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Expected Improvement of Penalty-Based Boundary Intersection for Expensive Multiobjective Optimization
Computationally expensive multiobjective optimization problems are difficult to solve using solely evolutionary algorithms (EAs) and require surrogate models, such as the Kriging model. To solve such problems efficiently, we propose infill criteria for appropriately selecting multiple additional sample points for updating the Kriging model. These criteria correspond to the expected improvement of the penalty-based boundary intersection (PBI) and the inverted PBI. These PBI-based measures are increasingly applied to EAs due to their ability to explore better nondominated solutions than those that are obtained by the Tchebycheff function. In order to add sample points uniformly in the multiobjective space, we assign territories and niche counts to uniformly distributed weight vectors for evaluating the proposed criteria. We investigate these criteria in various test problems and compare them with established infill criteria for multiobjective surrogate-based optimization. Both proposed criteria yield better diversity and convergence than those obtained with other criteria for most of the test problems.
The existing multiobjective expected improvement (EI) criteria are often computationally expensive because they are calculated using multivariate piecewise integrations, the number of which increases exponentially with the number of objectives. In order to solve this problem, this paper proposes a new approach to develop cheap-to-evaluate multiobjective EI criteria based on the proposed EI matrix (EIM). The elements in the EIM are the single-objective EIs that the studying point has beyond each Pareto front approximation point in each objective. Three multiobjective criteria are developed by combining the elements in the EIM into scalar functions in three different ways. These proposed multiobjective criteria are calculated using only 1-D integrations, whose number increases linearly with respect to the number of objectives. Moreover, all the three criteria are derived in closed form expressions, thus are significantly cheaper to evaluate than the state-of-the-art multiobjective criteria. The efficiencies of the proposed criteria are validated through 12 test problems. Besides the computational advantage, the proposed multiobjective EI criteria also show competitive abilities in approximating the Pareto fronts of the chosen test problems compared against the state-of-the-art multiobjective EI criteria.
A Similarity-Based Multiobjective Evolutionary Algorithm for Deployment Optimization of Near Space Communication System
The deployment of the airships plays a key role in maximizing the performance of the near space communication system. The main problem is how to strike a balance between the conflicting network speed and coverage for complex user distribution. In this paper, we propose a multiobjective deployment optimization model considering path loss, user demand, and inner structure. Under the framework of the multiobjective evolutionary algorithm (MOEA) based on decomposition (MOEA/D), we propose a similarity-based MOEA to optimize this problem. The proposed algorithm is motivated by the population’s perception on the decision variable space. The proposed algorithm perceives the decision variable space by deploying airships to latent regions. The perceptions of different solutions are related by the similarity between their deployments and utilized differently by crossover and mutation. The proposed algorithm is tested on five designed problems compared with MOEA/D with the other popular reproduction operators. We also test the proposed scheme integrated with another two popular algorithms. The experimental results show that the similarity-based MOEA/D outperforms the other algorithms significantly in detecting hotspots, tracking multiple hotspots and safely deploying airships for most cases. The proposed scheme also works well with the other algorithms.
Identification of variable interaction is essential for an efficient implementation of a divide-and-conquer algorithm for large-scale black-box optimization. In this paper, we propose an improved variant of the differential grouping (DG) algorithm, which has a better efficiency and grouping accuracy. The proposed algorithm, DG2, finds a reliable threshold value by estimating the magnitude of roundoff errors. With respect to efficiency, DG2 reuses the sample points that are generated for detecting interactions and saves up to half of the computational resources on fully separable functions. We mathematically show that the new sampling technique achieves the lower bound with respect to the number of function evaluations. Unlike its predecessor, DG2 checks all possible pairs of variables for interactions and has the capacity to identify overlapping components of an objective function. On the accuracy aspect, DG2 outperforms the state-of-the-art decomposition methods on the latest large-scale continuous optimization benchmark suites. DG2 also performs reliably in the presence of imbalance among contribution of components in an objective function. Another major advantage of DG2 is the automatic calculation of its threshold parameter (
An Evolutionary Multiobjective Model and Instance Selection for Support Vector Machines With Pareto-Based Ensembles
Support vector machines (SVMs) are among the most powerful learning algorithms for classification tasks. However, these algorithms require a high computational cost during the training phase, which can limit their application on large-scale datasets. Moreover, it is known that their effectiveness highly depends on the hyper-parameters used to train the model. With the intention of dealing with these, this paper introduces an evolutionary multiobjective model and instance selection (IS) approach for SVMs with Pareto-based ensemble, whose goals are, precisely, to optimize the size of the training set and the classification performance attained by the selection of the instances, which can be done using either a wrapper or a filter approach. Due to the nature of multiobjective evolutionary algorithms, several Pareto optimal solutions can be found. We study several ways of using such information to perform a classification task. To accomplish this, our proposal performs a processing over the Pareto solutions in order to combine them into a single ensemble. This is done in five different ways, which are based on: 1) a global Pareto ensemble; 2) error reduction; 3) a complementary error reduction; 4) maximized margin distance; and 5) boosting. Through a comprehensive experimental study we evaluate the suitability of the proposed approach and the Pareto processing, and we show its advantages over a single-objective formulation, traditional IS techniques, and learning algorithms.
Given a multivariate time series, possibly of high dimension, with unknown and time-varying joint distribution, it is of interest to be able to completely partition the time series into disjoint, contiguous subseries, each of which has different distributional or pattern attributes from the preceding and succeeding subseries. An additional feature of many time series is that they display self-affinity, so that subseries at one time scale are similar to subseries at another after application of an affine transformation. Such qualities are observed in time series from many disciplines, including biology, medicine, economics, finance, and computer science. This paper defines the relevant multiobjective combinatorial optimization problem with limited assumptions as a biobjective one, and a specialized evolutionary algorithm is presented which finds optimal self-affine time series partitionings with a minimum of choice parameters. The algorithm not only finds partitionings for all possible numbers of partitions given data constraints, but also for self-affinities between these partitionings and some fine-grained partitioning. The resulting set of Pareto-efficient solution sets provides a rich representation of the self-affine properties of a multivariate time series at different locations and time scales.
We describe an experimental platform that uses differential evolution to automatically discover high-performance multirotor controllers. All control parameters are tuned simultaneously, no modeling is required, and, as the evolution occurs on a real multirotor, the controllers are guaranteed to work in reality. The platform is able to run back-to-back experiments for over a week without human intervention. Self-adaptive rates are shown improve solution fitness whilst (at least) maintaining convergence times. This platform is the first to allow for evolutionary robotics experimentation to occur safely and repeatedly on real multirotors. High-performance controllers are evolved despite noisy fitness evaluations, real-world sensory noise, low population sizes, and limited numbers of evolutionary generations.
Keypoints Detection and Feature Extraction: A Dynamic Genetic Programming Approach for Evolving Rotation-Invariant Texture Image Descriptors
The goodness of the features extracted from the instances and the number of training instances are two key components in machine learning, and building an effective model is largely affected by these two factors. Acquiring a large number of training instances is very expensive in some situations such as in the medical domain. Designing a good feature set, on the other hand, is very hard and often requires domain expertise. In computer vision, image descriptors have emerged to automate feature detection and extraction; however, domain-expert intervention is typically needed to develop these descriptors. The aim of this paper is to utilize genetic programming to automatically construct a rotation-invariant image descriptor by synthesizing a set of formulas using simple arithmetic operators and first-order statistics, and determining the length of the feature vector simultaneously using only two instances per class. Using seven texture classification image datasets, the performance of the proposed method is evaluated and compared against eight domain-expert hand-crafted image descriptors. Quantitatively, the proposed method has significantly outperformed, or achieved comparable performance to, the competitor methods. Qualitatively, the analysis shows that the descriptors evolved by the proposed method can be interpreted.