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Effective knowledge transfer has been proven to achieve superior performance in evolutionary optimization. Evolutionary multitasking optimization (EMT), which can solve several optimization tasks simultaneously using evolutionary algorithms, continues to be a young research field but is growing rapidly. Due to the parallelism of population-based search, the performance of component tasks can be improved through effective knowledge transfer between different tasks. The main challenge in the EMT field is addressing the negative transfer. Aiming to overcome this challenge, this paper proposes an EMT algorithm that transfers effective knowledge through semi-supervised learning. In addition, a semi-supervised classification method is designed based on the cluster assumption, which is part of the geometric basis of semi-supervised learning. By using both labeled and unlabeled samples generated in the optimization process, the proposed method can identify individuals that contain valuable knowledge and select them to transfer the knowledge between tasks. In this way, the performance of the EMT algorithm can be significantly improved. The effectiveness of the proposed method is verified by empirical tests and comparison with two benchmarks. Further, a case study is conducted. The results indicate that the proposed algorithm can achieve highly competitive performance compared with the state-of-the-art EMT algorithms. [ABSTRACT FROM AUTHOR]

Multi-objective multitasking optimization (MTO) is an emerging research topic in the field of evolutionary computation, which can solve multiple optimization tasks simultaneously and improve the convergence speed of each task. Recently, it has been demonstrated that the useful knowledge is always hidden in valuable solutions. When solving MTO problems, the core issue is how to select valuable solutions from the source task to help the target task. In this study, a multi-objective evolutionary multitasking algorithm based on positive knowledge transfer mechanism is proposed. Specifically, a cheap surrogate model is introduced to evaluate the quality of the solutions, which can find valuable solutions. Moreover, a diversity maintenance method is designed to maintain the diversity of solutions in each task. Finally, the selection strategy of transferred solutions is put forward to find valuable solutions with good diversity, which can improve the efficiency of positive knowledge transfer. Experiments on two MTO test suites and a real-world case demonstrate that the proposed algorithm is effective and competitive. [ABSTRACT FROM AUTHOR]

It is a challenge to balance the convergence and the diversity in multi-objective optimization problems. In this paper, a new two-stage based evolutionary algorithm (MOEA/TS) is proposed, where the convergence and the diversity are handled in two independent phases. In the first stage, the convergence is accelerated by using the gradient information of constrained sub-problems. In the second stage, the diversity is improved by adopting the dominance based multi-objective evolutionary algorithm. The comparative experiments are presented in terms of two performance indicators for benchmark test problems. The results indicates that MOEA/TS has the competitive performance. [ABSTRACT FROM AUTHOR]

Estimation of distribution algorithm (EDA) is a stochastic optimization algorithm based on probability distribution model and has been widely applied in global optimization. However, the random sampling of Gaussian EDA (GEDA) usually suffers from the poor diversity and the premature convergence, which severely limits its performance. This paper analyzes the shortcomings of the random sampling and develops an efficient mixture sampling model (EMSM). EMSM can explore more promising regions and utilize the unsuccessful mutation vectors, which achieves a good tradeoff between the diversity and the convergence. Moreover, the feasibility analysis of EMSM is studied. A new GEDA variant named EMSM-EDA is developed, which combines EMSM with enhancing Gaussian estimation of distribution algorithm (EDA2). The experimental results on IEEE CEC2013 and IEEE CEC2014 test suites demonstrate that EMSM-EDA is efficient and competitive. [ABSTRACT FROM AUTHOR]

A gradient-based search method (GBSM) is developed to solve multi-objective optimization problems. It uses the multi-objective gradient information to construct descent directions, i.e., Pareto descent directions (PDDs), to accelerate the convergence. In addition, a multi-objective evolutionary algorithm based on decomposition is adopted to improve the diversity. The comparisons between GBSM with several selected multi-objective evolutionary algorithms and gradient based algorithms on benchmark functions indicate that the proposed method performs competitively and effectively. [ABSTRACT FROM AUTHOR]

Multimodal multiobjective evolutionary algorithms are expected to search for not only Pareto optimal front but also the corresponding multiple equivalent Pareto optimal sets. To this end, this paper designs a framework to ameliorate the performance of the existing multiobjective evolutionary algorithms (MOEAs) for solving multimodal multiobjective optimization problems (MMOPs). In this framework, an MMOP is transformed into a bi-objective optimization problem. The first objective is built by either decomposition-based method or indicator-based method in MOEAs to ensure the population convergence. A diversity indicator is another objective used to preserve the population diversity. Based on these two objectives, two diversity selection strategies are developed, which are responsible for balancing the diversity and the convergence in the decision and objective spaces, respectively, at the same time. According to the feedback information in the evolution, our framework adaptively selects one of them to pick out the promising individuals. Four variants based on our framework are built and are evaluated on 22 MMOPs benchmark functions. Six feature selection problems are also employed to test the performance of our framework. The experimental results confirm that our proposed framework performs well in all criteria. [ABSTRACT FROM AUTHOR]

The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate. [ABSTRACT FROM AUTHOR]

The architecture of multilayer perceptron (MLP) neural networks dictates the network's performance. However, aiming at the specific classification problems, suitable architectures of MLPs must be determined beforehand. More often, the design decisions rely on a trial and error learning and the experience knowledge. To automatically design an MLP's network architecture and optimize network parameters, a multiobjective bilevel programming model is built. In this model, a multiobjective optimization problem is constructed in the upper level for obtaining a set of Pareto optimal architectures of the MLPs, considering network complexity, training error rate, and validation error rate, while a single-objective optimization problem is established in the lower level to search for the optimum network parameters for a given network architecture. For dealing with this model efficiently, a novel multiobjective hierarchical learning algorithm (MOHLA) is proposed, in which an integer-coding NSGA-II is developed as the upper-level optimizer for a set of Pareto optimal network structures of the MLPs, while a non-iterative method is regarded as the lower-level solver for the MLPs' connection parameters. After a set of trained MLPs is obtained finally by using MOHLA, a selective ensemble strategy is adopted for improving identification accuracy. Three types of multiobjective bilevel programming models are investigated and compared in the experiments. Moreover, the proposed MOHLA is compared with several state-of-the-art learning approaches on various classification problems. The experimental results confirm that MOHLA performs well. [ABSTRACT FROM AUTHOR]

Concerning this issue that the solution search equation of artificial bee colony algorithm (ABC) does well in exploration but badly in exploitation, a bare bones ABC with parameter adaptation and fitness-based neighborhood is proposed, BABC for short reference. The proposed method employs a Gaussian search equation to produce a new candidate individual at the onlooker phase which exploits the valuable information hidden in the best individual to improve the exploitation, while, at the employed bee phase, a parameter adaptation strategy and a fitness-based neighborhood mechanism are integrated into the search equation which can take advantage of the information from the previous search and better individuals to enhance the search ability. The proposed framework can be applied to any ABC with minimal changes. Furthermore, the proposed framework is applied to the original ABC and several highly regarded ABC variants. The comparison results demonstrate that the proposed framework is able to significantly improve the performance of the original ABC and the modified ABC variants. [ABSTRACT FROM AUTHOR]

The key of multimodal optimization algorithms is to divide the population into multiple species, and each species searches for a global optimum. This article proposes a new differential evolution based on the Hill-Valley technique for multimodal optimization. This technique uses history information to classify individuals on the same peak as one species. Compared to other niching techniques, this technique is insensitive to parameters and does not waste additional computing resources. For each species, the evolutionary state recognition method is developed to judge the evolutionary state and the search strategy is designed according to the evolutionary state. In addition, the prediction mechanism is designed to save computing resources. The experimental results show that the performance of the proposed algorithm is better than other algorithms on the CEC2013 test set and the NESs test set. [ABSTRACT FROM AUTHOR]

Feature selection (FS) in data mining and machine learning has attracted extensive attention. The purpose of FS in a classification task is to find the optimal subset of features from given candidate features. Recently, more and more meta-heuristic algorithms have been used to deal with the FS problems. However, meta-heuristic algorithms suffer from certain issues, such as large search space for solutions and huge time consumption. Moreover, most of existing meta-heuristic algorithms focus only on the selection of an optimal feature subset, and pay little attention to the optimal design of the classifier. In this article, we propose a joint multiobjective optimization method for both feature selection and classifier design, called JMO-FSCD. The proposed approach uses neural network as a classifier and introduces a non-iterative algorithm for training the classifier so as to ensure good performance and fast learning. A new coding scheme is also designed for optimizing FS and classifier simultaneously. For demonstrating the superiority of the proposed approach, its performance is compared with those of six state-of-the-art FS algorithms. Experimental results on thirty-five benchmark data sets reflect the superior performance of the proposed JMO-FSCD. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithm based on the inverse model (IM-MOEA) is a popular method to solve multi-objective optimization problems (MOPs). However, IM-MOEA has some drawbacks such as low accuracy and difficulty in dealing with MOPs with irregular PFs. To address these issues, adaptive reference vector mechanism and nonrandom grouping strategy are employed in IM-MOEA, which enhances the reliability of the inverse model. In addition, a modified selection mechanism is used to choose candidate solutions. Further, an enhanced IM-MOEA with adaptive reference vectors and nonrandom grouping (AN-IMMOEA) is proposed in this paper. The experimental results on 27 MOPs indicate that the proposed method has a better performance than other MOEAs. [ABSTRACT FROM AUTHOR]

Multifactorial Optimization (MFO) has attracted considerable attention in the community of evolutionary computation, which aims to deal with multiple optimization tasks simultaneously by information transfer. Unfortunately, information transfer may cause both positive and negative effects. To address this issue, this paper exploits an explicit multipopulation evolutionary framework (MPEF) to intelligently take advantage of positive information transfer and effectively reduce negative information transfer. In MPEF, each task possesses an independent population and has its random mating probability for exploiting the information of other tasks. Moreover, the random mating probability of each task is adjusted adaptively. The benefits of using MPEF are twofold. 1) Various well-developed search engines can be easily embedded into MPEF for solving the single task of multifactorial optimization problems. 2) The positive information transfer can be exploited. Meanwhile, negative information transfer can be prevented. A multifactorial evolutionary algorithm (named MFMP) is realized as an instance by embedding a well-designed search engine into MPEF. The experimental results on some MFO benchmark problems demonstrate the advantage of MFMP over some state-of-the-art algorithms. Moreover, MFMP is also successfully employed to solve the spread spectrum radar polyphase code design (SSRPCD) problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose a finite-time discrete distributed learning algorithm, denoted as the FTDDL algorithm, using the Stochastic Configuration Network (SCN) and Zero Gradient Sum (ZGS) strategy. In distributed scenarios, the communication networks that store data are modeled as algebraic graphs and the learning problems are formulated as distributed optimization problems. The FTDDL algorithm persists the universal approximation of the SCN learner. The process of the FTDDL algorithm is divided into two phases, namely "distributed hidden parameters configuration" and "distributed output weights determination". It has been theoretically proved that the FTDDL algorithm works in distributed manner and achieves the same efficiency as the centralized SCN. According to the FTDDL algorithm, each node over the communication network transmits the updated output weights of the SCN with its direct neighbors. Thus, the FTDDL algorithm preserves data privacy and saves network bandwidth. The FTDDL algorithm is theoretically proved to converge to the global optimal output weights of the SCN within finite time. Compared with the other distributed learning algorithms using SCNs, the FTDDL algorithm can significantly reduce the iteration times. At last, some experiments are shown in Simulations part to verify the effectiveness of the FTDDL algorithm. [ABSTRACT FROM AUTHOR]

Inspired by the intelligent foraging behavior of honey bees, the artificial bee colony algorithm (ABC), a swarm-based stochastic optimization method, has shown to be very effective and efficient for solving optimization problems. However, since its solution search equation is good at exploration but poor at exploitation, ABC often suffers from a slow convergence speed. To better balance the tradeoff between exploration and exploitation, in this paper, we propose a depth-first search (DFS) framework. The key feature of the DFS framework is to allocate more computing resources to the food sources with better quality and easier to be improved for evolution. We apply the DFS framework to ABC, GABC and CABC, yielding DFSABC, DFSGABC and DFSCABC respectively. The experimental results on 22 benchmark functions show that the DFS framework can speed up convergence rate in most cases. To further improve the performance, we introduce two novel solution search equations: the first equation incorporates the information of elite solutions and can be applied to the employed bee phase, while the second equation not only exploits the information of the elite solutions but also employs the current best solution in the onlooker bee phase. Finally, two novel proposed search equations are combined with DFSABC to form a new variant of ABC, named DFSABC_elite. Through the comparison of DFSABC_elite with other variants of ABC and some non-ABC methods, the experimental results demonstrate that DFSABC_elite is significantly better than the compared algorithms on most of the test functions in terms of solution quality, robustness, and convergence speed. [ABSTRACT FROM AUTHOR]