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In dynamic optimization problems (DOPs), as the environment changes through time, the optima also dynamically change. How to adapt to the dynamic environment and quickly find the optima in all environments is a challenging issue in solving DOPs. Usually, a new environment is strongly relevant to its previous environment. If we know how it changes from the previous environment to the new one, then we can transfer the information of the previous environment, e.g., past solutions, to get new promising information of the new environment, e.g., new high-quality solutions. Thus, in this paper, we propose a neural network (NN)-based information transfer method, named NNIT, to learn the transfer model of environment changes by NN and then use the learned model to reuse the past solutions. When the environment changes, NNIT first collects the solutions from both the previous environment and the new environment and then uses an NN to learn the transfer model from these solutions. After that, the NN is used to transfer the past solutions to new promising solutions for assisting the optimization in the new environment. The proposed NNIT can be incorporated into population-based evolutionary algorithms (EAs) to solve DOPs. Several typical state-of-the-art EAs for DOPs are selected for comprehensive study and evaluated using the widely used moving peaks benchmark. The experimental results show that the proposed NNIT is promising and can accelerate algorithm convergence. [ABSTRACT FROM AUTHOR]

Most learning methods contain optimization as a substep, where the nondifferentiability and multimodality of objectives push forward the interplay of evolutionary optimization algorithms and machine learning models. The recently emerged evolutionary multimodal optimization (MMOP) technique enables the learning of diverse sets of effective parameters for the models simultaneously, providing new opportunities to the applications requiring both accuracy and diversity, such as ensemble, interactive, and interpretive learning. Targeting at locating multiple optima simultaneously in the multimodal landscape, this paper develops an efficient neighborhood-based niching algorithm. Bare-bones differential evolution is used as the baseline. Further, using Gaussian mutation with local mean and standard deviations, the neighborhoods capture niches that match well with the contours of peaks in the landscape. To increase diversity and enhance global exploration, the proposed algorithm embeds a diversity preserving operator to reinitialize converged or overlapped neighborhoods. The experimental results verify that the proposed algorithm has superior and consistent performance for a wide range of MMOP problems. Further, the algorithm has been successfully applied to train neural network ensembles, which validates its effectiveness and benefits of learning multimodal parameters. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is an advanced method for nonnegative feature extraction, with widespread applications. However, the NMF solution often entails to solve a global optimization problem with a nonconvex objective function and nonnegativity constraints. This paper presents a collective neurodynamic optimization (CNO) approach to this challenging problem. The proposed collective neurodynamic system consists of a population of recurrent neural networks (RNNs) at the lower level and a particle swarm optimization (PSO) algorithm with wavelet mutation at the upper level. The RNNs act as search agents carrying out precise local searches according to their neurodynamics and initial conditions. The PSO algorithm coordinates and guides the RNNs with updated initial states toward global optimal solution(s). A wavelet mutation operator is added to enhance PSO exploration diversity. Through iterative interaction and improvement of the locally best solutions of RNNs and global best positions of the whole population, the population-based neurodynamic systems are almost sure able to achieve the global optimality for the NMF problem. It is proved that the convergence of the group-best state to the global optimal solution with probability one. The experimental results substantiate the efficacy and superiority of the CNO approach to bound-constrained global optimization with several benchmark nonconvex functions and NMF-based clustering with benchmark data sets in comparison with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces the backward mean-field (MF) linear-quadratic-Gaussian (LQG) games (for short, BMFLQG) of weakly coupled stochastic large-population system. In contrast to the well-studied forward mean-field LQG games, the individual state in our large-population system follows the backward stochastic differential equation (BSDE) whose terminal instead initial condition should be prescribed. Two classes of BMFLQG games are discussed here and their decentralized strategies are derived through the consistency condition. In the first class, the individual agents of large-population system are weakly coupled in their state dynamics and the full information can be accessible to all agents. In the second class, the coupling structure lies in the cost functional with only partial information structure. In both classes, the asymptotic near-optimality property (namely, $\epsilon$- Nash equilibrium) of decentralized strategies are verified. To this end, some estimates to BSDE, are presented in the large-population setting. [ABSTRACT FROM AUTHOR]

Effective hashing for large-scale image databases is a popular research area, attracting much attention in computer vision and visual information retrieval. Several recent methods attempt to learn either graph embedding or semantic coding for fast and accurate applications. In this paper, a novel unsupervised framework, termed evolutionary compact embedding (ECE), is introduced to automatically learn the task-specific binary hash codes. It can be regarded as an optimization algorithm that combines the genetic programming (GP) and a boosting trick. In our architecture, each bit of ECE is iteratively computed using a weak binary classification function, which is generated through GP evolving by jointly minimizing its empirical risk with the AdaBoost strategy on a training set. We address this as greedy optimization by embedding high-dimensional data points into a similarity-preserved Hamming space with a low dimension. We systematically evaluate ECE on two data sets, SIFT 1M and GIST 1M, showing the effectiveness and the accuracy of our method for a large-scale similarity search. [ABSTRACT FROM PUBLISHER]

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem. [ABSTRACT FROM PUBLISHER]

This paper presents a Gaussian classifier-based evolutionary strategy (GCES) to solve multimodal optimization problems. An evolutionary technique for them must answer two crucial questions to guarantee its success: how to distinguish among the different basins of attraction and how to safeguard the already discovered good-quality solutions including both global and local optima. In GCES, multimodal optimization problems are regarded as classification ones, and Gaussian mixture models are employed to save the locations and basins of already and presently identified local or global optima. A sequential estimation technique for the covariance of a Gaussian model is introduced into GCES. To best adjust the global step size, a strategy named top-ranked sample selection is introduced, and a classification method instead of a common but problematic radius-triggered manner is proposed. Experiments are performed on a series of benchmark test functions to compare GCES with the state-of-the-art multimodal optimization approaches. The results show that GCES is not only simple to program and understand, but also provides better and consistent performance. [ABSTRACT FROM AUTHOR]