Large-scale optimization problems (LSOPs) have attracted increasing attention in the big data era. Recently, matrix-based evolutionary computation (MEC) has been proposed as a new diagram for solving LSOPs within a short running time. However, compared with its corresponding classical non-matrix-based evolutionary computation (EC) algorithm, the MEC has not yet essentially improved its problem-solving ability or convergence speed. Therefore, how to enhance the problem-solving ability and convergence speed of MEC while maintaining its advantage of fast computational speed (i.e., short running time) has become a significant research topic. With this concern, this paper proposes a novel random matrix-based particle swarm optimization (RMPSO) algorithm, together with two novel designs. Firstly, a random matrix-based learning strategy is proposed, which enables each particle to learn from its superior particles by utilizing random matrices. Therefore, the RMPSO can effectively enhance the global search efficiency of the particles to improve problem-solving ability while maintaining fast computational speed. Secondly, a matrix-based knowledge and data-driven analysis strategy based on the dynamic system theory is proposed to analyze the algorithm convergence of RMPSO and help configure its parameters for fast convergence speed. To evaluate the proposed RMPSO, extensive experiments are conducted using 20 LSOPs, including 12 scalable problems with up to 10,000 dimensions and all the 8 multimodal LSOPs used in the latest IEEE CEC Large-Scale Global Optimization competition. Experimental results show that the RMPSO outperforms the compared state-of-the-art algorithms, including the champion algorithms from the LSGO competition, particularly on LSOPs with many local optima.

Set meal design (SMD) for online-to-offline (O2O) restaurant services presents a complex optimization problem, requiring the simultaneous satisfaction of diverse customer preferences, operational constraints, and profit maximization objective. To address this challenge, this article proposes a comprehensive mathematical formulation for the O2O-SMD problem. This formulation integrates complex operational requirements, such as dish variety, pricing, nutritional balance, and profitability, into a unified optimization problem with well-defined objective and constraints. To efficiently solve the O2O-SMD problem, we propose a tensor-based ant colony optimization (TACO) algorithm. Distinct from traditional ant colony optimization (ACO) variants, the core of TACO lies in reformulating the fundamental ACO operations into a tensor computational structure, enabling parallel optimization over O2O-SMD tasks at the algorithmic level. Furthermore, a dedicated local search strategy is integrated to refine solutions and accelerate convergence of the algorithm. The performance of TACO is evaluated on real-world restaurant data and benchmark instances. The experimental results show that TACO significantly outperforms a wide range of comparison algorithms in terms of solution quality, scalability, and computational efficiency, confirming its effectiveness and practical value for real-world O2O-SMD problems.

Time series forecasting (TSF) plays a pivotal role in decision-making and risk mitigation by predicting future values from historical observations. Despite significant improvements in forecasting accuracy, existing TSF models face two critical challenges: increasing computational complexity hinders deployment on resource-constrained platforms, and vulnerability to random failures compromises prediction stability. To address these issues, we propose M3NAS-TSF, a multimodal multiobjective neural architecture search framework that automates the design of lightweight and failure-resilient TSF models. Specifically, to address computational complexity, we introduce a modular time series super-net that defines a flexible and compact search space, enabling the discovery of architectures with reduced model size. To enhance failure resilience, we develop a multimodal multiobjective neural architecture search algorithm that promotes architectural diversity through an architecture-aware niching strategy and an architectural diversity distance metric, ensuring a broad set of robust candidate models. We also propose a node distribution heatmap and a structural entropy index to assess architectural diversity without ground-truth Pareto sets. Extensive experiments on 40 forecasting cases demonstrate that M3NAS-TSF outperforms six representative baselines, achieving superior forecasting accuracy (the maximum reduction in the RMSE reached 14.50%) with a smaller model size while maintaining greater architectural diversity for failure resilience.

This paper proposes an evolutionary contribution and problem heuristic information ensemble-based computing resource allocation scheme for cooperative co-evolutionary algorithms. For problem heuristic information, this paper assembles the correlation sensitivity of variables in each subproblem and the dimension ratio of this subproblem; for evolutionary contribution, this paper assembles the historical and the current evolutionary contributions of each subproblem. By assembling these two crucial factors, the devised method computes the selection probability of each subproblem and then randomly picks one subproblem by the roulette wheel selection strategy to undergo optimization in each iteration. In this way, computing resources are preferentially allocated to those subproblems with high complexity manifested by the problem heuristic information and high fitness improvement reflected by the evolutionary contribution. With this method, cooperative co-evolutionary algorithms expectedly fully utilize the computing resources to achieve satisfactory performance in addressing large-scale optimization problems. By combining the devised method with 6 latest decomposition methods along with two evolutionary optimizers, this paper has conducted experiments to compare it with 7 state-of-the-art computing resource allocation methods on two popular suites of large-scale optimization problems. Experimental results have proved that the devised method outperforms the 7 compared methods in helping cooperative co-evolutionary algorithms achieve better performance.

Solving multimodal optimization problems (MMOPs) is a challenging task which needs locating multiple global optimal solutions simultaneously with high accuracy. Current popular niching-based evolutionary algorithms (EAs) for solving MMOPs usually divide the population into several separate species to search for different optimal solutions. However, achieving effective information exchange between species to enhance the performance of overall algorithm remains a challenge in current niching-based EAs, which will directly affect the efficiency of the multimodal optimization algorithm. In this paper, the process of the different species locating peaks in MMOPs is regarded as an evolutionary multitask (EMT) optimization problem and an EMT framework with bi-knowledge transfer for MMOPs is proposed. An explicit knowledge transfer (E-KT) strategy is designed to transfer the optimal individual of the species with the fastest convergence speed to other species, thereby facilitating the acceleration their convergence. Moreover, in order to further improve the information exchange between species, a species center-based implicit knowledge transfer (I-SCKT) strategy is designed to improve the diversity of the population. The performance of MTBKTMMOP is tested on the widely used CEC’2013 benchmark and five practical flexible job shop problems. The experimental results of MTBKTMMOP are compared with 9 state-of-the-art MMOPs algorithms and show that our MTBKTMMOP is superior to all of them. Besides, the experimental results also show that the MTBKTMMOP achieves breakthroughs in handling with a large number of optimal solutions or high-dimensional MMOPs, which provides a new and effective method for dealing with MMOPs.

The gateway placement optimization (GPO) is a critical issue in satellite network that aims to obtain an optimal scheme to deploy different gateways in a network to achieve high-performed satellite-ground communication. Existing studies usually treat the GPO as a single-objective optimization problem, which significantly deviates from real-world scenarios and limits practical applicability. However, numerous performances like the gateway traffic load balancing, the distance between gateways, the traffic load of satellites, and the number of gateways within the satellite’s management range should be considered in the GPO problem, indicating that it is inherently a many-objective optimization problem (MaOP). Therefore, in this paper, a new mathematical model is designed which constructs the GPO as an MaOP. To address it, this paper further proposes a bi-velocity coevolutionary multiswarm particle swarm optimization (BCMPSO) algorithm. The BCMPSO follows the multiple populations for multiple objectives framework, running different populations in parallel, each optimizing a specific objective to search different parts of the Pareto front sufficiently. Meanwhile, a binary PSO with a bi-velocity update mechanism and a discrete position update mechanism is proposed as the optimizer in each population. Comparison experiments with several state-of-the-art methods confirm the effectiveness and competitiveness of the BCMPSO for many-objective GPO.

Feature selection can increase the classification accuracy and reduce the scale of feature subset, which is important in various machine learning tasks. However, there are various preferences and limitations for the usage of features in different application scenes, and thus different scenes may require different feature subsets. To this end, multimodal feature selection, which aims to simultaneously find multiple feature subsets with low overlap and promising classification accuracy, is also important but does not attract enough attention yet. Therefore, a new multimodal feature selection model is formulated and two grouping-based crowding differential evolution approaches are proposed in this paper. Mutual information is utilized to cluster features with high correlation and the two proposed grouping-based crowding differential evolution approaches incorporate a shuffle-based grouping strategy and a threshold-based grouping strategy, respectively, so as to simultaneously search for multiple low-overlap feature subsets with promising classification accuracy. Experimental results on eight widely used datasets validate the effectiveness of the proposed approaches.

Prompt engineering has become an effective tool for numerous large language models (LLMs)-based tasks. However, it is still a challenge to adaptively optimize the prompt for the target task, where gradients are inaccessible via APIs and the search space is highly complex. Due to the ability to robustly handle complex and multimodal landscapes, and to adaptively explore complex search spaces without explicit gradient information, evolutionary computation (EC) algorithms have garnered significant attention in black-box optimization. However, the performance of different EC algorithms for prompt optimization remains uncertain, which cannot provide guidance for algorithm selection and design in prompt optimization. To alleviate this, a series of investigative experiments are conducted in this paper to evaluate the efficiency of EC algorithms in prompt optimization, which results in three novel findings. First, different EC algorithms, including XNES, CMA-ES, DE, and PSO, are compared on various few-shot learning tasks. The findings indicate that XNES can outperform other algorithms, achieving faster or smoother convergence and higher final accuracy under high-dimensional settings. Second, the role of truncation strategies is also investigated. Results show that moderate bounds effectively help the algorithm balance exploration and exploitation, whereas overly small or large bounds diminish performance. Third, the influence of different k-shot values is examined on the optimization performance for few-shot tasks, which shows that k=32 consistently provides the best trade-off between convergence speed and final model accuracy. In conclusion, these investigations validate the efficacy of the investigated EC algorithms and highlight the advantages of XNES for complex prompt optimization. They further underscore the importance offering valuable guidance for future black-box prompt tuning scenarios. These insights pave the way for future work on more diverse and complex tasks with larger LLMs.

Handling conflicting objectives and finding multiple Pareto optimal solutions are two challenging issues in solving multiobjective optimization problems (MOPs). Inspired by the efficiency of multitask optimization (MTO) in finding multiple optimal solutions of multitask optimization problem (MTOP), we propose to treat MOP as a MTOP and solve it by using MTO. By transforming the MOP into a MTOP, not only that the difficulty in handling conflicting objectives can be avoided, but also that MTO can help efficiently find well-distributed multiple optimal solutions for MOP. With the above idea, this paper proposes a new multiobjective optimization method via MTO, with the following three contributions. Firstly, a theorem is proposed to theoretically show the relationship between MOP and MTOP and how MOP can be transformed into a MTOP. Secondly, based on the theoretical analysis, a multiple tasks for multiple objectives (MTMO) framework is proposed for solving MOP efficiently. Thirdly, a MTMO-based evolutionary algorithm is developed to solve MOP, together with two novel strategies. One is a target point estimation strategy for transforming the MOP into a MTOP automatically and accurately. The other is an archive-based implicit knowledge transfer strategy for efficiently transferring knowledge across multiple tasks to enhance the optimization results of multiple tasks together. The superiority of the proposed algorithm is validated in extensive experiments on 15 MOPs with objective numbers varying from 3 to 20 and with six state-of-the-art algorithms as competitors. Therefore, solving MOP and even many-objective optimization problem via MTO is a new, promising, and efficient method.

The Kriging model has been widely used in regression-based surrogate-assisted evolutionary algorithms (SAEAs) for expensive multiobjective optimization by using one model to approximate one objective, and the fusion of all the models forms the fitness surrogate. However, when tackling expensive many-objective optimization problems, too many models are required to construct such a fitness surrogate, which incurs cumulative prediction uncertainty and higher computational cost. Considering that the fitness surrogate works to predict different objective values to help select promising solutions with good convergence and diversity, this article proposes a novel model reduction idea to change the many-models-based fitness surrogate to a two-models-based indicator surrogate (TIS) that directly approximates convergence and diversity indicators. Based on TIS, a hierarchical and ensemble SAEA (HES-EA) is proposed with three stages. First, the HES-EA transforms the many objectives of the real-evaluated solutions into two indicators (i.e., the convergence and diversity indicators) and divides these solutions into different clusters. Second, an HES consisting of a cluster surrogate and different TISs is trained through these clustered solutions and their indicators. Third, during the optimization process, the HES can predict the candidate solutions’ cluster information via the cluster surrogate and indicator information via the TISs. Promising solutions can thus be selected based on the predicted information via a clustering-based sequential selection strategy without real fitness evaluation consumption. Compared with state-of-the-art SAEAs on three widely used benchmark suites up to 184 instances and one real-world application, HES-EA shows its superiority in both optimization performance and computational cost.

Feature selection (FS), which aims to minimize the classification error and the number of selected features, can essentially be modeled as a multiobjective optimization problem. To deal with such multiobjective FS (MOFS) problems, many multiobjective evolutionary algorithms (MOEAs) have been proposed. These MOEAs can find multiple optimal solutions, whereas substantial computational resources are required for fitness evaluations (FEs). More seriously, due to the high dimensionality and sparsity of FS problems, many FEs will be spent on unpromising solutions, resulting in a meaningless loss of computational resources. In this paper, two innovations are made so as to improve the performance of MOEAs for MOFS. First, we propose a surrogate-assisted flip (SF) strategy for MOEAs to reduce the FE waste on potentially unpromising solutions and improve search efficiency. This SF strategy is free of FE consumption and theoretically can be embedded in any MOEA to deal with MOFS problems. The experimental results show that this SF can improve the performance of different MOEAs, especially in reducing the number of selected features. Second, based on SF, we propose a more efficient SF -assisted MOEA for dealing with high-dimensional MOFS problems. The proposed algorithm divides the whole search space into different subspaces based on redundant feature subsets clustering to achieve parallel search, so as to reduce the search difficulty. The experimental results show that this algorithm is even more competitive than other SF -assisted MOEAs.

Ant colony system algorithm (ACS), as an important evolutionary computation (EC) algorithm, has demonstrated significant advantages in solving complex optimization problems. However, traditional EC algorithms and traditional ACS algorithm often face the challenge of slow computational speed when dealing with large-scale problems. In recent years, matrix-based EC approaches have been proposed to accelerate the computational speed, which has obtained promising results in dealing with large-scale problems. However, most existing matrix-based EC algorithms are designed for continuous optimization problems, while the matrix-based approach integrated with ACS has not attracted enough attention, which will be efficient for solving large-scale discrete optimization problems. Therefore, in this paper, we propose a matrix-based ACS (MACS) algorithm and apply it to solve the traveling salesman problem (TSP). MACS is an innovative improvement over the traditional ACS algorithm, utilizing matrix operations to parallelly let ants select city and update pheromone. Experimental results show that the MACS algorithm has significantly better efficiency in accelerating computational speed while maintaining the remarkable problem-solving ability in solving large-scale TSP.

Ant Colony Optimization (ACO) has witnessed great success in tackling the Traveling Salesman Problem (TSP). In ACO, ants involved in the pheromone update play pivotal roles in its optimization effectiveness. Along this road, this paper designs an ant selection mechanism along with a non-linear weight method for ACO to update the pheromone effectively, leading to a novel ACO, called NLW-ACO. Particularly, NLW-ACO leverages the fitness values of ants to assign each ant a selection probability. Then, it adaptively chooses ants for pheromone update. Subsequently, a nonlinear weight is assigned to each selected ant based on its fitness value to update the pheromone matrix. Resultantly, better ants have higher selection probabilities and larger weights to take part in the pheromone update. This leads to that NLW-ACO compromises search convergence and search diversity appropriately to seek for the optimum. Experiments have been carried out on 10 TSP instances of diverse scales. The experimental findings substantiate that NLW-ACO significantly outperforms the 5 typical ACO methods, especially on large-scale TSP problems.

Sudoku puzzles are not only popular intellectual games but also NP-hard combinatorial problems related to various real-world applications, which have attracted much attention worldwide. Although many efficient tools, such as evolutionary computation (EC) algorithms, have been proposed for solving Sudoku puzzles, they still face great challenges with regard to hard and large instances of Sudoku puzzles. Therefore, to efficiently solve Sudoku puzzles, this paper proposes a genetic algorithm (GA)-based method with a novel local search technology called local search-based GA (LSGA). The LSGA includes three novel design aspects. First, it adopts a matrix coding scheme to represent individuals and designs the corresponding crossover and mutation operations. Second, a novel local search strategy based on column search and sub-block search is proposed to increase the convergence speed of the GA. Third, an elite population learning mechanism is proposed to let the population evolve by learning the historical optimal solution. Based on the above technologies, LSGA can greatly improve the search ability for solving complex Sudoku puzzles. LSGA is compared with some state-of-the-art algorithms at Sudoku puzzles of different difficulty levels and the results show that LSGA performs well in terms of both convergence speed and success rates on the tested Sudoku puzzle instances.

Surrogate-assisted evolutionary algorithms (SAE-As), mainly including regression-based SAEAs and classification-based SAEAs, are promising for solving expensive multi-objective optimization problems (EMOPs). Regression-based SAEAs usually use complex regression models to approximate the fitness evaluation, which will suffer from high training costs to obtain a fine-accuracy surrogate. In contrast, classification-based SAEAs can achieve solution selection via coarse binary relations predicted by classifiers, thus avoiding high requirements in prediction accuracy and training costs. However, most of the binary relations in existing classification-based SAEAs mainly only involve convergence comparison whereas diversity maintenance is neglected. Considering the capacity of the grid technique in maintaining both convergence and diversity, we propose a new classification method called grid classification to discretize the objective space into grids and train a lightweight grid classification-based surrogate (GCS), for which low training costs are needed. The GCS can evaluate the solution performance in terms of both convergence and diversity simultaneously according to the predicted grid locations, which opens up a new field for follow-up research on classification-based SAEAs. Following this, a GCS-assisted particle swarm optimization algorithm is proposed for tackling EMOPs. Experimental results on widely-used benchmark problems (including high-dimensional EMOPs) and a 222-high-dimensional real-world application problem show its competitiveness in terms of both optimization performance and computational cost.

Tourism is an important industry sector that requires tour companies to plan multiple routes for different tour groups, which is called tour multi-route planning. This paper focuses on tour multi-route planning, which can improve the economic benefit and allocation efficiency of tour resources. The main contributions of this paper are threefold. First, we propose a novel multiple routes planning model that captures the real-world tourism scenario and practical constraints. We also define four typical constraints for tourism planning and classify them into soft and hard constraints. Second, we develop a matrix-based differential evolution algorithm to jointly optimize multiple routes that can efficiently handle the high-dimensional optimization under various constraints. Third, we collect real-world data to construct problem instances and compare the performance of our algorithm with the conventional differential evolution algorithms in terms of runtimes. The experimental results show that our algorithm can effectively solve tour multi-route planning problems and achieve excellent runtimes performance, suitable for large-scale transportation network optimization.

Many-task optimization problem (MaTOP) is a kind of problem in that more than three optimization tasks are required to be solved simultaneously. How to utilize multiple different kinds of similarities among many tasks for knowledge transfer (KT) is a challenging issue in solving MaTOP. To this end, this paper proposes a multi-view transfer (MVT)-based differential evolution (MVTDE) for effectively transferring knowledge in solving MaTOP. In particular, a perspective of task alignment is regarded as a view of performing KT. By combining different views including marginal and conditional distribution alignment, MVT can better fully utilize various task similarities from different aspects to solve MaTOP efficiently. This paper is with two contributions. First, we propose the MVT method that incorporates multiple KT methods from the views of marginal and conditional distribution alignment to enhance the search efficiency on the target tasks. Second, we propose to control the occurrence of different KT methods in MVT according to probability parameters and propose a parameter update strategy to adaptively adjust the probability parameters according to the feedback of different KT methods. In the experimental study, we carry out comparative experiments on three widely used MaTOP benchmarks to validate the effectiveness of MVTDE. The results show that MVTDE obtains competitive performance compared to several state-of-the-art many-task optimization algorithms.

Traffic signal timing optimization (TSTO) is a significant topic in the smart city. However, there are two challenges when solving TSTO. Firstly, it often uses time-consuming simulation software to evaluate candidate solutions, therefore it is an expensive optimization problem. Secondly, as the traffic flow changes rapidly in TSTO, providing a timing scheme to respond to the change immediately is difficult. To address the above challenges, we propose a region-based evaluation particle swarm optimization algorithm (REPSO) with dual solution libraries, which has three novel designs. First, two solution libraries are built for undersaturated and oversaturated traffic flow states, respectively, which can be used to fast provide a signal timing scheme for a traffic flow in real-time. Second, a knowledge-assisted initialization strategy is proposed and adopted to assist the initialization of new solutions based on the knowledge in the two solution libraries. Third, a region-based evaluation strategy is proposed to reduce the number of fitness evaluations, which can also greatly reduce the construction time of the solution libraries. The performance of REPSO is validated by comparing with six signal timing methods in both undersaturated and oversaturated traffic flow states, showing the better general performance of REPSO.

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.

Cooperative coevolution (CC) algorithms based on variable decomposition methods are efficient in solving large-scale optimization problems (LSOPs). However, many decomposition methods, such as the differential grouping (DG) method and its variants, are based on the theorem of function additively separable, which may not work well on problems that are not additively separable and will result in a bottleneck for CC to solve various LSOPs. This deficiency motivates us to study how the decomposition method can decompose more kinds of separable functions, such as the multiplicatively separable function, to improve the general problem-solving ability of CC on LSOPs. With this concern, this article makes the first attempt to decompose multiplicatively separable functions and proposes a novel method called dual DG (DDG) for better LSOP decomposition and optimization. The novelty and advantage of DDG are that it can be suitable for not only additively separable functions but also multiplicatively separable functions, which can considerably expand the application scope of CC. In this article, we will first define the multiplicatively separable function, and then mathematically show its relationship to the additively separable function and how they can be transformed into each other. Based on this, the DDG can use two kinds of differences to detect the separable structure of both additively and multiplicatively separable functions. In addition, the time complexity of DDG is analyzed and a DDG-based CC algorithm framework is developed for solving LSOPs. To verify the superiority of DDG, experiments and comparisons with some state-of-the-art and champion algorithms are conducted not only on 30 LSOPs based on the test suite of the IEEE CEC large-scale global optimization competition, but also on a case study of the parameter optimization for a neural network-based application.

Learning and optimization are the two essential abilities of human beings for problem solving. Similarly, computer scientists have made great efforts to design artificial neural network (ANN) and evolutionary computation (EC) to simulate the learning ability and the optimization ability for solving real-world problems, respectively. These have been two essential branches in artificial intelligence (AI) and computer science. However, in humans, learning and optimization are usually integrated together for problem solving. Therefore, how to efficiently integrate these two abilities together to develop powerful AI remains a significant but challenging issue. Motivated by this, this paper proposes a novel learning-aided evolutionary optimization (LEO) framework that plus learning and evolution for solving optimization problems. The LEO is integrated with the evolution knowledge learned by ANN from the evolution process of EC to promote optimization efficiency. The LEO framework is applied to both classical EC algorithms and some state-of-the-art EC algorithms including a champion algorithm, with benchmarking against the IEEE Congress on Evolutionary Computation competition data. The experimental results show that the LEO can significantly enhance the existing EC algorithms to better solve both single-objective and multi-/many-objective global optimization problems, suggesting that learning plus evolution is more intelligent for problem solving. Moreover, the experimental results have also validated the time efficiency of the LEO, where the additional time cost for using LEO is greatly deserved. Therefore, the promising LEO can lead to a new and more efficient paradigm for EC algorithms to solve global optimization problems by plus learning and evolution.

In recent years, themulti-task learning forknowledge graph-basedrecommender system, termed MKR, has shown its promising performance and has attracted increasing interest, because a recommendation task and a knowledge graph embedding (KGE) task can help each other to improve the recommendation. However, MKR still has two difficult issues. The first is how fully to capture users’ historical behavior pattern in the recommendation task and how fully to utilize deep multi-relation semantic information in the KGE task. The second is how to deal with datasets with different sparsity. Tackling these challenging issues, this paper proposes an enhanced MKR (EMKR) approach with two novelties. First, we propose to utilize the attention mechanism to aggregate users’ historical behavior for more accurately mining preferences in the recommendation task, and utilize the relation-aware graph convolutional neural network to fully capture the deep multi-relation neighborhood features in the KGE task, so as to address the first issue. Second, a two-part modeling strategy is proposed for a better representation of users in the recommendation task to expand the expressive ability of the model for adapting to datasets with different sparsity, so as to address the second issue. Extensive experiments are conducted on widely-used datasets and 11 approaches are used for comparison. The results show that the proposed EMKR can achieve substantial gains over the compared state-of-the-art approaches, especially in the situation where user-item interactions are sparse.

The performance of a convolutional neural network (CNN) heavily depends on its hyperparameters. However, finding a suitable hyperparameters configuration is difficult, challenging, and computationally expensive due to three issues, which are 1) the mixed-variable problem of different types of hyperparameters; 2) the large-scale search space of finding optimal hyperparameters; and 3) the expensive computational cost for evaluating candidate hyperparameters configuration. Therefore, this article focuses on these three issues and proposes a novel estimation of distribution algorithm (EDA) for efficient hyperparameters optimization, with three major contributions in the algorithm design. First, a hybrid-model EDA is proposed to efficiently deal with the mixed-variable difficulty. The proposed algorithm uses a mixed-variable encoding scheme to encode the mixed-variable hyperparameters and adopts an adaptive hybrid-model learning (AHL) strategy to efficiently optimize the mixed-variables. Second, an orthogonal initialization (OI) strategy is proposed to efficiently deal with the challenge of large-scale search space. Third, a surrogate-assisted multi-level evaluation (SME) method is proposed to reduce the expensive computational cost. Based on the above, the proposed algorithm is named s urrogate-assisted hybrid-model EDA (SHEDA). For experimental studies, the proposed SHEDA is verified on widely used classification benchmark problems, and is compared with various state-of-the-art methods. Moreover, a case study on aortic dissection (AD) diagnosis is carried out to evaluate its performance. Experimental results show that the proposed SHEDA is very effective and efficient for hyperparameters optimization, which can find a satisfactory hyperparameters configuration for the CIFAR10, CIFAR100, and AD diagnosis with only 0.58, 0.97, and 1.18 GPU days, respectively.

Decomposition methods play a critical role in cooperative co-evolutionary algorithms (CCEAs) for solving large-scale optimization problems. Although some well-performing decomposition methods have been designed based on the interactions among variables (IaV), their grouping accuracy is still limited due to the poor performance on the overlapping problems and the computational roundoff errors of IaV in the implementation. To deal with these limitations, a graph-based deep decomposition (GDD) method is proposed to obtain more accurate grouping results, especially for the overlapping problems. On the one hand, the GDD mines the IaV information and obtains the minimum vertex separator of the interaction graph of variables, so as to group variables deeply and recursively. On the other hand, the GDD has the ability of fault tolerance to deal with the computational roundoff errors of IaV and can improve the grouping accuracy. For better experimental studies of overlapping problems, a novel overlapping function generator is designed with the random and complicate overlap type, and two new metrics are proposed to evaluate the grouping accuracy. Comprehensive experiments show that GDD can greatly improve the grouping accuracy and help CCEAs perform better than other existing algorithms, especially on the overlapping problems. In addition, the GDD is highly fault tolerant and can divide problems accurately even on the inaccurate IaV.

Knowledge transfer plays a vastly important role in solving multitask optimization problems (MTOPs). Many existing methods transfer task-specific knowledge, such as the high-quality solution from one task to other tasks to enhance the optimization ability, which, however, may not work well or even have a negative effect if the tasks have very different task-specific knowledge. Hence, this article proposes a meta-knowledge transfer (MKT)-based differential evolution (MKTDE) algorithm by using a more general MKT method to solve MTOPs more efficiently. The meta-knowledge defined in this article refers to the knowledge that can evolve task-specific knowledge during the evolutionary search. That is, the meta-knowledge is a kind of “knowledge of knowledge,” which denotes the knowledge of “how to solve problem via evolution” and “the feature/way/method of evolving high-quality solution.” The evolutionary search for solving different tasks can share common meta-knowledge even though these tasks involve heterogeneous data and have very different task-specific knowledge. Therefore, the MKT can associate the heterogeneous multisource data of different tasks via transferring the meta-knowledge to help solve MTOPs more efficiently in a more general way. Moreover, to further enhance the MKTDE, two novel and efficient methods are proposed. One is multiple populations for the multiple tasks framework using a unified search space for making knowledge transfer flexibly. The other is an elite solution transfer method for achieving positive high-quality solution transfer. The superior performance of the proposed MKTDE is verified via extensive numerical experiments on both widely used MTOP benchmark problems and real-world robot navigation problems, with comparisons with some state-of-the-art and the latest well-performing algorithms.

As transportation system plays a vastly important role in combatting newly-emerging and severe epidemics like the coronavirus disease 2019 (COVID-19), the vehicle routing problem (VRP) in epidemics has become an emerging topic that has attracted increasing attention worldwide. However, most existing VRP models are not suitable for epidemic situations, because they do not consider the prevention cost caused by issues such as viral tests and quarantine during the traveling. Therefore, this paper proposes a multi-objective VRP model for epidemic situations, named VRP4E, which considers not only the traditional travel cost but also the prevention cost of the VRP in epidemic situations. To efficiently solve the VRP4E, this paper further proposes a novel algorithm named multi-objective ant colony system algorithm for epidemic situations, termed MOACS4E, together with three novel designs. First, by extending the efficient “multiple populations for multiple objectives” framework, the MOACS4E adopts two ant colonies to optimize the travel and prevention costs respectively, so as to improve the search efficiency. Second, a pheromone fusion-based solution generation method is proposed to fuse the pheromones from different colonies to increase solution diversity effectively. Third, a solution quality improvement method is further proposed to improve the solutions for the prevention cost objective. The effectiveness of the MOACS4E is verified in experiments on 25 generated benchmarks by comparison with six state-of-the-art and modern algorithms. Moreover, the VRP4E in different epidemic situations and a real-world case in the Beijing-Tianjin-Hebei region, China, are further studied to provide helpful insights for combatting COVID-19-like epidemics.

Convolution neural network (CNN) is a kind of powerful and efficient deep learning approach that has obtained great success in many real-world applications. However, due to its complex network structure, the intertwining of hyperparameters, and the time-consuming procedure for network training, finding an efficient network configuration for CNN is a challenging yet tough work. To efficiently solve the hyperparameters setting problem, this paper proposes a distributed particle swarm optimization (DPSO) approach, which can optimize the hyperparameters to find high-performing CNNs. Compared to tedious, historical-experience-based, and personal-preference-based manual designs, the proposed DPSO approach can evolve the hyperparameters automatically and globally to obtain promising CNNs, which provides a new idea and approach for finding the global optimal hyperparameter combination. Moreover, by cooperating with the distributed computing techniques, the DPSO approach can have a considerable speedup when compared with the traditional particle swarm optimization (PSO) algorithm. Extensive experiments on widely-used image classification benchmarks have verified that the proposed DPSO approach can effectively find the CNN model with promising performance, and at the same time, has greatly reduced the computational time when compared with traditional PSO.

Due to the population-based and iterative-based characteristics of evolutionary computation (EC) algorithms, parallel techniques have been widely used to speed up the EC algorithms. However, the parallelism usually performs in the population level where multiple populations (or subpopulations) run in parallel or in the individual level where the individuals are distributed to multiple resources. That is, different populations or different individuals can be executed simultaneously to reduce running time. However, the research into generation-level parallelism for EC algorithms has seldom been reported. In this article, we propose a new paradigm of the parallel EC algorithm by making the first attempt to parallelize the algorithm in the generation level. This idea is inspired by the industrial pipeline technique. Specifically, a kind of EC algorithm called local version particle swarm optimization (PSO) is adopted to implement a pipeline-based parallel PSO (PPPSO, i.e., P3SO). Due to the generation-level parallelism in P3SO, when some particles still perform their evolutionary operations in the current generation, some other particles can simultaneously go to the next generation to carry out the new evolutionary operations, or even go to further next generation(s). The experimental results show that the problem-solving ability of P3SO is not affected while the evolutionary speed has been substantially accelerated in a significant fashion. Therefore, generation-level parallelism is possible in EC algorithms and may have significant potential applications in time-consumption optimization problems.

Data-driven evolutionary algorithms (DDEAs) aim to utilize data and surrogates to drive optimization, which is useful and efficient when the objective function of the optimization problem is expensive or difficult to access. However, the performance of DDEAs relies on their surrogate quality and often deteriorates if the amount of available data decreases. To solve these problems, this article proposes a new DDEA framework with perturbation-based ensemble surrogates (DDEA-PES), which contain two efficient mechanisms. The first is a diverse surrogate generation method that can generate diverse surrogates through performing data perturbations on the available data. The second is a selective ensemble method that selects some of the prebuilt surrogates to form a final ensemble surrogate model. By combining these two mechanisms, the proposed DDEA-PES framework has three advantages, including larger data quantity, better data utilization, and higher surrogate accuracy. To validate the effectiveness of the proposed framework, this article provides both theoretical and experimental analyses. For the experimental comparisons, a specific DDEA-PES algorithm is developed as an instance by adopting a genetic algorithm as the optimizer and radial basis function neural networks as the base models. The experimental results on widely used benchmarks and an aerodynamic airfoil design real-world optimization problem show that the proposed DDEA-PES algorithm outperforms some state-of-the-art DDEAs. Moreover, when compared with traditional nondata-driven methods, the proposed DDEA-PES algorithm only requires about 2% computational budgets to produce competitive results.

By efficiently building and exploiting surrogates, data-driven evolutionary algorithms (DDEAs) can be very helpful in solving expensive and computationally intensive problems. However, they still often suffer from two difficulties. First, many existing methods for building a single ad hoc surrogate are suitable for some special problems but may not work well on some other problems. Second, the optimization accuracy of DDEAs deteriorates if available data are not enough for building accurate surrogates, which is common in expensive optimization problems. To this end, this article proposes a novel DDEA with two efficient components. First, a boosting strategy (BS) is proposed for self-aware model managements, which can iteratively build and combine surrogates to obtain suitable surrogate models for different problems. Second, a localized data generation (LDG) method is proposed to generate synthetic data to alleviate data shortage and increase data quantity, which is achieved by approximating fitness through data positions. By integrating the BS and the LDG, the BDDEA-LDG algorithm is able to improve model accuracy and data quantity at the same time automatically according to the problems at hand. Besides, a tradeoff is empirically considered to strike a better balance between the effectiveness of surrogates and the time cost for building them. The experimental results show that the proposed BDDEA-LDG algorithm can generally outperform both traditional methods without surrogates and other state-of-the-art DDEA son widely used benchmarks and an arterial traffic signal timing real-world optimization problem. Furthermore, the proposed BDDEA-LDG algorithm can use only about 2% computational budgets of traditional methods for producing competitive results.