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With the advent of electric vehicles (EVs), issues connected to the electric vehicle charging scheduling (EVCS) problem, which is $\textsf {NP}$ -hard, have become important. In previous studies, EVCS has been mainly formulated as a constrained shortest-path problem; however, such formulations have not involved variables such as charging rates, traffic congestion, scalability, and waiting time at charging station (CS), that need to be considered in practical settings. Earlier research has also tended to focus on the strengths of particular evolutionary optimization algorithms like differential evolution (DE) or particle swarm optimization (PSO) over others or traditional mathematical programming methods, with only a limited study of hybrid approaches. In this paper, fast and slow charging options at a station are considered in the EVCS problem for practical use. In previous studies, EVs have been considered to have fixed speeds; however, in order to mitigate CS congestion and thus waiting times at CSs, dynamic speed control of EVs has been considered in this work. This work also investigates the scalability of different EVCS solutions. A hybrid approach using PSO and the Firefly algorithm (FFA) with a Lévy flights search strategy is designed and implemented to solve the EVCS. Also, different hybrid methods variants of PSO and FFA have been evaluated in this paper to find the best performing hybrid variant. Experimental results validate the effectiveness of our approach on both synthetic and the real-world transportation networks. [ABSTRACT FROM AUTHOR]

Pattern mining (PM) refers to the process of discovering patterns of interest to users from data. However, most studies have considered only one pattern, such as frequent pattern or high-utility pattern. With the continuous requirement of businesses in various industries, the single-objective PM methods are difficult to meet the increasingly diverse needs of users. In this paper, a multi-objective problem model for high quality pattern mining (HQPM) is proposed, where the objectives are support, occupancy, and utility. In order to solve the proposed three-objective problem efficiently, an improved multi-objective evolutionary algorithm for HQPM (MOEA-PM) is proposed. Two kinds of population initialization strategies are designed, which is used to ensure the population is effectively distributed in the feasible solution space. By taking the properties of the model into consideration, an auxiliary tool is proposed to accelerate the convergence of the algorithm. Experimental results on real-world datasets show that the proposed three-objective problem model with the MOEA-PM algorithm can discover patterns that are both frequently occurring and has a high utility in the transaction datasets, while at the same time being relatively complete. Compared with the state-of-the-art MOEA-based HQPM algorithms, MOEA-PM has better performance in terms of efficiency, quality, and convergence speed. [ABSTRACT FROM AUTHOR]

In many diagnostic imaging settings, including positron emission tomography (PET), images are typically used for multiple tasks such as detecting disease and quantifying disease. Unlike conventional image reconstruction that optimizes a single objective, this work proposes a multi-objective optimization algorithm for PET image reconstruction to identify a set of images that are optimal for more than one task. This work is reliant on a genetic algorithm to evolve a set of solutions that satisfies two distinct objectives. In this paper, we defined the objectives as the commonly used Poisson log-likelihood function, typically reflective of quantitative accuracy, and a variant of the generalized scan-statistic model, to reflect detection performance. The genetic algorithm uses new mutation and crossover operations at each iteration. After each iteration, the child population is selected with non-dominated sorting to identify the set of solutions along the dominant front or fronts. After multiple iterations, these fronts approach a single non-dominated optimal front, defined as the set of PET images for which none the objective function values can be improved without reducing the opposing objective function. This method was applied to simulated 2D PET data of the heart and liver with hot features. We compared this approach to conventional, single-objective approaches for trading off performance: maximum likelihood estimation with increasing explicit regularization and maximum a posteriori estimation with varying penalty strength. Results demonstrate that the proposed method generates solutions with comparable to improved objective function values compared to the conventional approaches for trading off performance amongst different tasks. In addition, this approach identifies a diverse set of solutions in the multi-objective function space which can be challenging to estimate with single-objective formulations. [ABSTRACT FROM AUTHOR]

The article presents issues related to hybrid nature-inspired population-based algorithms of global optimization and their industrial applications. To this end, the article presents a general concept of nature-inspired population-based optimization methods and the ways in which those methods can be hybridized with other techniques. Concrete literature-based examples have been used to illustrate each type of hybridization. This article also demonstrates the publication popularity of selected hybrid nature-inspired population-based optimization algorithms and indicates their most common application areas. Moreover, this article refers to the computational and implementation complexity of the algorithms in question. Next, the focus shifts to industrial applications of hybrid nature-inspired population-based optimization methods. References have been made to numerous works that present different versions of hybrid optimization algorithms, showing the areas of their practical application. Moreover, this article discusses the problems inherent in hybrid optimization methods as well as indicates open research points in this field. [ABSTRACT FROM AUTHOR]

In the field of optimization and machine learning, the statistical assessment of results has played a key role in conducting algorithmic performance comparisons. Classically, null hypothesis statistical tests have been used. However, recently, alternatives based on Bayesian statistics have shown great potential in complex scenarios, especially when quantifying the uncertainty in the comparison. In this work, we delve deep into the Bayesian statistical assessment of experimental results by proposing a framework for the analysis of several algorithms on several problems/instances. To this end, experimental results are transformed to their corresponding rankings of algorithms, assuming that these rankings have been generated by a probability distribution (defined on permutation spaces). From the set of rankings, we estimate the posterior distribution of the parameters of the studied probability models, and several inferences concerning the analysis of the results are examined. Particularly, we study questions related to the probability of having one algorithm in the first position of the ranking or the probability that two algorithms are in the same relative position in the ranking. Not limited to that, the assumptions, strengths, and weaknesses of the models in each case are studied. To help other researchers to make use of this kind of analysis, we provide a Python package and source code implementation at https://zenodo.org/record/6320599. [ABSTRACT FROM AUTHOR]

This work assesses the efficacy of evolutionary algorithms (EAs) using an intuitive multidimensional scaling (MDS) visualization of the evolution of a population. We propose the use of landmark MDS (LMDS) to overcome computational challenges inherent to visualizing many-objective and complex problems with MDS. For the benchmark problems we tested, LMDS is akin to MDS visually, whilst requiring less than 1% of the time and memory necessary to produce an MDS visualization of the same objective space solutions, leading to the possibility of online visualizations for multi- and many-objective optimization evaluation. Using multi- and many-objective problems from the DTLZ and WFG benchmark test suites, we analyze how Landmark MDS visualizations can offer far greater insight into algorithm performance than using traditional algorithm performance metrics such as hypervolume alone, and can be used to complement explicit performance metrics. Ultimately, this visualization allows the visual identification of problem features and assists the decision maker in making intuitive recommendations for algorithm parameters/operators for creating and testing better EAs to solve multi- and many-objective problems. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

We introduce an evolutionary algorithm called recombinator- $k$ -means for optimizing the highly nonconvex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically recombining them with a repurposed variant of the $k$ -means++ seeding algorithm. The recombination also uses a reweighting mechanism that realizes a progressively sharper stochastic selection policy and ensures that the population eventually coalesces into a single solution. We compare this scheme with a state-of-the-art alternative, a more standard genetic algorithm with deterministic pairwise-nearest-neighbor crossover and an elitist selection policy, of which we also provide an augmented and efficient implementation. Extensive tests on large and challenging datasets (both synthetic and real word) show that for fixed population sizes recombinator- $k$ -means is generally superior in terms of the optimization objective, at the cost of a more expensive crossover step. When adjusting the population sizes of the two algorithms to match their running times, we find that for short times the (augmented) pairwise-nearest-neighbor method is always superior, while at longer times recombinator- $k$ -means will match it and, on the most difficult examples, take over. We conclude that the reweighted whole-population recombination is more costly but generally better at escaping local minima. Moreover, it is algorithmically simpler and more general (it could be applied even to $k$ -medians or $k$ -medoids, for example). Our implementations are publicly available at https://github.com/carlobaldassi/RecombinatorKMeans.jl. [ABSTRACT FROM AUTHOR]

Dynamic multiobjective optimization problems (DMOPs) aim to optimize multiple (often conflicting) objectives that are changing over time. Recently, there are a number of promising algorithms proposed based on transfer learning methods to solve DMOPs. However, it is very challenging to reduce the negative effect in transfer learning and find more effective transferred solutions. To fill this research gap, this article proposes a clustering-based transfer (CBT) learning method to solve DMOPs. When the environment changes, two novel operations (clustering-based selection (CBS) and CBT) are used to guide knowledge transfer. Specifically, CBS aims to find a population with nondominated solutions and dominated solutions as the training data for the new environment. Then, CBT further collects the previous Pareto-optimal solutions and some noise solutions as the training data for the previous environment. Two training data sets from different environments are, respectively, divided into multiple clusters and transfer learning is conducted on two similar clusters with high probability to reduce the negative effect, which can train an accurate prediction model to identify the promising solutions for the new environment. Empirical studies have been conducted on 14 benchmark DMOPs and one real-life path planning problem of unmanned air/ground vehicles, which validate the effectiveness of our proposed method. Especially, our method can significantly reduce negative transfer on 12 out of 14 cases when compared with direct transfer learning. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) possess strong problem-solving abilities and have been applied in a wide range of applications. However, they still suffer from a high computational burden and poor generalization ability. To overcome the limitations, numerous studies consider conducting knowledge extraction across distinct optimization task domains. Among these research strands, one representative tributary is evolutionary multitask optimization (EMTO) that aims to resolve multiple optimization tasks simultaneously. The underlying attribute of implicit parallelism for EAs can well incorporate with the framework of EMTO, giving rise to the ascending EMTO studies. This review is intended to present a detailed exposition on the research in the EMTO area. We reveal the core components for designing the EMTO algorithms. Subsequently, we organize the works lying in the fusions between EMTO and traditional EAs. By analyzing the associations for diverse strategies in different branches of EMTO, this review uncovers the research trends and the potentially important directions, with additional interesting real-world applications mentioned. [ABSTRACT FROM AUTHOR]

Real-world multiobjective optimization problems usually involve conflicting objectives that change over time, which requires the optimization algorithms to quickly track the Pareto-optimal front (POF) when the environment changes. In recent years, evolutionary algorithms based on prediction models have been considered promising. However, most existing approaches only make predictions based on the linear correlation between a finite number of optimal solutions in two or three previous environments. These incomplete information extraction strategies may lead to low prediction accuracy in some instances. In this article, an incremental support vector machine (ISVM)-based dynamic multiobjective evolutionary algorithm, in short called ISVM-DMOEA, is proposed. We treat the solving of dynamic multiobjective optimization problems (DMOPs) as an online learning process, using the continuously obtained optimal solution to update an ISVM without discarding the solution information at earlier time. ISVM is then used to filter random solutions and generate an initial population for the next moment. To overcome the obstacle of insufficient training samples, a synthetic minority oversampling strategy is implemented before the training of ISVM. The advantage of this approach is that the nonlinear correlation between solutions can be explored online by ISVM, and the information contained in all historical optimal solutions can be exploited to a greater extent. The experimental results and comparison with the chosen state-of-the-art algorithms demonstrate that the proposed algorithm can effectively tackle DMOPs. [ABSTRACT FROM AUTHOR]

The energy-efficient flexible job shop scheduling problem (FJSP) has attracted much attention in deterministic cases; however, uncertainty is seldom incorporated into energy-efficient FJSP and the neglecting of uncertainty will greatly diminish the application value of scheduling results. These make it necessary to handle uncertainty in the problem. In this study, energy-efficient fuzzy FJSP (EFFJSP) is considered and a bi-population evolutionary algorithm with feedback (FBEA) is proposed to minimize fuzzy makespan and fuzzy total energy consumption and maximize minimum agreement index. The computation of fuzzy energy consumption is given and four heuristics are proposed to produce the initial population. An effective method is presented to evaluate the quality of two populations and a feedback mechanism based on population quality is adopted to dynamically adjust the size of each population. A novel process of reproduction, crossover and mutation is developed based on feedback. An enhanced local search is also used to produce high-quality solutions. Extensive experiments are conducted to test the performance of FBEA. FBEA can provide promising results for EFFJSP. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are well suited for computationally expensive optimization. However, most existing SAEAs only focus on low- or medium-dimensional expensive optimization. Thus, a novel SAEA for high-dimensional expensive optimization, denoted as surrogate-assisted multipopulation particle swarm optimizer (SA-MPSO), is proposed and fully investigated in this work. The proposed algorithm employs a parameter-free clustering technique, denoted as affinity propagation clustering, to generate several subswarms. A surrogate-assisted learning strategy-based particle swarm optimizer is proposed for guiding the search of each subswarm. Furthermore, a model management strategy is adapted to choose the promising particles for real fitness evaluations. Finally, a subswarm diversity maintenance scheme and a surrogate-based trust region local search technique are introduced to enhance both exploration and exploitation. The experimental results on commonly used benchmark test problems with dimensions varying from 30 to 100 and airfoil design problem have shown that SA-MPSO outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

Evolutionary multitask optimization (EMTO) studies how to simultaneously solve multiple optimization tasks via evolutionary algorithms (EAs) while making the useful knowledge acquired from solving one task to assist solving other tasks, aiming to improve the overall performance of solving each individual task. Recent years have seen a large body of EMTO works based on different kinds of EAs and studying one or more aspects in how to represent, extract, transfer, and reuse knowledge. A key challenge to EMTO is the occurrence of negative knowledge transfer between tasks, which becomes severer when the total number of tasks increases. To address this issue, we propose an adaptive EMTO (AEMTO) framework. This framework can adapt knowledge transfer frequency, knowledge source selection, and knowledge transfer intensity in a synergistic way to make the best use of knowledge transfer, especially when facing many tasks. We implement the proposed AEMTO framework and evaluate our implementation on three suites of MTO problems with 2, 10, and 50 tasks and one real-world MTO problem with 2000 tasks in comparison to several state-of-the-art EMTO methods with certain adaptation strategies regarding knowledge transfer and the single-task optimization counterpart of the proposed method. Experimental results have demonstrated the effectiveness of the adaptive knowledge transfer strategies used in AEMTO and the overall performance superiority of AEMTO. [ABSTRACT FROM AUTHOR]

To prevent the population from getting stuck in local areas and then missing the constrained Pareto front fragments in dealing with constrained multiobjective optimization problems (CMOPs), it is important to guide the population to evenly explore the promising areas that are not dominated by all examined feasible solutions. To this end, we first introduce a cost value-based distance into the objective space, and then use this distance and the constraints to define an indicator to evaluate the contribution of each individual to exploring the promising areas. Theoretical studies show that the proposed indicator can effectively guide population to focus on exploring the promising areas without crowding in local areas. Accordingly, we propose a new constraint handling technique (CHT) based on this indicator. To further improve the diversity of population in the promising areas, the proposed indicator-based CHT divides the promising areas into multiple subregions, and then gives priority to removing the individuals with the worst fitness values in the densest subregions. We embed the indicator-based CHT in evolutionary algorithm and propose an indicator-based constrained multiobjective algorithm for solving CMOPs. Numerical experiments on several benchmark suites show the effectiveness of the proposed algorithm. Compared with six state-of-the-art constrained evolutionary multiobjective optimization algorithms, the proposed algorithm performs better in dealing with different types of CMOPs, especially in those problems that the individuals are easy to appear in the local infeasible areas that dominate the constrained Pareto front fragments. [ABSTRACT FROM AUTHOR]

Evolutionary multitask optimization (EMTO) has recently attracted widespread attention in the evolutionary computation community, which solves two or more tasks simultaneously to improve the convergence characteristics of tasks when individually optimized. Effective knowledge between tasks is transferred by taking advantage of the parallelism of population-based search. Without any prior knowledge about tasks, it is a challenging problem of how to adaptively transfer effective knowledge between tasks and reduce the impact of negative transfer in EMTO. However, these two issues are rarely studied simultaneously in the existing literature. Besides, in complex many-task environments, the potential relationships among individuals from highly diverse populations associated with tasks directly determine the effectiveness of cross-task knowledge transfer. Keeping those in mind, we propose a multitask evolutionary algorithm based on anomaly detection (MTEA-AD). Specifically, each task is assigned a population and an anomaly detection model. Each anomaly detection model is used to learn the relationship among individuals between the current task and the other tasks online. Individuals that may carry negative knowledge are identified as outliers, and candidate transferred individuals identified by the anomaly detection model are selected to assist the current task, which may carry common knowledge across the current task and other tasks. Furthermore, to realize the adaptive control of the degree of knowledge transfer, the successfully transferred individuals that survive to the next generation through the elitism are used to update the anomaly detection parameter. The fair competition between offspring and candidate transferred individuals can effectively reduce the risk of negative transfer. Finally, the empirical studies on a series of synthetic benchmarks and a practical study are conducted to verify the effectiveness of MTEA-AD. The experimental results demonstrate that our proposal can adaptively adjust the degree of knowledge transfer through the anomaly detection model to achieve highly competitive performance compared to several state-of-the-art EMTO methods. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This letter presents a multi-objective optimization strategy for switched reluctance generator based on fuzzy inference non-dominated sorting genetic algorithm III, which is able to search and rank solutions in Pareto front with the preference of designer to overcome the secondary choice difficulty. Mamdani fuzzy inference system is established in line with the decision maker's way of thinking, and is introduced into non-dominated sorting genetic algorithm III, the competitive optimal solutions with relative intensity value are achieved with consideration of the designer's preferences so that the practical decision-making efficiency is improved. The effectiveness of the proposed multi-objective optimization strategy for switched reluctance generator is validated by the simulation verification. [ABSTRACT FROM AUTHOR]

This article proposes an evolutionary algorithm using multiple penalties and multiple local surrogates (MPMLS) for expensive constrained optimization. In each generation, MPMLS defines and optimizes a number of subproblems. Each subproblem penalizes the constraints in the original problem using a different penalty coefficient and has its own search subregion. A local surrogate is built for optimizing each subproblem. Two major advantages of MPMLS are: 1) it can maintain good population diversity so that the search can approach the optimal solution of the original problem from different directions and 2) it only needs to build local surrogates so that the computational overhead of the model building can be reduced. Numerical experiments demonstrate that our proposed algorithm performs much better than some other state-of-the-art evolutionary algorithms. [ABSTRACT FROM AUTHOR]

It is particularly challenging for evolutionary algorithms to quickly converge to the Pareto front in large-scale multiobjective optimization. To tackle this problem, this article proposes a large-scale multiobjective evolutionary algorithm assisted by some selected individuals generated by directed sampling (DS). At each generation, a set of individuals closer to the ideal point is chosen for performing a DS in the decision space, and those nondominated ones of the sampled solutions are used to assist the reproduction to improve the convergence in evolutionary large-scale multiobjective optimization. In addition, elitist nondominated sorting is adopted complementarily for environmental selection with a reference vector-based method in order to maintain diversity of the population. Our experimental results show that the proposed algorithm is highly competitive on large-scale multiobjective optimization test problems with up to 5000 decision variables compared to five state-of-the-art multiobjective evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Evolutionary Algorithms (EA) are widely applied in Neural Architecture Search (NAS) and have achieved appealing results. Different EA-based NAS algorithms may utilize different encoding schemes for network representation, while they have the same workflow. Specifically, the first step is the initialization of the population with different encoding schemes, and the second step is the evaluation of the individuals by the fitness function. Then, the EA-based NAS algorithm executes evolution operations, e.g., selection, mutation, and crossover, to eliminate weak individuals and generate more competitive ones. Lastly, evolution continues until the max generation and the best neural architectures will be chosen. Because each individual needs complete training and validation on the target dataset, the EA-based NAS always consumes significant computation and time inevitably, which results in the bottleneck of this approach. To ameliorate this issue, this article proposes a distributed framework to boost the computation of the EA-based NAS algorithm. This framework is a server/worker model where the server distributes individuals requested by the computing nodes and collects the validated individuals and hosts the evolution operations. Meanwhile, the most time-consuming phase (i.e., individual evaluation) of the EA-based NAS is allocated to the computing nodes, which send requests asynchronously to the server and evaluate the fitness values of the individuals. Additionally, a new packet structure of the message delivered in the cluster is designed to encapsulate various network representations and support different EA-based NAS algorithms. We design an EA-based NAS algorithm as a case to investigate the efficiency of the proposed framework. Extensive experiments are performed on an illustrative cluster with different scales, and the results reveal that the framework can achieve a nearly linear reduction of the search time with the increase of the computational nodes. Furthermore, the length of the exchanged messages among the cluster is tiny, which benefits the framework expansion. [ABSTRACT FROM AUTHOR]