOP as an unconstrained two-objective optimization problem that focuses on dose-volume constraints and specifically designed a multi-objective coevolutionary optimization algorithm named MOEA/FMOP. The MOEA/FMOP utilizes a cooperative strategy to process dual populations with two different resolutions of fluence maps. One high-resolution population focuses on convergence and fine-tuning, while the other roughly encoded one serves to improve global convergence and maintain diversity. The resolutions of the populations are encoded and initialized according to the clinical methodology. In comparison to conventional MOEAs, MOEA/FMOP outperforms over five real-world cancer cases (including prostate, rectum, liver, nasopharynx and breast cases) in terms of hyper volume (HV) from the perspective of the performance indicator. Moreover, in the realm of clinical evaluation using dose-volume histograms (DVH), MOEA/FMOP exhibits a better capability to generate high-quality solutions concurrently.
Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training, and improved data utilization. A likely reason is that such functions discourage overfitting, leading to effective regularization. This paper demonstrates theoretically that this is indeed the case for TaylorGLO. Learning rule decomposition reveals that evolved loss functions balance two factors: the pull toward zero error, and a push away from it to avoid overfitting. This is a general principle that may be used to understand other regularization techniques as well (as demonstrated in this paper for label smoothing). The theoretical analysis leads to a constraint that can be utilized to find more effective loss functions in practice; the mechanism also results in networks that are more robust (as demonstrated in this paper with adversarial inputs). The analysis in this paper thus constitutes a first step towards understanding regularization, and demonstrates the power of evolutionary neural architecture search in general.
This paper focuses on the flight schedule optimization that is required to minimize both the delay time and the altitude change from the desired altitudes of all aircrafts as the two objectives while maximizing the "constraint tolerance" which means the acceptable range of changing constraints as the third objective, and proposes Constrained Multi-objective Optimization Evolutionary Algorithm based on Dual Sets with Local Search and Archive (CMOEA/DS-LSA) for its optimization. CMOEA/DS-LSA is designed to find the feasible solutions (i.e., the flight schedules) from the infeasible ones while improving them by the local search and evolving them from the diverse solutions stored in an archive. In particular, the effectiveness of CMOEA/DS-LSA is investigated in not only the unimodal flight scheduling problems (which have the only one optimal solution) but also the multimodal problems (which have more than one optimal solution). The intensive simulations have revealed the following implications: (1) CMOEA/DS-LSA outperforms the conventional methods (i.e., Constrained NSGA-II (CNSGA-II) and Two-stage Non-dominated Sorting and Directed Mating (TNSDM)) in both the unimodal and multimodal problems from the viewpoint of AITDR, which evaluates both the two objectives (i.e., the delay time and altitude change) and the constraint tolerance simultaneously; and (2) CMOEA/DS-LSA can find the multiple solutions while the conventional methods can find only one solution in the multimodal problems.
Handcrafting heuristics often demands extensive domain knowledge and significant development effort. Recently, heuristic search powered by large language models (LLMs) has emerged as a new approach, offering enhanced automation and promising performance. Existing methods rely on an evolutionary computation (EC) framework with carefully designed prompt strategies. However, the large heuristic search space poses significant challenges for these EC-based methods. This paper proposes a simple yet effective LLM-driven Heuristic Neighborhood Search (LHNS) paradigm to iteratively search in the heuristic neighborhood in a principled way for efficient heuristic design. Three distinct methods are designed under this neighborhood search paradigm and demonstrated on three widely studied problems. Results indicate that LHNS exhibits very competitive performance and surpasses existing EC-based methods in efficiency. It also demonstrates sufficient robustness in the absence of problem-specific knowledge regarding the target problem. The efficiency and robust adaptability make it a practical new solution for efficient heuristic design.
Multi-objective optimization problems are characterized by conflicting objectives, making it impossible to identify a single optimal solution. Instead, solution methods aim to produce a diverse set of non-dominated solutions, aka Pareto optimal solutions, each offering different tradeoffs among the objectives. Evolutionary multi-objective algorithms (EMOAs) are commonly employed to generate these varied sets of solutions. However, the abundance of solutions presents a significant challenge for decision-makers (DMs) in identifying the most preferred solution. The problem becomes even more pronounced as the number of objectives increases, requiring exponentially more computational resources and more solutions to properly represent the Pareto optimal set. Interactive EMOAs (iEMOAs) mitigate this challenge by integrating DM preferences into the optimization process to limit the search to regions of the Pareto front that are interesting to the DM. Despite their advantages, existing methods often struggle with effectively learning and utilizing DM preferences. This study investigates tree-based learning methods for preference modeling in iEMOAs by conducting a systematic comparison of decision trees (DTs) and random forests (RFs). Additionally, it examines the impact of active learning as a solution selection strategy for improving preference elicitation. Experimental results demonstrate that RF achieves significantly higher accuracy than DT in learning DM preferences. Furthermore, integrating active learning enhances preference learning within RF, further improving its accuracy. These findings highlight the potential of active learning for enhancing preference-driven optimization, offering more effective strategies for interactive multi-objective decision-making.
