A Recommender System Approach for Very Large-scale Multiobjective Optimization

We define very large multi-objective optimization problems to be multiobjective optimization problems in which the number of decision variables is greater than 100,000 dimensions. This is an important class of problems as many real-world problems require optimizing hundreds of thousands of variables. Existing evolutionary optimization methods fall short of such requirements when dealing with problems at this very large scale. Inspired by the success of existing recommender systems to handle very large-scale items with limited historical interactions, in this paper we propose a method termed Very large-scale Multiobjective Optimization through Recommender Systems (VMORS). The idea of the proposed method is to transform the defined such very large-scale problems into a problem that can be tackled by a recommender system. In the framework, the solutions are regarded as users, and the different evolution directions are items waiting for the recommendation. We use Thompson sampling to recommend the most suitable items (evolutionary directions) for different users (solutions), in order to locate the optimal solution to a multiobjective optimization problem in a very large search space within acceptable time. We test our proposed method on different problems from 100,000 to 500,000 dimensions, and experimental results show that our method not only shows good performance but also significant improvement over existing methods.

EvoX: A Distributed GPU-accelerated Library towards Scalable Evolutionary Computation

During the past decades, evolutionary computation (EC) has demonstrated promising potential in solving various complex optimization problems of relatively small scales. Nowadays, however, ongoing developments in modern science and engineering are bringing increasingly grave challenges to the conventional EC paradigm in terms of scalability. As problem scales increase, on the one hand, the encoding spaces (i.e., dimensions of the decision vectors) are intrinsically larger; on the other hand, EC algorithms often require growing numbers of function evaluations (and probably larger population sizes as well) to work properly. To meet such emerging challenges, not only does it require delicate algorithm designs, but more importantly, a high-performance computing framework is indispensable. Hence, we develop a distributed GPU-accelerated algorithm library -- EvoX. First, we propose a generalized workflow for implementing general EC algorithms. Second, we design a scalable computing framework for running EC algorithms on distributed GPU devices. Third, we provide user-friendly interfaces to both researchers and practitioners for benchmark studies as well as extended real-world applications. To comprehensively assess the performance of EvoX, we conduct a series of experiments, including: (i) scalability test via numerical optimization benchmarks with problem dimensions/population sizes up to millions; (ii) acceleration test via a neuroevolution task with multiple GPU nodes; (iii) extensibility demonstration via the application to reinforcement learning tasks on the OpenAI Gym. The code of EvoX is available at https://github.com/EMI-Group/EvoX.

Differentiable Search of Accurate and Robust Architectures

Deep neural networks (DNNs) are found to be vulnerable to adversarial attacks, and various methods have been proposed for the defense. Among these methods, adversarial training has been drawing increasing attention because of its simplicity and effectiveness. However, the performance of the adversarial training is greatly limited by the architectures of target DNNs, which often makes the resulting DNNs with poor accuracy and unsatisfactory robustness. To address this problem, we propose DSARA to automatically search for the neural architectures that are accurate and robust after adversarial training. In particular, we design a novel cell-based search space specially for adversarial training, which improves the accuracy and the robustness upper bound of the searched architectures by carefully designing the placement of the cells and the proportional relationship of the filter numbers. Then we propose a two-stage search strategy to search for both accurate and robust neural architectures. At the first stage, the architecture parameters are optimized to minimize the adversarial loss, which makes full use of the effectiveness of the adversarial training in enhancing the robustness. At the second stage, the architecture parameters are optimized to minimize both the natural loss and the adversarial loss utilizing the proposed multi-objective adversarial training method, so that the searched neural architectures are both accurate and robust. We evaluate the proposed algorithm under natural data and various adversarial attacks, which reveals the superiority of the proposed method in terms of both accurate and robust architectures. We also conclude that accurate and robust neural architectures tend to deploy very different structures near the input and the output, which has great practical significance on both hand-crafting and automatically designing of accurate and robust neural architectures.

An Evolutionary Multitasking Algorithm with Multiple Filtering for High-Dimensional Feature Selection

Recently, evolutionary multitasking (EMT) has been successfully used in the field of high-dimensional classification. However, the generation of multiple tasks in the existing EMT-based feature selection (FS) methods is relatively simple, using only the Relief-F method to collect related features with similar importance into one task, which cannot provide more diversified tasks for knowledge transfer. Thus, this paper devises a new EMT algorithm for FS in high-dimensional classification, which first adopts different filtering methods to produce multiple tasks and then modifies a competitive swarm optimizer to efficiently solve these related tasks via knowledge transfer. First, a diversified multiple task generation method is designed based on multiple filtering methods, which generates several relevant low-dimensional FS tasks by eliminating irrelevant features. In this way, useful knowledge for solving simple and relevant tasks can be transferred to simplify and speed up the solution of the original high-dimensional FS task. Then, a competitive swarm optimizer is modified to simultaneously solve these relevant FS tasks by transferring useful knowledge among them. Numerous empirical results demonstrate that the proposed EMT-based FS method can obtain a better feature subset than several state-of-the-art FS methods on eighteen high-dimensional datasets.

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning have raised higher demands for network architectures considering multiple design criteria: number of parameters/floating-point operations, and inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed $\texttt{EvoXBench}$, to generate benchmark test problems for EMO algorithms to run efficiently -- without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of $\texttt{EvoXBench}$ is available from $\href{https://github.com/EMI-Group/EvoXBench}{\rm{here}}$.

Architecture Augmentation for Performance Predictor Based on Graph Isomorphism

Neural Architecture Search (NAS) can automatically design architectures for deep neural networks (DNNs) and has become one of the hottest research topics in the current machine learning community. However, NAS is often computationally expensive because a large number of DNNs require to be trained for obtaining performance during the search process. Performance predictors can greatly alleviate the prohibitive cost of NAS by directly predicting the performance of DNNs. However, building satisfactory performance predictors highly depends on enough trained DNN architectures, which are difficult to obtain in most scenarios. To solve this critical issue, we propose an effective DNN architecture augmentation method named GIAug in this paper. Specifically, we first propose a mechanism based on graph isomorphism, which has the merit of efficiently generating a factorial of $\boldsymbol n$ (i.e., $\boldsymbol n!$) diverse annotated architectures upon a single architecture having $\boldsymbol n$ nodes. In addition, we also design a generic method to encode the architectures into the form suitable to most prediction models. As a result, GIAug can be flexibly utilized by various existing performance predictors-based NAS algorithms. We perform extensive experiments on CIFAR-10 and ImageNet benchmark datasets on small-, medium- and large-scale search space. The experiments show that GIAug can significantly enhance the performance of most state-of-the-art peer predictors. In addition, GIAug can save three magnitude order of computation cost at most on ImageNet yet with similar performance when compared with state-of-the-art NAS algorithms.

Balancing Exploration and Exploitation for Solving Large-scale Multiobjective Optimization via Attention Mechanism

Large-scale multiobjective optimization problems (LSMOPs) refer to optimization problems with multiple conflicting optimization objectives and hundreds or even thousands of decision variables. A key point in solving LSMOPs is how to balance exploration and exploitation so that the algorithm can search in a huge decision space efficiently. Large-scale multiobjective evolutionary algorithms consider the balance between exploration and exploitation from the individual's perspective. However, these algorithms ignore the significance of tackling this issue from the perspective of decision variables, which makes the algorithm lack the ability to search from different dimensions and limits the performance of the algorithm. In this paper, we propose a large-scale multiobjective optimization algorithm based on the attention mechanism, called (LMOAM). The attention mechanism will assign a unique weight to each decision variable, and LMOAM will use this weight to strike a balance between exploration and exploitation from the decision variable level. Nine different sets of LSMOP benchmarks are conducted to verify the algorithm proposed in this paper, and the experimental results validate the effectiveness of our design.