Chao Qian

Yu-Ran Gu, Chao Bian, Chao Qian

Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of constraint, while many real-world problems often involve several constraints. In this paper, we consider the problem of submodular maximization under the intersection of two commonly used constraints, i.e., $k$-matroid constraint and $m$-knapsack constraint, and propose a new algorithm SPROUT by incorporating partial enumeration into the simultaneous greedy framework. We prove that SPROUT can achieve a polynomial-time approximation guarantee better than the state-of-the-art algorithms. Then, we introduce the random enumeration and smooth techniques into SPROUT to improve its efficiency, resulting in the SPROUT++ algorithm, which can keep a similar approximation guarantee. Experiments on the applications of movie recommendation and weighted max-cut demonstrate the superiority of SPROUT++ in practice.

Ren-Jian Wang, Ke Xue, Yutong Wang et al.

Diversity plays a significant role in many problems, such as ensemble learning, reinforcement learning, and combinatorial optimization. How to define the diversity measure is a longstanding problem. Many methods rely on expert experience to define a proper behavior space and then obtain the diversity measure, which is, however, challenging in many scenarios. In this paper, we propose the problem of learning a behavior space from human feedback and present a general method called Diversity from Human Feedback (DivHF) to solve it. DivHF learns a behavior descriptor consistent with human preference by querying human feedback. The learned behavior descriptor can be combined with any distance measure to define a diversity measure. We demonstrate the effectiveness of DivHF by integrating it with the Quality-Diversity optimization algorithm MAP-Elites and conducting experiments on the QDax suite. The results show that the behavior learned by DivHF is much more consistent with human requirements than the one learned by direct data-driven approaches without human feedback, and makes the final solutions more diverse under human preference. Our contributions include formulating the problem, proposing the DivHF method, and demonstrating its effectiveness through experiments.

Chao Qian, Tianheng Ling, Gregor Schiele

To process sensor data in the Internet of Things(IoTs), embedded deep learning for 1-dimensional data is an important technique. In the past, CNNs were frequently used because they are simple to optimise for special embedded hardware such as FPGAs. This work proposes a novel LSTM cell optimisation aimed at energy-efficient inference on end devices. Using the traffic speed prediction as a case study, a vanilla LSTM model with the optimised LSTM cell achieves 17534 inferences per second while consuming only 3.8 $μ$J per inference on the FPGA XC7S15 from Spartan-7 family. It achieves at least 5.4$\times$ faster throughput and 1.37$\times$ more energy efficient than existing approaches.

Chao Qian, Tianheng Ling, Gregor Schiele

Deploying Deep Learning (DL) on embedded end devices is a scorching trend in pervasive computing. Since most Microcontrollers on embedded devices have limited computing power, it is necessary to add a DL accelerator. Embedded Field Programmable Gate Arrays (FPGAs) are suitable for deploying DL accelerators for embedded devices, but developing an energy-efficient DL accelerator on an FPGA is not easy. Therefore, we propose the ElasticAI-Workflow that aims to help DL developers to create and deploy DL models as hardware accelerators on embedded FPGAs. This workflow consists of two key components: the ElasticAI-Creator and the Elastic Node. The former is a toolchain for automatically generating DL accelerators on FPGAs. The latter is a hardware platform for verifying the performance of the generated accelerators. With this combination, the performance of the accelerator can be sufficiently guaranteed. We will demonstrate the potential of our approach through a case study.

Ke Xue, Ruo-Tong Chen, Xi Lin et al.

In modern chip design, placement aims at placing millions of circuit modules, which is an essential step that significantly influences power, performance, and area (PPA) metrics. Recently, reinforcement learning (RL) has emerged as a promising technique for improving placement quality, especially macro placement. However, current RL-based placement methods suffer from long training times, low generalization ability, and inability to guarantee PPA results. A key issue lies in the problem formulation, i.e., using RL to place from scratch, which results in limits useful information and inaccurate rewards during the training process. In this work, we propose an approach that utilizes RL for the refinement stage, which allows the RL policy to learn how to adjust existing placement layouts, thereby receiving sufficient information for the policy to act and obtain relatively dense and precise rewards. Additionally, we introduce the concept of regularity during training, which is considered an important metric in the chip design industry but is often overlooked in current RL placement methods. We evaluate our approach on the ISPD 2005 and ICCAD 2015 benchmark, comparing the global half-perimeter wirelength and regularity of our proposed method against several competitive approaches. Besides, we test the PPA performance using commercial software, showing that RL as a regulator can achieve significant PPA improvements. Our RL regulator can fine-tune placements from any method and enhance their quality. Our work opens up new possibilities for the application of RL in placement, providing a more effective and efficient approach to optimizing chip design. Our code is available at \url{https://github.com/lamda-bbo/macro-regulator}.

Tianheng Ling, Chao Qian, Lukas Johannes Haßler et al.

Transformer-based models have shown strong performance across diverse time-series tasks, but their deployment on resource-constrained devices remains challenging due to high memory and computational demand. While prior work targeting Microcontroller Units (MCUs) has explored hardware-specific optimizations, such approaches are often task-specific and limited to 8-bit fixed-point precision. Field-Programmable Gate Arrays (FPGAs) offer greater flexibility, enabling fine-grained control over data precision and architecture. However, existing FPGA-based deployments of Transformers for time-series analysis typically focus on high-density platforms with manual configuration. This paper presents a unified and fully automated deployment framework for Tiny Transformers on embedded FPGAs. Our framework supports a compact encoder-only Transformer architecture across three representative time-series tasks (forecasting, classification, and anomaly detection). It combines quantization-aware training (down to 4 bits), hardware-aware hyperparameter search using Optuna, and automatic VHDL generation for seamless deployment. We evaluate our framework on six public datasets across two embedded FPGA platforms. Results show that our framework produces integer-only, task-specific Transformer accelerators achieving as low as 0.033 mJ per inference with millisecond latency on AMD Spartan-7, while also providing insights into deployment feasibility on Lattice iCE40. All source code will be released in the GitHub repository (https://github.com/Edwina1030/TinyTransformer4TS).

Tianheng Ling, Chao Qian, Lukas Einhaus et al.

This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our approach demonstrates that matching the quantisation scheme to the real data distribution can reduce computational overhead while maintaining acceptable precision. Moreover, our approach is robust when applied to real-world data and mixed-precision quantisation, where most objects are quantised to 4 bits. Our findings inform model quantisation and deployment decisions while providing a foundation for advancing quantisation techniques.

Chengrui Gao, Haopu Shang, Ke Xue et al.

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To date, the community has created numerous open-source neural solvers with distinct motivations and inductive biases. While considerable efforts are devoted to designing powerful single solvers, our findings reveal that existing solvers typically demonstrate complementary performance across different problem instances. This suggests that significant improvements could be achieved through effective coordination of neural solvers at the instance level. In this work, we propose the first general framework to coordinate the neural solvers, which involves feature extraction, selection model, and selection strategy, aiming to allocate each instance to the most suitable solvers. To instantiate, we collect several typical neural solvers with state-of-the-art performance as alternatives, and explore various methods for each component of the framework. We evaluated our framework on two extensively studied combinatorial optimization problems, Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP). Experimental results show that the proposed framework can effectively distribute instances and the resulting composite solver can achieve significantly better performance (e.g., reduce the optimality gap by 0.88\% on TSPLIB and 0.71\% on CVRPLIB) than the best individual neural solver with little extra time cost.

Tianheng Ling, Vipin Singh, Chao Qian et al.

Extreme weather events, intensified by climate change, increasingly challenge aging combined sewer systems, raising the risk of untreated wastewater overflow. Accurate forecasting of sewer overflow basin filling levels can provide actionable insights for early intervention, helping mitigating uncontrolled discharge. In recent years, AI-based forecasting methods have offered scalable alternatives to traditional physics-based models, but their reliance on cloud computing limits their reliability during communication outages. To address this, we propose an end-to-end forecasting framework that enables energy-efficient inference directly on edge devices. Our solution integrates lightweight Transformer and Long Short-Term Memory (LSTM) models, compressed via integer-only quantization for efficient on-device execution. Moreover, an automated hardware-aware deployment pipeline is used to search for optimal model configurations by jointly minimizing prediction error and energy consumption on an AMD Spartan-7 XC7S15 FPGA. Evaluated on real-world sewer data, the selected 8-bit Transformer model, trained on 24 hours of historical measurements, achieves high accuracy (MSE 0.0376) at an energy cost of 0.370 mJ per inference. In contrast, the optimal 8-bit LSTM model requires significantly less energy (0.009 mJ, over 40x lower) but yields 14.89% worse accuracy (MSE 0.0432) and much longer training time. This trade-off highlights the need to align model selection with deployment priorities, favoring LSTM for ultra-low energy consumption or Transformer for higher predictive accuracy. In general, our work enables local, energy-efficient forecasting, contributing to more resilient combined sewer systems. All code can be found in the GitHub Repository (https://github.com/tianheng-ling/EdgeOverflowForecast).

Rong-Xi Tan, Ming Chen, Ke Xue et al.

The pursuit of universal black-box optimization (BBO) algorithms is a longstanding goal. However, unlike domains such as language or vision, where scaling structured data has driven generalization, progress in offline BBO remains hindered by the lack of unified representations for heterogeneous numerical spaces. Thus, existing offline BBO approaches are constrained to single-task and fixed-dimensional settings, failing to achieve cross-domain universal optimization. Recent advances in language models (LMs) offer a promising path forward: their embeddings capture latent relationships in a unifying way, enabling universal optimization across different data types possible. In this paper, we discuss multiple potential approaches, including an end-to-end learning framework in the form of next-token prediction, as well as prioritizing the learning of latent spaces with strong representational capabilities. To validate the effectiveness of these methods, we collect offline BBO tasks and data from open-source academic works for training. Experiments demonstrate the universality and effectiveness of our proposed methods. Our findings suggest that unifying language model priors and learning string embedding space can overcome traditional barriers in universal BBO, paving the way for general-purpose BBO algorithms. The code is provided at https://github.com/lamda-bbo/universal-offline-bbo.

Tianheng Ling, Islam Mansour, Chao Qian et al.

Recent advancements in IoT technologies have underscored the importance of using sensor data to understand environmental contexts effectively. This paper introduces a novel embedded system designed to autonomously label sensor data directly on IoT devices, thereby enhancing the efficiency of data collection methods. We present an integrated hardware and software solution equipped with specialized labeling sensors that streamline the capture and labeling of diverse types of sensor data. By implementing local processing with lightweight labeling methods, our system minimizes the need for extensive data transmission and reduces dependence on external resources. Experimental validation with collected data and a Convolutional Neural Network model achieved a high classification accuracy of up to 91.67%, as confirmed through 4-fold cross-validation. These results demonstrate the system's robust capability to collect audio and vibration data with correct labels.

Ren-Jian Wang, Ke Xue, Cong Guan et al.

Quality-Diversity (QD) algorithms have emerged as a powerful optimization paradigm with the aim of generating a set of high-quality and diverse solutions. To achieve such a challenging goal, QD algorithms require maintaining a large archive and a large population in each iteration, which brings two main issues, sample and resource efficiency. Most advanced QD algorithms focus on improving the sample efficiency, while the resource efficiency is overlooked to some extent. Particularly, the resource overhead during the training process has not been touched yet, hindering the wider application of QD algorithms. In this paper, we highlight this important research question, i.e., how to efficiently train QD algorithms with limited resources, and propose a novel and effective method called RefQD to address it. RefQD decomposes a neural network into representation and decision parts, and shares the representation part with all decision parts in the archive to reduce the resource overhead. It also employs a series of strategies to address the mismatch issue between the old decision parts and the newly updated representation part. Experiments on different types of tasks from small to large resource consumption demonstrate the excellent performance of RefQD: it not only uses significantly fewer resources (e.g., 16\% GPU memories on QDax and 3.7\% on Atari) but also achieves comparable or better performance compared to sample-efficient QD algorithms. Our code is available at \url{https://github.com/lamda-bbo/RefQD}.

Rong-Xi Tan, Ke Xue, Shen-Huan Lyu et al.

Offline model-based optimization (MBO) aims to identify a design that maximizes a black-box function using only a fixed, pre-collected dataset of designs and their corresponding scores. A common approach in offline MBO is to train a regression-based surrogate model by minimizing mean squared error (MSE) and then find the best design within this surrogate model by different optimizers (e.g., gradient ascent). However, a critical challenge is the risk of out-of-distribution errors, i.e., the surrogate model may typically overestimate the scores and mislead the optimizers into suboptimal regions. Prior works have attempted to address this issue in various ways, such as using regularization techniques and ensemble learning to enhance the robustness of the model, but it still remains. In this paper, we argue that regression models trained with MSE are not well-aligned with the primary goal of offline MBO, which is to select promising designs rather than to predict their scores precisely. Notably, if a surrogate model can maintain the order of candidate designs based on their relative score relationships, it can produce the best designs even without precise predictions. To validate it, we conduct experiments to compare the relationship between the quality of the final designs and MSE, finding that the correlation is really very weak. In contrast, a metric that measures order-maintaining quality shows a significantly stronger correlation. Based on this observation, we propose learning a ranking-based model that leverages learning to rank techniques to prioritize promising designs based on their relative scores. We show that the generalization error on ranking loss can be well bounded. Empirical results across diverse tasks demonstrate the superior performance of our proposed ranking-based models than twenty existing methods.

Tianheng Ling, Julian Hoever, Chao Qian et al.

In industrial and environmental monitoring, achieving real-time and precise fluid flow measurement remains a critical challenge. This study applies linear quantization in FPGA-based soft sensors for fluid flow estimation, significantly enhancing Neural Network model precision by overcoming the limitations of traditional fixed-point quantization. Our approach achieves up to a 10.10% reduction in Mean Squared Error and a notable 9.39% improvement in inference speed through targeted hardware optimizations. Validated across multiple data sets, our findings demonstrate that the optimized FPGA-based quantized models can provide efficient, accurate real-time inference, offering a viable alternative to cloud-based processing in pervasive autonomous systems.

Ren-Jian Wang, Ke Xue, Zeyu Qin et al.

Ensuring safety of large language models (LLMs) is important. Red teaming--a systematic approach to identifying adversarial prompts that elicit harmful responses from target LLMs--has emerged as a crucial safety evaluation method. Within this framework, the diversity of adversarial prompts is essential for comprehensive safety assessments. We find that previous approaches to red-teaming may suffer from two key limitations. First, they often pursue diversity through simplistic metrics like word frequency or sentence embedding similarity, which may not capture meaningful variation in attack strategies. Second, the common practice of training a single attacker model restricts coverage across potential attack styles and risk categories. This paper introduces Quality-Diversity Red-Teaming (QDRT), a new framework designed to address these limitations. QDRT achieves goal-driven diversity through behavior-conditioned training and implements a behavioral replay buffer in an open-ended manner. Additionally, it trains multiple specialized attackers capable of generating high-quality attacks across diverse styles and risk categories. Our empirical evaluation demonstrates that QDRT generates attacks that are both more diverse and more effective against a wide range of target LLMs, including GPT-2, Llama-3, Gemma-2, and Qwen2.5. This work advances the field of LLM safety by providing a systematic and effective approach to automated red-teaming, ultimately supporting the responsible deployment of LLMs.

Zi-Hang Cheng, Haopu Shang, Chao Qian

Network intrusion detection is one of the most important issues in the field of cyber security, and various machine learning techniques have been applied to build intrusion detection systems. However, since the number of features to describe the network connections is often large, where some features are redundant or noisy, feature selection is necessary in such scenarios, which can both improve the efficiency and accuracy. Recently, some researchers focus on using multi-objective evolutionary algorithms (MOEAs) to select features. But usually, they only consider the number of features and classification accuracy as the objectives, resulting in unsatisfactory performance on a critical metric, detection rate. This will lead to the missing of many real attacks and bring huge losses to the network system. In this paper, we propose DR-MOFS to model the feature selection problem in network intrusion detection as a three-objective optimization problem, where the number of features, accuracy and detection rate are optimized simultaneously, and use MOEAs to solve it. Experiments on two popular network intrusion detection datasets NSL-KDD and UNSW-NB15 show that in most cases the proposed method can outperform previous methods, i.e., lead to fewer features, higher accuracy and detection rate.

Yu-Chang Wu, Shen-Huan Lyu, Haopu Shang et al.

Selective classification enables models to make predictions only when they are sufficiently confident, aiming to enhance safety and reliability, which is important in high-stakes scenarios. Previous methods mainly use deep neural networks and focus on modifying the architecture of classification layers to enable the model to estimate the confidence of its prediction. This work provides a generalization bound for selective classification, disclosing that optimizing feature layers helps improve the performance of selective classification. Inspired by this theory, we propose to explicitly improve the selective classification model at the feature level for the first time, leading to a novel Confidence-aware Contrastive Learning method for Selective Classification, CCL-SC, which similarizes the features of homogeneous instances and differentiates the features of heterogeneous instances, with the strength controlled by the model's confidence. The experimental results on typical datasets, i.e., CIFAR-10, CIFAR-100, CelebA, and ImageNet, show that CCL-SC achieves significantly lower selective risk than state-of-the-art methods, across almost all coverage degrees. Moreover, it can be combined with existing methods to bring further improvement.

Shengcai Liu, Ning Lu, Wenjing Hong et al.

The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.

Chao Qian, Dan-Xuan Liu, Chao Feng et al.

Evolutionary algorithms (EAs) are general-purpose optimization algorithms, inspired by natural evolution. Recent theoretical studies have shown that EAs can achieve good approximation guarantees for solving the problem classes of submodular optimization, which have a wide range of applications, such as maximum coverage, sparse regression, influence maximization, document summarization and sensor placement, just to name a few. Though they have provided some theoretical explanation for the general-purpose nature of EAs, the considered submodular objective functions are defined only over sets or multisets. To complement this line of research, this paper studies the problem class of maximizing monotone submodular functions over sequences, where the objective function depends on the order of items. We prove that for each kind of previously studied monotone submodular objective functions over sequences, i.e., prefix monotone submodular functions, weakly monotone and strongly submodular functions, and DAG monotone submodular functions, a simple multi-objective EA, i.e., GSEMO, can always reach or improve the best known approximation guarantee after running polynomial time in expectation. Note that these best-known approximation guarantees can be obtained only by different greedy-style algorithms before. Empirical studies on various applications, e.g., accomplishing tasks, maximizing information gain, search-and-tracking and recommender systems, show the excellent performance of the GSEMO.

Chao Qian

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multi-objective EA, i.e., GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties but without explicit formulation. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this paper studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., $f=g-c$) with a size constraint, where $g$ is a non-negative monotone approximately submodular function and $c$ is a non-negative modular function, resulting in the objective function $f$ being non-monotone non-submodular. We prove that the GSEMO can achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.

Chao Qian, Hang Xiong, Ke Xue

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

Chao Bian, Chao Qian, Yang Yu et al.

Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect caused by noise. Sampling is a popular strategy, which evaluates the objective a couple of times, and employs the mean of these evaluation results as an estimate of the objective value. In this work, we introduce a novel sampling method, median sampling, into EAs, and illustrate its properties and usefulness theoretically by solving OneMax, the problem of maximizing the number of 1s in a bit string. Instead of the mean, median sampling employs the median of the evaluation results as an estimate. Through rigorous theoretical analysis on OneMax under the commonly used onebit noise, we show that median sampling reduces the expected runtime exponentially. Next, through two special noise models, we show that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be better than mean sampling; otherwise, it may fail and mean sampling can be better. The results may guide us to employ median sampling properly in practical applications.

Chao Bian, Chao Qian, Ke Tang et al.

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint $k$. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter $d$ or budget $k$ allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

Yibo Zhang, Chao Qian, Ke Tang

In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $β$ and $α$ to characterize how close a function is to continuous DR-submodulr and submodular, respectively. Under a convex polytope constraint, we prove that LDGM can achieve a $(1-e^{-β}-ε)$-approximation guarantee after $O(1/ε)$ iterations, which is the same as the best previous gradient-based algorithm. Moreover, in some special cases, a variant of LDGM can achieve a $((α/2)(1-e^{-α})-ε)$-approximation guarantee for (weakly) submodular functions. We also compare LDGM with the gradient-based algorithm Frank-Wolfe under noise, and show that LDGM can be more robust. Empirical results on budget allocation verify the effectiveness of LDGM.

Chao Qian, Chao Bian, Yang Yu et al.

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Most previous studies on sampling are empirical, and the few theoretical studies mainly showed the effectiveness of sampling with a sufficiently large sample size. In this paper, we theoretically examine what strategies can work when sampling with any fixed sample size fails. By constructing a family of artificial noisy examples, we prove that sampling is always ineffective, while using parent or offspring populations can be helpful on some examples. We also construct an artificial noisy example to show that when using neither sampling nor populations is effective, a tailored adaptive sampling (i.e., sampling with an adaptive sample size) strategy can work. These findings may enhance our understanding of sampling to some extent, but future work is required to validate them in natural situations.

Chao Qian, Chao Bian, Wu Jiang et al.

In many real-world optimization problems, the objective function evaluation is subject to noise, and we cannot obtain the exact objective value. Evolutionary algorithms (EAs), a type of general-purpose randomized optimization algorithm, have been shown to be able to solve noisy optimization problems well. However, previous theoretical analyses of EAs mainly focused on noise-free optimization, which makes the theoretical understanding largely insufficient for the noisy case. Meanwhile, the few existing theoretical studies under noise often considered the one-bit noise model, which flips a randomly chosen bit of a solution before evaluation; while in many realistic applications, several bits of a solution can be changed simultaneously. In this paper, we study a natural extension of one-bit noise, the bit-wise noise model, which independently flips each bit of a solution with some probability. We analyze the running time of the (1+1)-EA solving OneMax and LeadingOnes under bit-wise noise for the first time, and derive the ranges of the noise level for polynomial and super-polynomial running time bounds. The analysis on LeadingOnes under bit-wise noise can be easily transferred to one-bit noise, and improves the previously known results. Since our analysis discloses that the (1+1)-EA can be efficient only under low noise levels, we also study whether the sampling strategy can bring robustness to noise. We prove that using sampling can significantly increase the largest noise level allowing a polynomial running time, that is, sampling is robust to noise.

Chao Qian, Yang Yu, Zhi-Hua Zhou

Evolutionary algorithms (EAs) are population-based general-purpose optimization algorithms, and have been successfully applied in various real-world optimization tasks. However, previous theoretical studies often employ EAs with only a parent or offspring population and focus on specific problems. Furthermore, they often only show upper bounds on the running time, while lower bounds are also necessary to get a complete understanding of an algorithm. In this paper, we analyze the running time of the ($μ$+$λ$)-EA (a general population-based EA with mutation only) on the class of pseudo-Boolean functions with a unique global optimum. By applying the recently proposed switch analysis approach, we prove the lower bound $Ω(n \ln n+ μ+ λn\ln\ln n/ \ln n)$ for the first time. Particularly on the two widely-studied problems, OneMax and LeadingOnes, the derived lower bound discloses that the ($μ$+$λ$)-EA will be strictly slower than the (1+1)-EA when the population size $μ$ or $λ$ is above a moderate order. Our results imply that the increase of population size, while usually desired in practice, bears the risk of increasing the lower bound of the running time and thus should be carefully considered.

Chao Qian, Yang Yu, Zhi-Hua Zhou

Many optimization tasks have to be handled in noisy environments, where we cannot obtain the exact evaluation of a solution but only a noisy one. For noisy optimization tasks, evolutionary algorithms (EAs), a kind of stochastic metaheuristic search algorithm, have been widely and successfully applied. Previous work mainly focuses on empirical studying and designing EAs for noisy optimization, while, the theoretical counterpart has been little investigated. In this paper, we investigate a largely ignored question, i.e., whether an optimization problem will always become harder for EAs in a noisy environment. We prove that the answer is negative, with respect to the measurement of the expected running time. The result implies that, for optimization tasks that have already been quite hard to solve, the noise may not have a negative effect, and the easier a task the more negatively affected by the noise. On a representative problem where the noise has a strong negative effect, we examine two commonly employed mechanisms in EAs dealing with noise, the re-evaluation and the threshold selection strategies. The analysis discloses that the two strategies, however, both are not effective, i.e., they do not make the EA more noise tolerant. We then find that a small modification of the threshold selection allows it to be proven as an effective strategy for dealing with the noise in the problem.