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.

This paper develops a new Tourist Route Planning (TRP) model by incorporating the entrance fees and the experience values of scenic spots, the travelling costs between scenic spots, and the budget of the tourist. Resultantly, the new TRP aims at finding an optimal route by maximizing the travelling experience value of the tourist with the constraint that the total cost of the route including the travelling costs and the spot entrance fees does not exceed the given budget. To effectively solve this new TRP, this paper adapts the five classical ant colony optimization algorithms (ACO), namely ant system (AS), elite AS (EAS), rank-based AS (RAS), max-min AS (MMAS), and ant colony system (ACS). To this end, this paper first introduces a new heuristic information measure by integrating the experience values and the entrance fees of the scenic spots, and the traveling costs between scenic spots. Further, a new local search strategy encompassing 2-opt and one spot insertion operator is designed to further improve the quality of the route under the budget constraint. Abundant experiments have been carried out on various TRP instances of three scales, namely small-scale, medium-scale, and large-scale, involving different numbers of scenic spots and different settings of budgets. The experimental results demonstrate that all the adapted five ACO algorithms are very effective for addressing the new TRP. Among them, RAS performs the best on small-scale TRP instances, and ACS obtains the best results on medium-scale TRP instances, while MMAS is the most effective one in addressing large-scale TRP instances.

Multipoint dynamic aggregation (MPDA) is a multirobot task allocation problem, which requires the collaborative scheduling of multiple robots to complete time-varying tasks distributed on a map. Most existing studies consider the scenarios with homogeneous robots and tasks. To model the application scenarios where different types of robots are required, we propose a heterogeneous MPDA problem, which incorporates different types of robots and tasks with dependency. Correspondingly, a novel metaheuristic algorithm called multistage particle swarm optimization is designed and consists of two parts: 1) a multistage strategy and 2) a specially designed particle swarm optimization (PSO) algorithm. The multistage strategy imposes temporary constraints to force cooperation between robots, which can reduce and smoothen the search space. The proposed PSO contains a mixed updating mechanism consisting of a continuous velocity updating rule and a discrete position updating rule, which is effective for updating the permutation-based solutions of MPDA. The experiments on a newly designed benchmark test set show that the proposed algorithm is more effective and efficient than the state-of-the-art methods.

As electric vehicles become more prevalent, a novel vehicle routing problem (VRP) has emerged, known as the capacitated electric VRP (CEVRP). CEVRP requires determining not only the service order of customers but also the charging plans for vehicles, thereby increasing the complexity of solution construction. In response to this challenge, we propose a bilevel hybrid genetic algorithm (BHGA). BHGA models CEVRP as two levels of subproblem: 1) the upper level capacitated VRP, focusing on the service order and 2) the lower level fixed route vehicle charging problem, focusing on the charging plans. In dealing with the upper level subproblem, the hybrid genetic search algorithm is adopted to construct the routes to visit customers and an advanced screening strategy is proposed to optimize the local search process and effectively guide the evolution of population. For the lower level subproblem, an efficient heuristic method called focus enumeration is designed, which is specifically used to insert charging stations into routes to ensure battery constraint. The collaboration of the advanced screening strategy and the focus enumeration assists in more unified solving of the two subproblems. The experiments show that BHGA significantly surpasses state-of-the-art algorithms on benchmark instances and has successfully updated eleven best known solutions, demonstrating its outstanding performance.

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.

Leading exemplars play significant roles in updating particles to seek optimal solutions for Particle Swarm Optimization (PSO). Along this road, this paper devises an Individual-level Dominant Exemplar Selection (IDES) framework for PSO, giving rise to a new PSO variant named IDESPSO. Specifically, instead of using their own personally best positions and the globally best position of the entire swarm to update particles, IDES first randomly chooses two different exemplars for each particle from all personally best positions. Then, it compares the two selected exemplars with the personally best position of this particle. Based on the comparison results, different updating strategies are utilized to update different particles. This method notably enriches the variety among the chosen leading exemplars, thereby substantially bolstering the updating diversity of particles. Under IDES, this paper further develops seven selection strategies to help IDESPSO pick up promising exemplars for particles to evolve. Specifically, the seven selection schemes are the roulette wheel selection, the tournament selection, and five hybridizations of two basic models. A series of experiments have been undertaken on the universally used CEC2014 problem suite to compare IDESPSO with the seven selection schemes and two classic PSOs. The empirical results show that IDESPSO paired with anyone of the seven selection methods, markedly outperforms the two classical PSO variants, highlighting its significant performance.

Ant selection for updating the pheromone is one most crucial operation in ant colony optimization (ACO). In this direction, this paper designs an adaptive ant selection strategy (AAS) to adaptively and dynamically select ants to update the pheromone for ACO. Therefore, a new ACO, called AAS-ACO is developed. Specifically, AAS-ACO first assigns a non-linear selection probability to each ant based on its path ranking. As a result, better ants preserve exponentially higher selection probabilities. Then, based on the selection probabilities, ants are adaptively selected for the pheromone update. By this means, on the one hand, the number of ants involved in the pheromone update is uncertain; on the other hand, relatively better ants instead of absolutely better ones are adaptively selected to update the pheromone, leading to the promotion of search diversity. Subsequently, a dynamic weighting strategy is designed to adjust the amount of the pheromone deposited by the best ant in the current iteration to enhance the search convergence. With the two schemes, AAS-ACO is expected to maintain a suitable compromise between search diversity and search convergence to seek the optimal solutions to TSP. Experiments on 10 classical TSP instances varying from 100 to 1000 cities have proven the significant superiority of AAS-ACO to 5 classic ACOs, especially on high-dimensional TSP problems.

Federated learning has emerged as a promising paradigm for privacy-preserving collaboration among different parties. Recently, with the popularity of federated learning, an influx of approaches have delivered towards different realistic challenges. In this survey, we provide a systematic overview of the important and recent developments of research on federated learning. First, we introduce the study history and terminology definition of this area. Then, we comprehensively review three basic lines of research: generalization, robustness, and fairness, by introducing their respective background concepts, task settings, and main challenges. We also offer a detailed overview of representative literature on both methods and datasets. We further benchmark the reviewed methods on several well-known datasets. Finally, we point out several open issues in this field and suggest opportunities for further research.

In high dimensional environment, the interaction among particles significantly affects their movements in searching the vast solution space and thus plays a vital role in assisting particle swarm optimization (PSO) to attain good performance. To this end, this paper designs a random contrastive interaction (RCI) strategy for PSO, resulting in RCI-PSO, to tackle large-scale optimization problems (LSOPs) effectively and efficiently. Unlike existing interaction mechanisms for low-dimensional problems, RCI randomly chooses several different peers from the current swarm to construct a random interaction topology for each particle. Then, it lets the particle interact with the selected peers based on their current evolutionary information instead of their historical evolutionary information. Within the topology, RCI only propagates the evolutionary information of two contrastive dominators with the largest difference in fitness to direct the evolution of the particle. Therefore, particles with no more than two dominators in their topologies are not updated. Furthermore, a dynamic topology size adjustment scheme is devised to gradually enlarge the interaction topology. In this way, the swarm gradually switches from exploring the immense search space dispersedly to exploiting the found optimal regions intensively as the evolution continues. With these two strategies, RCI-PSO expectedly compromises search diversity and search convergence well at the swarm level and the particle level. At last, extensive experiments executed on two public LSOP suites verify that RCI-PSO performs competitively with or even much better than totally 40 state-of-theart large-scale approaches and preserves a good capability and scalability in tackling complex LSOPs.

Different from existing studies where low-dimensional optimizers are utilized to optimize the path of an unmanned aerial vehicle (UAV), this paper attempts to employ large-scale swarm optimizers to solve the path planning problem of UAV, such that the path can be subtler and smoother. To this end, a variation encoding scheme is devised to encode particles. Specifically, each dimension of a particle is encoded by a triad consisting of the relative movements of UAV along the three coordinate axes. With this encoding scheme, a large number of anchor points can be optimized to form the path and repetitive anchor points can be avoided. Subsequently, this paper embeds this encoding scheme into four representative and well-performed large-scale swarm optimizers, namely the stochastic dominant learning swarm optimizer (SDLSO), the level-based learning swarm optimizer (LLSO), the competitive swarm optimizer (CSO), and the social learning particle swarm optimizer (SL-PSO), to optimize the path of UAV. Experiments have been conducted on 16 scenes with 4 different numbers of peaks in the landscapes. Experimental results have demonstrated that the devised encoding scheme is effective to cooperate with the four large-scale swarm optimizers to solve the path planning problem of UAV and SDLSO achieves the best performance.

Ant Colony Optimization (ACO) has shown very promising performance in solving Traveling Salesman Problem (TSP). However, most existing ACO algorithms utilize either the absolutely best ants or all ants to update the pheromone matrix. This leads to either serious diversity loss or slow convergence. To alleviate these predicaments, this paper designs a random pairwise competition based ant selection for pheromone updating. Specifically, a number of ants are randomly selected from the ant colony and then are randomly paired together. Subsequently the better one in each pair is selected to update the pheromone matrix. In this way, a good balance between search diversity and search convergence is potentially maintained. Integrating this selection strategy along with a local search scheme into the ACO framework, a new ACO algorithm called random pairwise competition based ACO (RPCACO) is developed. Experiments conducted on 8 TSP instances from the TSPLIB benchmark set demonstrate that RPCACO is more effective and efficient than the five classical ACO algorithms in solving TSP.

Multiple traveling salesmen problem (MTSP) is an extension of traditional traveling salesman problem (TSP). It involves both the city assignment optimization and the route optimization of each salesman. Genetic algorithms (GA) have been widely used to solve MTSP thanks to its easiness in implementation and good global search ability. To help GA effectively solve MTSP, researchers have developed various encoding schemes. However, there is no systematic and comparative study on the effectiveness of these encoding strategies. To fill this gap, this paper conducts investigations to compare four popular encoding strategies for MTSP, namely the one-chromosome encoding, the two-chromosome encoding, the two-part-chromosome encoding and the multi-chromosome encoding. Experimental results on different MTSP instances with different numbers of cities and salesmen show that the multi-chromosome encoding is far better than the other encoding strategies.

EEG channel selection aims to choose informative and representative channels to reduce data redundancy. It is very beneficial for improving the utility and efficiency of emotion recognition. Previous studies on EEG channel selection have not considered the influence of genders despite long-standing belief in gender differences with respect to emotion analysis. In this paper, we collected EEG signals from 20 subjects containing 10 males and 10 females by letting them watch short emotional videos. Then, to reduce data redundancy, we propose an enhanced genetic algorithm to select the optimal channel subsets separately for male and female subjects by incorporating a novel evolution operation. Experimental results show that the proposed algorithm achieves higher accuracy in terms of emotion recognition than several compared methods with a smaller channel subset. Besides, experimental results also indicate that the gender differences in neural patterns indeed exist. Through this study, the gender-sensitive channel selection offers a new avenue for further development of EEG based emotion recognition.

Mutation plays a crucial role in assisting differential evolution (DE) to effectively solve optimization problems. The key to mutation lies in the selection of parent individuals participating in the mutation. Along this road, this paper devises a binomial distribution-assisted individual selection strategy for DE. Specifically, this paper takes advantage of the probability distribution function of the binomial distribution to assign weights to individuals based on their fitness rankings. In this way, the selection of individuals focuses more on medium better individuals instead of the top best ones. Therefore, high mutation diversity can be preserved and thus it is likely that falling into local regions can be effectively avoided. Embedding this selection strategy into DE, a novel DE variant called binomial distribution assisted DE (BDDE) is developed. Experiments conducted on the CEC2017 benchmark suite have verified the effectiveness of BDDE in solving optimization problems. Particularly, BDDE gains much better performance against the well-known and representative mutation strategies.

Cooperative co-evolutionary algorithms (CCEAs) have witnessed giant success in solving large-scale optimization problems (LSOPs). However, most existing CCEAs use low-dimensional EAs to optimize the decomposed sub-problems. Such utilization of low-dimensional EAs may limit the effectiveness of CCEAs because some of the decomposed sub-problems may still be high-dimensional. Since there exist many non-decomposition based large-scale EAs, it is interesting to investigate the optimization effectiveness of CCEAs by using these non-decomposition based large-scale EAs to solve the decomposed sub-problems. To this end, this paper incorporates two state-of-the-art large-scale swarm optimizers into CCEAs with five state-of-the-art decomposition strategies to solve LSOPs. Experiments conducted on the CEC'2010 and CEC'2013 LSOP benchmark sets have shown that the two large-scale swarm optimizers help CCEAs with the five decomposition strategies achieve much better performance than the most widely used low-dimensional EA.

This paper proposes a stochastic dominant cognitive experience-guided learning framework for particle swarm optimization (SDCEGPSO) to enhance its search ability in complex environment. Specifically, different from classical PSOs, SDCEGPSO randomly selects dominant cognitive experiences to guide the learning of particles. To this end, the cognitive experiences of all particles, namely their personal best positions, are sorted from the best to the worst. Then, each particle randomly chooses a personal best position better than its own to learn. For the cognitive experience selection, this paper designs three selection methods, namely the random selection, the roulette wheel selection, and the tournament selection. With this learning framework, particles have diverse guiding exemplars to learn from and thus high search diversity is expectedly maintained. Experiments conducted on the 50-D and 100-D CEC2014 problem suite have verified the effectiveness of SDCEGPSO. Compared with the classical global PSO (GPSO) and local PSO (LPSO), SDCEGPSO with the three selection schemes achieve significantly better performance. Besides, among the three selection schemes, the binary tournament selection is the most effective one to help SDCEGPSO solve optimization problems.

Expensive optimization problems (EOPs) are becoming more and more ubiquitous nowadays. To effectively solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) have been developed. Specifically, a SAEA usually maintains a surrogate model to simulate the real objective function of an EOP. Such a surrogate model is trained based on real-evaluated solutions. Then, it is utilized to evaluate the fitness of individuals in the EA instead of the real expensive fitness evaluation. Though many SAEAs have been designed, they mainly concentrate on dealing with low-dimensional EOPs with fewer than 300 dimensions. Their performance on large-scale EOPs with more than 300 dimensions is unknown. To fill this gap, this paper conducts a comparative study on two types of state-of-the-art SAEAs with a total of four algorithms on four classical EOPs. To make comprehensive comparisons, we range the dimension size from 50 to 1000. As far as we know, this is the first time to assess SAEAs on EOPs with such a wide range of dimension sizes and such high dimensionality. The comparison results show that the optimization performance of the compared four SAEAs on high-dimensional EOPs with more than 500 dimensions is not as satisfactory as their performance on low-dimensional EOPs because of their slow convergence. Therefore, research on large-scale SAEAs for high-dimensional EOPs still deserves intensive attention.

Multiple traveling salesmen problem with visiting constraints (VCMTSP) is a general version of the classical multiple traveling salesmen problem (MTSP), where each city can be only accessed by a number of salesmen. To cope with this new problem, we adapt the genetic algorithm (GA) for MTSP by using a dual-chromosome representation scheme with one chromosome denoting the visiting sequence of cities and the other representing the assignment of cities to salesmen. To further promote the effectiveness of GA in solving VCMTSP, we modify three popular crossover operators, namely the cycle crossover (CX), the order crossover (OX), and the partially mapped crossover (PMX). Similar to the execution for traditional TSP, the three crossover operators are all executed on the city sequence chromosome, while the adaption of them lies in the modification of the salesman assignment in the second chromosome. To this end, a correction mechanism according to the accessibility matrix is conducted to make the generated solutions after crossover feasible. Extensive experiments conducted on totally 16 VCMTSP instances generated from the benchmark TSPLIB set demonstrate that the adapted GA could effectively cope with VCMTSP, and the GA with the modified PMX achieves the best overall performance.

The scaling factor (F) in the mutation operation and the crossover rate (CR) in the crossover operation are considerably critical in assisting differential evolution (DE) to attain good optimization performance. As a result, DE is very sensitive to these two parameters. To address this predicament, many adaptive parameter control methods have been proposed for these two parameters. However, there are no comprehensive comparisons among these adaptive parameter methods. To make up for this defect, this paper mainly investigates the effectiveness of six widely utilized adaptive strategies, namely the ones in JADE, IDE, jDE, SinDE, FDSADE, and RDE. For fairness, this paper selects the binomial crossover and the mutation “DE/current-to-pbest/1” to accompany the six adaptive parameter strategies. Experimental results on the commonly adopted CEC2014 benchmark suite have demonstrated that the adaptive parameter control methods in IDE and JADE help DE achieve the best overall performance. With these investigations, it is envisaged that this paper provides a fundamental guideline for new learners and those looking for an appropriate adaptive parameter technique for their newly created DE algorithms.

Electric Vehicle Routing Problem (EVRP) is considerably challenging due to the capacity and electricity constraints of electric vehicles (EVs). Most existing studies on EVRP consider no limits on charging times when optimizing the routes of EVs. However, due to the long time of charging, the charging times of EVs are usually limited due to the urgent service demands of customers. To simulate this practical problem, this paper first formulates the EVRP with both capacity and charging time constraints (EVRP-CC). To tackle this new optimization problem, this paper further devises a two-stage solution construction method for ant colony optimization (ACO) to build feasible solutions to EVRP-CC. Subsequently, we embed the proposed method into five popular and classical ACO algorithms, namely ant system (AS), ranking based ant system (Rank-AS), elite ant system (EAS), max-min ant system (MMAS), and ant colony system (ACS), to solve EVRP-CC. Extensive experiments conducted on several instances generated from the widely used EVRP benchmark set demonstrate that the proposed solution construction method is effective to help ACO to solve EVRP-CC. In particular, Rank-AS with the proposed solution construction method achieves the best overall performance in solving EVRP-CC.

This paper proposes a ranking weight based roulette wheel selection (RWRWS) method for a promising particle swarm optimizer, called comprehensive learning particle swarm optimizer (CLPSO), to further improve its optimization performance. Specifically, the proposed RWRWS adopts a non-linear weight function to enhance the selection probabilities of promising personal best positions during the exemplar construction. In this way, it is expected that the construction efficiency of generating a promising leading exemplar for each particle could be improved and thus the optimization performance of CLPSO is expectedly elevated. To validate the feasibility and effectiveness of RWRWS, we carry out extensive experiments on a widely acknowledged benchmark problem set by comparing it with other three selection methods, namely the fitness-based roulette wheel selection (FRWS), the ranking based roulette wheel selection (RRWS), and the tournament selection (TS). Experimental results demonstrate that RWRWS helps CLPSO attain the best overall performance among the four selection methods.

High-dimensional problems are ubiquitous in many fields, yet still remain challenging to be solved. To tackle such problems with high effectiveness and efficiency, this article proposes a simple yet efficient stochastic dominant learning swarm optimizer. Particularly, this optimizer not only compromises swarm diversity and convergence speed properly, but also consumes as little computing time and space as possible to locate the optima. In this optimizer, a particle is updated only when its two exemplars randomly selected from the current swarm are its dominators. In this way, each particle has an implicit probability to directly enter the next generation, making it possible to maintain high swarm diversity. Since each updated particle only learns from its dominators, good convergence is likely to be achieved. To alleviate the sensitivity of this optimizer to newly introduced parameters, an adaptive parameter adjustment strategy is further designed based on the evolutionary information of particles at the individual level. Finally, extensive experiments on two high dimensional benchmark sets substantiate that the devised optimizer achieves competitive or even better performance in terms of solution quality, convergence speed, scalability, and computational cost, compared to several state-of-the-art methods. In particular, experimental results show that the proposed optimizer performs excellently on partially separable problems, especially partially separable multimodal problems, which are very common in real-world applications. In addition, the application to feature selection problems further demonstrates the effectiveness of this optimizer in tackling real-world problems.

Deep convolutional neural network (CNN) shows excellent effectiveness on hyperspectral image (HSI) classification. However, the architecture design of CNN requires abundant expert knowledge and experience, which poses great prohibition to its wide application in real-world engineering. To alleviate the issue, this article proposes an evolving block-based CNN (EB-CNN) to search the optimal architecture based on the genetic algorithm (GA) automatically. Specifically, two kinds of basic blocks with totally six different configurations are first designed to construct the search space. Then, a flexible encoding strategy is devised for the GA to allow different chromosomes to evolve with different lengths. In this manner, the width of each layer and the depth of the architecture can be simultaneously optimized. Furthermore, a novel swapping mutation operator is proposed for the GA to speed up the search efficiency and save computing resources. With the abovementioned techniques, the proposed algorithm automatically seeks the optimal CNN architecture for HSI classification, leading to its better usability than handcrafted CNNs. At last, extensive experiments conducted on five commonly used HSI datasets demonstrate that the proposed EB-CNN achieves highly competitive or even better performance, as compared with the state-of-the-art peer algorithms.

This paper proposes an adaptive version of an existing promising large-scale optimizer named level-based learning swarm optimizer (LLSO). Though such an optimizer has shown promising performance in dealing with large-scale optimization, it is much sensitive to its two introduced parameters. To alleviate this dilemma, this paper devises two simple yet effective adaptive adjustment strategies for the two parameters, leading to an adaptive LLSO(ALLSO). Specifically, this paper first defines a novel aggregation indicator based on the difference between the global best fitness and the averaged fitness of the swarm, to roughly evaluate the evolution state of the swarm. Then, based on this indicator, two adaptive adjustment strategies are devised to dynamically determine the values of the two parameters during the evolution. With these two strategies, the swarm is expected to maintain a potentially good balance between intensification and diversification. Extensive experiments conducted on two widely used large- scale benchmark sets demonstrate that the two adaptive strategies effectively improve the performance of LLSO.

Surrogate-assisted evolutionary algorithms (SAEAs) have become one popular method to solve complex and computationally expensive optimization problems. However, most existing SAEAs suffer from performance degradation with the dimensionality increasing. To solve this issue, this article proposes a classifier-assisted level-based learning swarm optimizer on the basis of the level-based learning swarm optimizer (LLSO) and the gradient boosting classifier (GBC) to improve the robustness and scalability of SAEAs. Particularly, the level-based learning strategy in LLSO has a tight correspondence with the classification characteristic by setting the number of levels in LLSO to be the same as the number of classes in GBC. Together, the classification results feedback the distribution of promising candidates to accelerate the evolution of the optimizer, while the evolved population helps to improve the accuracy of the classifier. To select informative and valuable candidates for real evaluations, we devise an${L}1$-exploitation strategy to extensively exploit promising areas. Then, the candidate selection is conducted between the predicted${L}1$offspring and the already real-evaluated${L}1$individuals based on their Euclidean distances. Extensive experiments on commonly used benchmark functions demonstrate that the proposed optimizer can achieve competitive or better performance with a very small training dataset compared with three state-of-the-art SAEAs.

Surrogated assisted evolutionary algorithms are commonly used to solve real-world expensive optimization problems. However, in some situations, no online data is available during the evolution process. In this situation, we have to build surrogate models based on offline historical data, which is known as offline data-driven optimization. Since no new data can be used to improve the surrogate models, offline data-driven optimization remains a challenging problem. In this paper, we propose a Gaussian process assisted offline estimation of multivariate Gaussian distribution algorithm to address the offline data-driven optimization problem. Instead of using surrogate models to predict the fitness values of individuals, we utilize a surrogate model to predict the rankings of individuals based on the frequently used lower confidence bound. In this way, the robustness of the proposed algorithm could be enhanced. Experiments are conducted on five commonly used benchmark problems. The experimental results demonstrate that the proposed offline surrogate model and the multivariate Gaussian estimation of distribution algorithm are able to achieve competitive performance.

The allocation of epidemic-control resources has been an increasingly active topic in the physical world. Most existing studies focus on the allocation of abstract and continuous epidemic control resources, and then formulate differentiable convex programming problems. However, real-world resources are usually discrete materials, goods, or services, so that resource allocation problems become non-convex. As a complementary study, this paper builds three discrete resource allocation problems based on an improved Susceptible-Exposed-Infectious- Vigilant (SEIV) spread model: the cost-constraint optimization problem (CCOP), rate-constraint optimization problem (RCOP), and eradication optimization problem (EOP). Then, existing swarm-based metaheuristic algorithms are adapted to effectively solve the problems. Thereinto, the Heuristic Majority-Voting Binary Particle Swarm Optimizer (HMV-BPSO) is present, which introduces a heuristic factor which concerns the probability distribution of resources to guide the evolution of particles and helps improve the performance of original MV-BPSO. Numerical experiments are developed to verify the effectiveness of swarm- based metaheuristic algorithms on epidemic control. Results show that HMV-BPSO can produce higher-quality solutions than other algorithms.

The rapid development of online social networks not only enables prompt and convenient dissemination of desirable information but also incurs fast and wide propagation of undesirable information. A common way to control the spread of pollutants is to block some nodes, but such a strategy may affect the service quality of a social network and leads to a high control cost if too many nodes are blocked. This paper considers the node selection problem as a biobjective optimization problem to find a subset of nodes to be blocked so that the effect of the control is maximized while the cost of the control is minimized. To solve this problem, we design an ant colony optimization algorithm with an adaptive dimension size selection under the multiobjective evolutionary algorithm framework based on decomposition (MOEA/D-ADACO). The proposed algorithm divides the biobjective problem into a set of single-objective subproblems and each ant takes charge of optimizing one subproblem. Moreover, two types of pheromone and heuristic information are incorporated into MOEA/D-ADACO, that is, pheromone and heuristic information of dimension size selection and that of node selection. While constructing solutions, the ants first determine the dimension size according to the former type of pheromone and heuristic information. Then, the ants select a specific number of nodes to build solutions according to the latter type of pheromone and heuristic information. Experiments conducted on a set of real-world online social networks confirm that the proposed biobjective optimization model and the developed MOEA/D-ADACO are promising for the pollutant spreading control.

Large-scale optimization with high dimensionality and high computational cost becomes ubiquitous nowadays. To tackle such challenging problems efficiently, devising distributed evolutionary computation algorithms is imperative. To this end, this paper proposes a distributed swarm optimizer based on a special master-slave model. Specifically, in this distributed optimizer, the master is mainly responsible for communication with slaves, while each slave iterates a swarm to traverse the solution space. An asynchronous and adaptive communication strategy based on the request-response mechanism is especially devised to let the slaves communicate with the master efficiently. Particularly, the communication between the master and each slave is adaptively triggered during the iteration. To aid the slaves to search the space efficiently, an elite-guided learning strategy is especially designed via utilizing elite particles in the current swarm and historically best solutions found by different slaves to guide the update of particles. Together, this distributed optimizer asynchronously iterates multiple swarms to collaboratively seek the optimum in parallel. Extensive experiments on a widely used large-scale benchmark set substantiate that the distributed optimizer could: 1) achieve competitive effectiveness in terms of solution quality as compared to the state-of-the-art large-scale methods; 2) accelerate the execution of the algorithm in comparison with the sequential one and obtain almost linear speedup as the number of cores increases; and 3) preserve a good scalability to solve higher dimensional problems.

In pedagogy, teachers usually separate mixed-level students into different levels, treat them differently and teach them in accordance with their cognitive and learning abilities. Inspired from this idea, we consider particles in the swarm as mixed-level students and propose a level-based learning swarm optimizer (LLSO) to settle large-scale optimization, which is still considerably challenging in evolutionary computation. At first, a level-based learning strategy is introduced, which separates particles into a number of levels according to their fitness values and treats particles in different levels differently. Then, a new exemplar selection strategy is designed to randomly select two predominant particles from two different higher levels in the current swarm to guide the learning of particles. The cooperation between these two strategies could afford great diversity enhancement for the optimizer. Further, the exploration and exploitation abilities of the optimizer are analyzed both theoretically and empirically in comparison with two popular particle swarm optimizers. Extensive comparisons with several state-of-the-art algorithms on two widely used sets of large-scale benchmark functions confirm the competitive performance of the proposed optimizer in both solution quality and computational efficiency. Finally, comparison experiments on problems with dimensionality increasing from 200 to 2000 further substantiate the good scalability of the developed optimizer.

Large-scale optimization has become a significant yet challenging area in evolutionary computation. To solve this problem, this paper proposes a novel segment-based predominant learning swarm optimizer (SPLSO) swarm optimizer through letting several predominant particles guide the learning of a particle. First, a segment-based learning strategy is proposed to randomly divide the whole dimensions into segments. During update, variables in different segments are evolved by learning from different exemplars while the ones in the same segment are evolved by the same exemplar. Second, to accelerate search speed and enhance search diversity, a predominant learning strategy is also proposed, which lets several predominant particles guide the update of a particle with each predominant particle responsible for one segment of dimensions. By combining these two learning strategies together, SPLSO evolves all dimensions simultaneously and possesses competitive exploration and exploitation abilities. Extensive experiments are conducted on two large-scale benchmark function sets to investigate the influence of each algorithmic component and comparisons with several state-of-the-art meta-heuristic algorithms dealing with large-scale problems demonstrate the competitive efficiency and effectiveness of the proposed optimizer. Further the scalability of the optimizer to solve problems with dimensionality up to 2000 is also verified.

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima.

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization (ACO) algorithms in preserving high diversity, this paper intends to extend ACO algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ACO algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima.

This paper presents a random-based dynamic grouping strategy (RDG) for cooperative coevolution to deal with large scale multi-objective optimization problems (MOPs) by decomposing the whole dimension into several groups of variables with an equal size. First, a decomposer pool containing different group sizes is designed. Then, a group size is dynamically selected with probability in the evolution process. The probability of each group size in the pool is computed based on the historical performance measured by C-metric, a common metric in multi-objective optimization. Under the selected group size, random grouping is executed to decompose the whole dimension into groups. Through this, both the group size and the group components are dynamic. Finally, combining RDG with a traditional and famous multi-objective evolutionary algorithm (MOEA) named MOEA/D, we develop MOEA/D-RDG to cope with large scale MOPs. The efficacy of the proposed MOEA/D-RDG is verified on two sets of MOPs (UF1-UF10 and WFG1-WFG9) through comparing with two MOEA/D variants.

Large scale optimization has become an important and challenging area in evolutionary computation. To solve this kind of problems efficiently, this paper proposes a multiple parents guided differential evolution (MPGDE) algorithm. Instead of using only one parent to guide each individual in traditional DE variants, multiple top ranked parents are utilized to direct each individual to search the space. Since the failed parents or trial vectors may also contain useful information, we maintain an archive to preserve these failed individuals and utilize a niching method to update the archive during evolution. Combining the above together, we put forward a new mutation strategy for DE. Cooperated with existing self-adaptive strategies for parameters in DE, MPGDE can afford a good balance between exploration and exploitation, so that promising performance can be obtained. Extensive experiments are conducted on 20 CEC'2010 large scale benchmark functions with 1000 dimensions to verify the efficacy and effectiveness of the developed MPGDE in comparison with several state-of-the-art algorithms dealing with large scale problems.