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On the Use of Quality Diversity Algorithms for the Travelling Thief Problem 论旅行大盗问题中质量分集算法的使用
Pub Date : 2024-01-17 DOI: 10.1145/3641109
Adel Nikfarjam, Aneta Neumann, Frank Neumann
In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The travelling thief problem (TTP) belongs to this category and is formed by the integration of the travelling salesperson problem (TSP) and the knapsack problem (KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity (QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quality solutions but also to illustrate the distribution of high-performing solutions in the behavioural space. We introduce a multi-dimensional archive of phenotypic elites (MAP-Elites) based evolutionary algorithm using well-known TSP and KP search operators, taking the TSP and KP score as the behavioural descriptor. MAP-Elites algorithms are QD-based techniques to explore high-performing solutions in a behavioural space. Afterwards, we conduct comprehensive experimental studies that show the usefulness of using the QD approach applied to the TTP. First, we provide insights regarding high-quality TTP solutions in the TSP/KP behavioural space. Afterwards, we show that better solutions for the TTP can be obtained by using our QD approach, and it can improve the best-known solution for a number of TTP instances used for benchmarking in the literature.
在现实世界的优化过程中,经常会遇到几个子问题相互作用而形成主问题的情况。子问题之间存在相互依赖关系,因此不可能只关注一个部分来解决这样的问题。旅行小偷问题(TTP)就属于这类问题,它是由旅行推销员问题(TSP)和背包问题(KP)整合而成的。在本文中,我们通过质量多样性(QD)方法研究了 TSP 和 KP 的相互依存关系。QD 算法提供了一个强大的工具,不仅能获得高质量的解决方案,还能说明高性能解决方案在行为空间中的分布情况。我们介绍了一种基于多维表型精英档案(MAP-Elites)的进化算法,该算法使用著名的 TSP 和 KP 搜索算子,将 TSP 和 KP 分数作为行为描述符。MAP-Elites 算法是一种基于 QD 的技术,用于探索行为空间中的高效解决方案。随后,我们进行了全面的实验研究,展示了将 QD 方法应用于 TTP 的实用性。首先,我们提供了有关 TSP/KP 行为空间中高质量 TTP 解决方案的见解。之后,我们证明了使用我们的 QD 方法可以获得更好的 TTP 解决方案,并且可以改进文献中用于基准测试的一些 TTP 实例的已知最佳解决方案。
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引用次数: 1
Evolutionary Optimization with Simplified Helper Task for High-dimensional Expensive Multiobjective Problems 针对高维昂贵多目标问题的简化辅助任务进化优化法
Pub Date : 2024-01-11 DOI: 10.1145/3637065
Xunfeng Wu, Qiuzhen Lin, Junwei Zhou, Songbai Liu, C. C. Coello Coello, Victor C. M. Leung
In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have been sufficiently studied for tackling computationally expensive multiobjective optimization problems (EMOPs), as they can quickly estimate the qualities of solutions by using surrogate models to substitute for expensive evaluations. However, most existing SAEAs only show promising performance for solving EMOPs with no more than 10 dimensions, and become less efficient for tackling EMOPs with higher dimensionality. Thus, this article proposes a new SAEA with a simplified helper task for tackling high-dimensional EMOPs. In each generation, one simplified task will be generated artificially by using random dimension reduction on the target task (i.e., the target EMOPs). Then, two surrogate models are trained for the helper task and the target task, respectively. Based on the trained surrogate models, evolutionary multitasking optimization is run to solve these two tasks, so that the experiences of solving the helper task can be transferred to speed up the convergence of tackling the target task. Moreover, an effective model management strategy is designed to select new promising samples for training the surrogate models. When compared to five competitive SAEAs on four well-known benchmark suites, the experiments validate the advantages of the proposed algorithm on most test cases.
近年来,代用辅助进化算法(SAEAs)在解决计算成本高昂的多目标优化问题(EMOPs)方面得到了充分研究,因为它们可以通过使用代用模型来替代昂贵的评估,从而快速估计解决方案的质量。然而,大多数现有的 SAEA 只在求解不超过 10 维的 EMOP 时表现出良好的性能,而在求解维数更高的 EMOP 时,其效率就会降低。因此,本文提出了一种带有简化辅助任务的新 SAEA,用于解决高维 EMOP。在每一代中,将通过对目标任务(即目标 EMOPs)进行随机降维,人为生成一个简化任务。然后,分别为辅助任务和目标任务训练两个代理模型。在训练好的代用模型的基础上,运行进化多任务优化来解决这两个任务,从而将解决辅助任务的经验用于加速目标任务的收敛。此外,还设计了有效的模型管理策略,以选择新的有前途的样本来训练代用模型。与四个著名基准套件上的五个竞争性 SAEA 相比,实验验证了所提算法在大多数测试案例中的优势。
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引用次数: 0
Multi-Objective Hyperparameter Optimization in Machine Learning – An Overview 机器学习中的多目标超参数优化综述
Pub Date : 2023-09-05 DOI: 10.1145/3610536
Florian Karl, Tobias Pielok, Julia Moosbauer, Florian Pfisterer, Stefan Coors, Martin Binder, Lennart Schneider, Janek Thomas, Jakob Richter, Michel Lang, E.C. Garrido-Merchán, Juergen Branke, B. Bischl
Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies, both from the domain of evolutionary algorithms and Bayesian optimization. We illustrate the utility of MOO in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability and robustness.
超参数优化构成了典型的现代机器学习工作流程的很大一部分。这是因为机器学习方法和相应的预处理步骤通常只有在超参数适当调优时才能产生最佳性能。但在许多应用中,我们不仅对优化机器学习管道的预测准确性感兴趣;在确定最优配置时,必须考虑额外的度量或约束,从而导致多目标优化问题。由于缺乏多目标超参数优化的知识和现成的软件实现,这在实践中经常被忽视。在这项工作中,我们向读者介绍了多目标超参数优化的基础知识,并激发了它在应用ML中的实用性。此外,我们从进化算法和贝叶斯优化的领域对现有的优化策略进行了广泛的调查。考虑到操作条件、预测时间、稀疏性、公平性、可解释性和鲁棒性等目标,我们说明了MOO在几个特定ML应用中的效用。
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引用次数: 0
Multi-objective Feature Attribution Explanation For Explainable Machine Learning 可解释机器学习的多目标特征归因解释
Pub Date : 2023-08-29 DOI: 10.1145/3617380
Ziming Wang, Changwu Huang, Yun Li, Xin Yao
The feature attribution-based explanation (FAE) methods, which indicate how much each input feature contributes to the model’s output for a given data point, are one of the most popular categories of explainable machine learning techniques. Although various metrics have been proposed to evaluate the explanation quality, no single metric could capture different aspects of the explanations. Different conclusions might be drawn using different metrics. Moreover, during the processes of generating explanations, existing FAE methods either do not consider any evaluation metric or only consider the faithfulness of the explanation, failing to consider multiple metrics simultaneously. To address this issue, we formulate the problem of creating FAE explainable models as a multi-objective learning problem that considers multiple explanation quality metrics simultaneously. We first reveal conflicts between various explanation quality metrics, including faithfulness, sensitivity, and complexity. Then, we define the considered multi-objective explanation problem and propose a multi-objective feature attribution explanation (MOFAE) framework to address this newly defined problem. Subsequently, we instantiate the framework by simultaneously considering the explanation’s faithfulness, sensitivity, and complexity. Experimental results comparing with six state-of-the-art FAE methods on eight datasets demonstrate that our method can optimize multiple conflicting metrics simultaneously and can provide explanations with higher faithfulness, lower sensitivity, and lower complexity than the compared methods. Moreover, the results have shown that our method has better diversity, i.e., it provides various explanations that achieve different trade-offs between multiple conflicting explanation quality metrics. Therefore, it can provide tailored explanations to different stakeholders based on their specific requirements.
基于特征归因的解释(FAE)方法表明每个输入特征对给定数据点的模型输出有多大贡献,是最受欢迎的可解释机器学习技术之一。尽管已经提出了各种度量来评估解释质量,但没有一个度量可以捕获解释的不同方面。使用不同的指标可能会得出不同的结论。此外,在产生解释的过程中,现有的FAE方法要么不考虑任何评价指标,要么只考虑解释的可信度,未能同时考虑多个指标。为了解决这个问题,我们将创建FAE可解释模型的问题表述为同时考虑多个解释质量度量的多目标学习问题。我们首先揭示了各种解释质量度量之间的冲突,包括忠实度、敏感性和复杂性。然后,我们定义了考虑的多目标解释问题,并提出了一个多目标特征归因解释(MOFAE)框架来解决这个新定义的问题。随后,我们通过同时考虑解释的忠实性、敏感性和复杂性来实例化框架。与6种最先进的FAE方法在8个数据集上的对比实验结果表明,我们的方法可以同时优化多个冲突指标,并提供比所比较方法更高的信度、更低的灵敏度和更低的复杂性的解释。此外,结果表明我们的方法具有更好的多样性,即它提供了多种解释,在多个相互冲突的解释质量指标之间实现了不同的权衡。因此,它可以根据不同利益相关者的具体需求,为他们提供量身定制的解释。
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引用次数: 1
Multiobjective Evolutionary Component Effect on Algorithm behavior 多目标进化分量对算法行为的影响
Pub Date : 2023-07-31 DOI: 10.1145/3612933
Yuri Lavinas, M. Ladeira, G. Ochoa, C. Aranha
The performance of multiobjective evolutionary algorithms (MOEAs) varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from their components. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still unknown what are the most influential components that lead to performance improvements. This study specifies a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a tuned Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) designed by the iterated racing (irace) configuration package on constrained problems of 3 groups: (1) analytical real-world problems, (2) analytical artificial problems and (3) simulated real-world. We then compare the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the anytime hypervolume values. Looking at the objective space behavior, the MOEAs studied converged before half of the search to generally good HV values in the analytical artificial problems and the analytical real-world problems. For the simulated problems, the HV values are still improving at the end of the run. In terms of decision space behavior, we see a diverse set of the trajectories of the STNs in the analytical artificial problems. These trajectories are more similar and frequently reach optimal solutions in the other problems.
多目标进化算法(moea)的性能因问题而异,这使得开发新算法或将现有算法应用于新问题变得困难。为了简化新的多目标算法的开发和应用,人们对多目标算法的自动设计越来越感兴趣。这些自动设计的元启发式方法可以胜过人类开发的同类方法。但是,目前还不清楚哪些组件对性能改进影响最大。本研究指定了一种新的方法来研究自动设计算法的最终配置的影响。我们将该方法应用于迭代赛车(irace)配置包设计的基于分解的优化多目标进化算法(MOEA/D),该算法针对三组约束问题:(1)解析性现实问题,(2)解析性人工问题和(3)模拟现实问题。然后,我们比较了算法组件在搜索轨迹网络(stn)、人口多样性和任何时间超容量值方面的影响。从客观空间行为来看,在分析性人工问题和分析性现实问题中,所研究的moea在一半的搜索前收敛到一般较好的HV值。对于模拟问题,运行结束时HV值仍在改善。在决策空间行为方面,我们在分析性人工问题中看到了一组不同的stn轨迹。这些轨迹更加相似,并且在其他问题中经常达到最优解。
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引用次数: 0
Editorial to the “Best of GECCO 2022” Special Issue: Part I “最佳GECCO 2022”特刊社论:第一部分
Pub Date : 2023-06-29 DOI: 10.1145/3606034
John H. Fieldsend, Markus Wagner
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引用次数: 0
Crossover for Cardinality Constrained Optimization 基数约束优化的交叉
Pub Date : 2023-06-28 DOI: 10.1145/3603629
T. Friedrich, Timo Kötzing, Aishwarya Radhakrishnan, Leon Schiller, Martin Schirneck, Georg Tennigkeit, Simon Wietheger
To understand better how and why crossover can benefit constrained optimization, we consider pseudo-Boolean functions with an upper bound B on the number of 1-bits allowed in the length-n bit string (i.e., a cardinality constraint). We investigate the natural translation of the OneMax test function to this setting, a linear function where B bits have a weight of 1+ 1/n and the remaining bits have a weight of 1. Friedrich et al. [TCS 2020] gave a bound of Θ (n2) for the expected running time of the (1+1) EA on this function. Part of the difficulty when optimizing this problem lies in having to improve individuals meeting the cardinality constraint by flipping a 1 and a 0 simultaneously. The experimental literature proposes balanced operators, preserving the number of 1-bits, as a remedy. We show that a balanced mutation operator optimizes the problem in O(n log n) if n-B = O(1). However, if n-B = Θ (n), we show a bound of Ω (n2), just as for classic bit mutation. Crossover together with a simple island model gives running times of O(n2 / log n) (uniform crossover) and (O(nsqrt {n})) (3-ary majority vote crossover). For balanced uniform crossover with Hamming-distance maximization for diversity, we show a bound of O(n log n). As an additional contribution, we present an extensive analysis of different balanced crossover operators from the literature.
为了更好地理解交叉如何以及为什么可以受益于约束优化,我们考虑在长度为n位的字符串中允许的1位的数量上有上限B的伪布尔函数(即基数约束)。我们研究OneMax测试函数到这个设置的自然转换,一个线性函数,其中B位的权值为1+ 1/n,其余位的权值为1。Friedrich等人[TCS 2020]给出了(1+1)EA对该函数的预期运行时间的界为Θ (n2)。优化这个问题的部分困难在于必须通过同时翻转1和0来改善满足基数约束的个体。实验文献提出平衡算子,保留1位的数量,作为补救措施。我们证明了当n- b = O(1)时,平衡突变算子在O(n log n)内优化问题。然而,如果n- b = Θ (n),我们显示一个Ω (n2)的界,就像经典的位突变一样。结合简单的孤岛模型进行交叉,得到的运行时间为O(n2 / log n)(均匀交叉)和(O(nsqrt {n})) (3-ary多数投票交叉)。对于多样性的汉明距离最大化的平衡均匀交叉,我们给出了O(n log n)的界。作为额外的贡献,我们从文献中对不同的平衡交叉算子进行了广泛的分析。
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引用次数: 1
A Species-based Particle Swarm Optimization with Adaptive Population Size and Deactivation of Species for Dynamic Optimization Problems 基于种群大小自适应和种群失活的动态优化问题粒子群算法
Pub Date : 2023-06-14 DOI: 10.1145/3604812
Delaram Yazdani, D. Yazdani, Donya Yazdani, M. Omidvar, A. Gandomi, X. Yao
Population clustering methods, which consider the position and fitness of the individuals to form sub-populations in multi-population algorithms, have shown high efficiency in tracking the moving global optimum in dynamic optimization problems. However, most of these methods use a fixed population size, making them inflexible and inefficient when the number of promising regions is unknown. The lack of a functional relationship between the population size and the number of promising regions significantly degrades performance and limits an algorithm’s agility to respond to dynamic changes. To address this issue, we propose a new species-based particle swarm optimization with adaptive population size and number of sub-populations for solving dynamic optimization problems. The proposed algorithm also benefits from a novel systematic adaptive deactivation component that, unlike the previous deactivation components, adapts the computational resource allocation to the sub-populations by considering various characteristics of both the problem and the sub-populations. We evaluate the performance of our proposed algorithm for the Generalized Moving Peaks Benchmark and compare the results with several peer approaches. The results indicate the superiority of the proposed method.
种群聚类方法在多种群算法中考虑个体的位置和适应度形成子种群,在跟踪动态优化问题的全局移动最优方面表现出很高的效率。然而,这些方法大多使用固定的人口规模,使得它们在有希望的地区数量未知时缺乏灵活性和效率。缺乏种群大小和有希望区域数量之间的函数关系会显著降低性能,并限制算法响应动态变化的敏捷性。为了解决这一问题,我们提出了一种新的基于物种的粒子群优化算法,该算法具有自适应种群大小和亚种群数量。该算法还受益于一种新的系统自适应去激活组件,该组件不同于以前的去激活组件,通过考虑问题和子种群的各种特征,使计算资源分配适应子种群。我们评估了我们提出的广义移动峰值基准算法的性能,并将结果与几种同类方法进行了比较。结果表明了该方法的优越性。
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引用次数: 1
P2P Energy Trading through Prospect Theory, Differential Evolution, and Reinforcement Learning 基于前景理论、差分进化和强化学习的P2P能源交易
Pub Date : 2023-06-10 DOI: 10.1145/3603148
Ashutosh Timilsina, Simone Silvestri
Peer-to-peer (P2P) energy trading is a decentralized energy market where local energy prosumers act as peers, trading energy among each other. Existing works in this area largely overlook the importance of user behavioral modeling and assume users’ sustained active participation and full compliance in the decision-making process. To overcome these unrealistic assumptions, and their deleterious consequences, in this article, we propose an automated P2P energy-trading framework that specifically considers the users’ perception by exploiting prospect theory. We formalize an optimization problem that maximizes the buyers’ perceived utility while matching energy production and demand. We prove that the problem is NP-hard and we propose a Differential Evolution-based Algorithm for Trading Energy (DEbATE) heuristic. Additionally, we propose two automated pricing solutions to improve the sellers’ profit based on reinforcement learning. The first solution, named Pricing mechanism with Q-learning and Risk-sensitivity (PQR), is based on Q-learning. Additionally, given the scalability issues of PQR, we propose a Deep Q-Network-based algorithm called ProDQN that exploits deep learning and a novel loss function rooted in prospect theory. Results based on real traces of energy consumption and production, as well as realistic prospect theory functions, show that our approaches achieve 26% higher perceived value for buyers and generate 7% more reward for sellers, compared to recent state-of-the-art approaches.
点对点(P2P)能源交易是一个分散的能源市场,在这个市场中,当地的能源消费者充当对等体,彼此之间进行能源交易。该领域的现有工作在很大程度上忽视了用户行为建模的重要性,并假设用户在决策过程中持续积极参与和完全遵守。为了克服这些不切实际的假设及其有害的后果,在本文中,我们提出了一个自动化的P2P能源交易框架,该框架通过利用前景理论特别考虑了用户的感知。我们形式化了一个优化问题,使买家的感知效用最大化,同时匹配能源生产和需求。我们证明了这个问题是np困难的,并提出了一种基于差分进化的能量交易启发式算法。此外,我们提出了两种基于强化学习的自动定价方案来提高卖家的利润。第一个解决方案是基于Q-learning的定价机制与风险敏感性(PQR)。此外,考虑到PQR的可扩展性问题,我们提出了一种基于深度q - network的算法,称为ProDQN,该算法利用深度学习和基于前景理论的新型损失函数。基于能源消耗和生产的真实轨迹,以及现实前景理论函数的结果表明,与最近最先进的方法相比,我们的方法为买家带来了26%的感知价值,为卖家带来了7%的回报。
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引用次数: 1
A Multi-Objective Evolutionary Approach to Discover Explainability Trade-Offs when Using Linear Regression to Effectively Model the Dynamic Thermal Behaviour of Electrical Machines 使用线性回归有效地模拟电机动态热行为时,发现可解释性权衡的多目标进化方法
Pub Date : 2023-05-19 DOI: 10.1145/3597618
Tiwonge Msulira Banda, Alexandru-Ciprian Zavoianu, Andrei V. Petrovski, Daniel Wöckinger, G. Bramerdorfer
Modelling and controlling heat transfer in rotating electrical machines is very important as it enables the design of assemblies (e.g., motors) that are efficient and durable under multiple operational scenarios. To address the challenge of deriving accurate data-driven estimators of key motor temperatures, we propose a multi-objective strategy for creating Linear Regression (LR) models that integrate optimised synthetic features. The main strength of our approach is that it provides decision makers with a clear overview of the optimal trade-offs between data collection costs, the expected modelling errors and the overall explainability of the generated thermal models. Moreover, as parsimonious models are required for both microcontroller deployment and domain expert interpretation, our modelling strategy contains a simple but effective step-wise regularisation technique that can be applied to outline domain-relevant mappings between LR variables and thermal profiling capabilities. Results indicate that our approach can generate accurate LR-based dynamic thermal models when training on data associated with a limited set of load points within the safe operating area of the electrical machine under study.
旋转电机中的传热建模和控制是非常重要的,因为它可以设计在多种操作场景下高效耐用的组件(例如电机)。为了解决获得关键电机温度的准确数据驱动估计值的挑战,我们提出了一种多目标策略,用于创建集成优化合成特征的线性回归(LR)模型。我们的方法的主要优势在于,它为决策者提供了数据收集成本、预期建模误差和生成的热模型的总体可解释性之间的最佳权衡的清晰概述。此外,由于微控制器部署和领域专家解释都需要简约的模型,我们的建模策略包含一个简单但有效的逐步正则化技术,可以应用于概述LR变量和热剖面能力之间的领域相关映射。结果表明,我们的方法可以生成准确的基于lr的动态热模型,当训练与所研究的电机安全操作区域内有限负载点集相关的数据时。
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引用次数: 0
期刊
ACM Transactions on Evolutionary Learning
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