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Under frequency fitness assignment (FFA), the fitness corresponding to an objective value is its encounter frequency in fitness assignment steps and is subject to minimization. FFA renders optimization processes invariant under bijective transformations of the objective function value. On TwoMax, Jump, and Trap functions of dimension s, the classical (1 + 1)-EA with standard mutation at rate 1/s can have expected runtimes exponential in s. In our experiments, a (1 + 1)-FEA, the same algorithm but using FFA, exhibits mean runtimes that seem to scale as ${s}^{textit {2}}$ ln ${s}$ . Since Jump and Trap are bijective transformations of OneMax, it behaves identical on all three. On OneMax, LeadingOnes, and Plateau problems, it seems to be slower than the (1 + 1)-EA by a factor linear in s. The (1 + 1)-FEA performs much better than the (1 + 1)-EA on W-Model and MaxSat instances. We further verify the bijection invariance by applying the Md5 checksum computation as transformation to some of the above problems and yield the same behaviors. Finally, we show that FFA can improve the performance of a memetic algorithm for job shop scheduling.

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As an essential component in multi- and many-objective optimization, decision-making process either selects a subset of solutions from the whole Pareto front or guides the search toward a small part of the Pareto front during the evolutionary process. In recent years, for many-objective optimization problems (MaOPs), a number of evolutionary algorithms have been developed to search for Pareto optimal solutions. However, there is a lack of research works focusing on designing decision-making approaches. In order to overcome this deficiency, we propose a novel knee-based decision-making method to search for several solutions of interest (SOIs) from a large number of solutions on the Pareto front, each of which contains the best convergence performance at least within its neighborhood and can be identified as a global or local knee solution. The optimization performance achieved by all SOIs approximates the performance of the whole Pareto front as much as possible. Furthermore, in order to relieve the difficulties in the decision-making process on MaOPs, a new visualization approach is developed based on this proposed decision-making approach. It provides information about the shape and location of the Pareto front, the possible bulge, as well as the convergence degree and distribution of solutions. The experimental results on several benchmark functions demonstrate the superiority of the proposed design in the selection of SOIs and visualization of high-dimensional objective space.

Several models have been developed to predict how the COVID-19 pandemic spreads, and how it could be contained with nonpharmaceutical interventions, such as social distancing restrictions and school and business closures. This article demonstrates how evolutionary AI can be used to facilitate the next step, i.e., determining most effective intervention strategies automatically. Through evolutionary surrogate-assisted prescription, it is possible to generate a large number of candidate strategies and evaluate them with predictive models. In principle, strategies can be customized for different countries and locales, and balance the need to contain the pandemic and the need to minimize their economic impact. Early experiments suggest that workplace and school restrictions are the most important and need to be designed carefully. They also demonstrate that results of lifting restrictions can be unreliable, and suggest creative ways in which restrictions can be implemented softly, e.g., by alternating them over time. As more data becomes available, the approach can be increasingly useful in dealing with COVID-19 as well as possible future pandemics.

Feature selection is a complex optimization problem with important real-world applications. Normally, its main target is to reduce the dimensionality of the dataset and increase the effectiveness of the classification. Owing to the population-inspired characteristics, different evolutionary algorithms (EAs) have been proposed to solve feature selection problems over the past decades. However, the majority of them only consider single-objective optimization while many real-world problems have multiple objectives, which creates a genuine demand for designing more suitable and effective EAs to handle multiobjective feature selection. A multiobjective feature selection problem usually consists of two objectives: one is to minimize the number of selected features and the other is to minimize the error of classification. In this article, we propose a duplication analysis-based EA (DAEA) for biobjective feature selection in classification. In the proposed algorithm, we make improvements on the basic dominance-based EA framework in three aspects: first, the reproduction process is modified to improve the quality of offspring; second, a duplication analysis method is proposed to filter out the redundant solutions; and third, a diversity-based selection method is adopted to further select the reserved solutions. In the experiments, we have compared the proposed algorithm with five state-of-the-art multiobjective EAs (MOEAs) and tested them on 20 classification datasets, using two widely used performance metrics. According to the empirical results, DAEA performs the best on most datasets, indicating that DAEA not only gains outstanding optimization performance but also obtains good classification and generalization results.

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.

Multiobjective optimization is increasingly used in engineering to design new systems and to identify design tradeoffs. Yet, design problems often have objective functions and constraints that are expensive and highly nonlinear. Combinations of these features lead to poor convergence and diversity loss with common algorithms that have not been specifically designed for constrained optimization. Constrained benchmark problems exist, but they do not necessarily represent the challenges of engineering problems. In this article, a framework to design electro-mechanical actuators, called multiobjective design of actuators (MODAct), is presented and 20 constrained multiobjective optimization test problems are derived from the framework with a specific focus on constraints. The full source code is made available to ease its use. The effects of the constraints are analyzed through their impact on the Pareto front as well as on the convergence performance. A constraint landscape analysis approach is followed and extended with three new metrics to characterize the search and objective spaces. The features of MODAct are compared to existing test suites to highlight the differences. In addition, a convergence analysis using NSGA-II, NSGA-III, and C-TAEA on MODAct and existing test suites suggests that the design problems are indeed difficult due to the constraints. In particular, the number of simultaneously violated constraints in newly generated solutions seems key in understanding the convergence challenges. Thus, MODAct offers an efficient framework to analyze and handle constraints in future optimization algorithm design.

This article proposes a novel and computationally efficient explicit intertask information transfer strategy between optimization tasks by aligning the subspaces. In evolutionary multitasking, the tasks might have biases embedded in function landscapes and decision spaces, which often causes the threat of predominantly negative transfer. However, the complementary information among different tasks can give an enhanced performance of solving complicated problems when properly harnessed. In this article, we distill this insight by introducing an intertask knowledge transfer strategy implemented in the low-dimension subspaces via a learnable alignment matrix. Specifically, to unveil the significant features of the function landscapes, the task-specific low-dimension subspaces is established based on the distribution information of subpopulations possessed by tasks, respectively. Next, the alignment matrix between pairwise subspaces is learned by minimizing the discrepancies of the subspaces. Given the aligned subspaces by applying the alignment matrix to subspaces’ base vectors, the individuals from different tasks are then projected into aligned subspaces and reproduce therein. Moreover, since this method only considers the leading eigenvectors, it turns out to be intrinsically regularized and noise-insensitive. Comprehensive experiments are conducted on the synthetic and practical benchmark problems so as to assess the efficacy of the proposed method. According to the experimental results, the proposed method exhibits a superior performance compared with existing evolutionary multitask optimization algorithms.

The problem of inferring nonlinear and complex dynamical systems from available data is prominent in many fields, including engineering, biological, social, physical, and computer sciences. Many evolutionary algorithm (EA)-based network reconstruction methods have been proposed to address this problem, but they ignore several useful information of network structure, such as community structure, which widely exists in various complex networks. Inspired by the community structure, this article develops a community-based evolutionary multiobjective network reconstruction framework to promote the reconstruction performance of EA-based network reconstruction methods due to their good performance; we refer this framework as CEMO-NR. CEMO-NR is a generic framework and any population-based multiobjective metaheuristic algorithm can be employed as the base optimizer. CEMO-NR employs the community structure of networks to divide the original decision space into multiple small decision spaces, and then any multiobjective EA (MOEA) can be used to search for improved solutions in the reduced decision space. To verify the performance of CEMO-NR, this article also designs a test suite for complex network reconstruction problems. Three representative MOEAs are embedded into CEMO-NR and compared with their original versions, respectively. The experimental results have demonstrated the significant improvement benefiting from the proposed CEMO-NR in 30 multiobjective network reconstruction problems (MONRPs).