A Mixture-of-Experts Prediction Framework for Evolutionary Dynamic Multiobjective Optimization

Dynamic multiobjective optimization requires the robust tracking of varying Pareto-optimal solutions (POS) in a changing environment. When a change is detected in the environment, prediction mechanisms estimate the POS by utilizing information from previous populations to accelerate search toward the true POS. To achieve a robust prediction of POS, a mixture-of-experts-based ensemble framework is proposed. Unlike existing approaches, the framework utilizes multiple prediction mechanisms to improve the overall prediction. A gating network is applied to manage switching among the various predictors based on performance of the predictors at different time intervals of the optimization process. The efficacy of the proposed framework is validated through experimental studies based on 13 dynamic multiobjective benchmark optimization problems. The simulation results show that the proposed framework improves the dynamic optimization performance significantly, particularly for: 1) problems with distinct dynamic POS in decision space over time and 2) problems with highly nonlinear decision variable linkages.

Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction

Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.

A robust vision-based sensor fusion approach for real-time pose estimation

Object pose estimation is of great importance to many applications, such as augmented reality, localization and mapping, motion capture, and visual servoing. Although many approaches based on a monocular camera have been proposed, only a few works have concentrated on applying multicamera sensor fusion techniques to pose estimation. Higher accuracy and enhanced robustness toward sensor defects or failures are some of the advantages of these schemes. This paper presents a new Kalman-based sensor fusion approach for pose estimation that offers higher accuracy and precision, and is robust to camera motion and image occlusion, compared to its predecessors. Extensive experiments are conducted to validate the superiority of this fusion method over currently employed vision-based pose estimation algorithms.

Twenty years of mixture of experts

In this paper, we provide a comprehensive survey of the mixture of experts (ME). We discuss the fundamental models for regression and classification and also their training with the expectation-maximization algorithm. We follow the discussion with improvements to the ME model and focus particularly on the mixtures of Gaussian process experts. We provide a review of the literature for other training methods, such as the alternative localized ME training, and cover the variational learning of ME in detail. In addition, we describe the model selection literature which encompasses finding the optimum number of experts, as well as the depth of the tree. We present the advances in ME in the classification area and present some issues concerning the classification model. We list the statistical properties of ME, discuss how the model has been modified over the years, compare ME to some popular algorithms, and list several applications. We conclude our survey with future directions and provide a list of publicly available datasets and a list of publicly available software that implement ME. Finally, we provide examples for regression and classification. We believe that the study described in this paper will provide quick access to the relevant literature for researchers and practitioners who would like to improve or use ME, and that it will stimulate further studies in ME.

PREDICTING UNKNOWN MOTION FOR MODEL INDEPENDENT VISUAL SERVOING

Prediction in real-time image sequences is a key-feature for visual servoing applications. It is used to compensate for the time-delay introduced by the image feature extraction process in the visual feedback loop. In order to track targets in a three-dimensional space in real-time with a robot arm, the target's movement and the robot end-effector's next position are predicted from the previous movements. A modular prediction architecture is presented, which is based on the Kalman filtering principle. The Kalman filter is an optimal stochastic estimation technique which needs an accurate system model and which is particularly sensitive to noise. The performances of this filter diminish with nonlinear systems and with time-varying environments. Therefore, we propose an adaptive Kalman filter using the modular framework of mixture of experts regulated by a gating network. The proposed filter has an adaptive state model to represent the system around its current state as close as possible. Different realizations of these state model adaptive Kalman filters are organized according to the divide-and-conquer principle: they all participate to the global estimation and a neural network mediates their different outputs in an unsupervised manner and tunes their parameters. The performances of the proposed approach are evaluated in terms of precision, capability to estimate and compensate abrupt changes in targets trajectories, as well as to adapt to time-variant parameters. The experiments prove that, without the use of models (e.g. the camera model, kinematic robot model, and system parameters) and without any prior knowledge about the targets movements, the predictions allow to compensate for the time-delay and to reduce the tracking error.

Variational learning for switching state-space models

We introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learnsthe parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time-series models -- hidden Markov models and linear dynamical systems -- and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs, Jordan, Nowlan, & Hinton, 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact expectation maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log-likelihood and makes use of both the forward and backward recursions for hidden Markov models and the Kalman filter recursions for linear dynamical systems. We tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.