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Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems. 树状高斯过程回归求解离线数据驱动的连续多目标优化问题。
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-12-01 DOI: 10.1162/evco_a_00329
Atanu Mazumdar, Manuel López-Ibáñez, Tinkle Chugh, Jussi Hakanen, Kaisa Miettinen

For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data, and an optimizer, for example, a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs.

对于离线数据驱动的多目标优化问题(MOPs),在优化过程中没有新数据可用。首先使用提供的离线数据构建近似模型(或代理),然后使用优化器(例如,多目标进化算法)以代理作为目标函数来寻找问题的帕累托最优解。与在线数据驱动的MOPs相比,这些代理不能随着新数据的更新而更新,因此在优化过程中不能通过考虑新数据来提高近似精度。高斯过程回归(GPR)模型由于能够提供不确定性信息而被广泛用作替代方法。然而,当数据集的大小很大时,构建gpr在计算上变得非常昂贵。使用稀疏GPRs减少了构建代理的计算成本。然而,稀疏gpr并不适合解决离线数据驱动的MOPs,在这种情况下,需要在Pareto最优解附近有良好的代理精度。本文提出了具有连续决策变量的离线数据驱动MOPs的树状GPR (TGPR-MO)替代算法。该方法首先利用回归树将决策空间划分为子区域,并在决策空间中接近Pareto最优解的区域依次构建gpr,以准确地近似目标函数之间的权衡。TGPR-MO替代品的计算成本较低,因为gpr仅在决策空间的较小区域中利用数据子集构建。TGPR-MO替代物在具有不同数据大小、采样策略、目标函数数量和决策变量的基于距离的可视化问题上进行了测试。实验结果表明,TGPR-MO替代算法计算成本低,可以处理大数据集。此外,与全gpr和稀疏gpr相比,TGPR-MO替代品产生的解更接近帕累托最优解。
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引用次数: 0
Symmetry Breaking for Voting Mechanisms* 投票机制的对称性打破。
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00327
Preethi Sankineni;Andrew M. Sutton
Recently, Rowe and Aishwaryaprajna (2019) introduced a simple majority vote technique that efficiently solves Jump with large gaps, OneMax with large noise, and any monotone function with a polynomial-size image. In this paper, we identify a pathological condition for this algorithm: the presence of spin-flip symmetry in the problem instance. Spin-flip symmetry is the invariance of a pseudo-Boolean function to complementation. Many important combinatorial optimization problems admit objective functions that exhibit this pathology, such as graph problems, Ising models, and variants of propositional satisfiability. We prove that no population size exists that allows the majority vote technique to solve spin-flip symmetric functions of unitation with reasonable probability. To remedy this, we introduce a symmetry-breaking technique that allows the majority vote algorithm to overcome this issue for many landscapes. This technique requires only a minor modification to the original majority vote algorithm to force it to sample strings in {0,1}n from a dimension n-1 hyperplane. We prove a sufficient condition for a spin-flip symmetric function to possess in order for the symmetry-breaking voting algorithm to succeed, and prove its efficiency on generalized TwoMax, a spin-flip symmetric variant of Jump, and families of constructed 3-NAE-SAT and 2-XOR-SAT formulas. We also prove that the algorithm fails on the one-dimensional Ising model, and suggest different techniques for overcoming this. Finally, we present empirical results that explore the tightness of the runtime bounds and the performance of the technique on randomized satisfiability variants.
最近,Rowe和Aishwaryaprajna(2019)介绍了一种简单的多数投票技术,该技术有效地解决了具有大间隙的Jump、具有大噪声的OneMax以及具有多项式大小图像的任何单调函数。在本文中,我们确定了该算法的一个病理条件:在问题实例中存在自旋翻转对称性。自旋翻转对称性是伪布尔函数对互补的不变性。许多重要的组合优化问题都承认了表现出这种病理性的目标函数,如图问题、伊辛模型和命题可满足性的变体。我们证明了不存在允许多数投票技术以合理概率求解单位化的自旋翻转对称函数的种群大小。为了解决这个问题,我们引入了一种对称性破坏技术,该技术允许多数投票算法在许多景观中克服这个问题。这种技术只需要对原始多数投票算法进行微小修改,就可以强制它在{0,1}n从维度n-1超平面。我们证明了自旋翻转对称函数具有对称性破缺投票算法成功的充分条件,并证明了它在广义TwoMax、Jump的自旋翻转对称变体以及构造的3-NAE-SAT和2-XOR-SAT公式族上的有效性。我们还证明了该算法在一维Ising模型上的失败,并提出了克服这一问题的不同技术。最后,我们给出了经验结果,探索了运行时边界的紧密性和该技术在随机可满足性变体上的性能。
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引用次数: 0
Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-Optimization 基于二维预优化的三维建筑质量多样性高效优化
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00326
Alexander Hagg;Martin L. Kliemank;Alexander Asteroth;Dominik Wilde;Mario C. Bedrunka;Holger Foysi;Dirk Reith
Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing hundreds of thousands of evaluations. Even with the assistance of surrogate models, quality diversity needs hundreds or even thousands of evaluations, which can make its use infeasible. In this study, we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1,024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.
高质量的多样性算法可用于有效地创建多样化的解决方案集,以告知工程师的直觉。但是,质量多样性在非常昂贵的问题中并不有效,需要数十万次评估。即使在替代模型的帮助下,质量多样性也需要数百甚至数千次评估,这可能使其使用变得不可行。在本研究中,我们试图通过在低维优化问题上使用预优化策略,然后将解决方案映射到高维情况来解决这个问题。对于设计最小化风害的建筑物的用例,我们展示了我们可以从建筑物足迹周围的2D流动特征预测3D建筑物周围的流动特征。对于一组不同的建筑设计,通过使用质量多样性算法对2D足迹的空间进行采样,可以训练出比使用Sobol序列等空间填充算法选择的一组足迹更准确的预测模型。仅对16栋建筑进行3D模拟,就创建了一套1,024栋建筑设计,这些设计具有较低的预测风扰。我们表明,我们可以通过产生具有质量多样性的训练数据来产生更好的机器学习模型,而不是使用常见的采样技术。该方法可以在计算成本昂贵的3D领域中引导生成设计,并允许工程师扫描设计空间,在早期设计阶段了解风干扰。
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引用次数: 0
Approaching the Traveling Tournament Problem with Randomized Beam Search 用随机束搜索求解巡回比赛问题
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00319
Nikolaus Frohner;Bernhard Neumann;Giulio Pace;Günther R. Raidl
The traveling tournament problem is a well-known sports league scheduling problem famous for its practical hardness. Given an even number of teams with symmetric distances between their venues, a double round-robin tournament has to be scheduled minimizing the total travel distances over all teams. We consider the most common constrained variant without repeaters and a streak limit of three, for which we study a beam search approach based on a state-space formulation guided by heuristics derived from different lower bound variants. We solve the arising capacitated vehicle routing subproblems either exactly for small- to medium-sized instances up to 18 teams or heuristically also for larger instances up to 24 teams. In a randomized variant of the search, we employ random team ordering and add small amounts of Gaussian noise to the nodes' guidance for diversification when multiple runs are performed. This allows for a simple yet effective parallelization of the beam search. A final comparison is done on the NL, CIRC, NFL, and GALAXY benchmark instances with 12 to 24 teams, for which we report a mean gap difference to the best known feasible solutions of 1.2% and five new best feasible solutions.
巡回赛问题是一个著名的体育联赛调度问题,其实际难度较大。假设参赛队伍的数量为偶数,且参赛队伍之间的距离对称,那么双轮循环赛的安排必须使所有队伍的总行程距离最小。我们考虑了最常见的无中继器约束变体和条带限制为3的约束变体,为此我们研究了一种基于由不同下界变体派生的启发式指导的状态空间公式的波束搜索方法。我们可以精确地解决多达18个团队的中小型实例或启发式地解决多达24个团队的大型实例中出现的有能力车辆路由子问题。在搜索的随机化变体中,我们采用随机团队排序,并在执行多次运行时向节点的多样化指导添加少量高斯噪声。这允许一个简单而有效的波束搜索并行化。最后对NL、CIRC、NFL和GALAXY的12至24支球队进行了比较,我们报告了最知名可行解决方案的平均差距差异为1.2%,以及五个新的最佳可行解决方案。
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引用次数: 1
Characterizing Permutation-Based Combinatorial Optimization Problems in Fourier Space 傅立叶空间中基于置换的组合优化问题的表征
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00315
Anne Elorza;Leticia Hernando;Jose A. Lozano
Comparing combinatorial optimization problems is a difficult task. They are defined using different criteria and terms: weights, flows, distances, etc. In spite of this apparent discrepancy, on many occasions, they tend to produce problem instances with similar properties. One avenue to compare different problems is to project them onto the same space, in order to have homogeneous representations. Expressing the problems in a unified framework could also lead to the discovery of theoretical properties or the design of new algorithms. This article proposes the use of the Fourier transform over the symmetric group as the tool to project different permutation-based combinatorial optimization problems onto the same space. Based on a previous study (Kondor, 2010), which characterized the Fourier coefficients of the quadratic assignment problem, we describe the Fourier coefficients of three other well-known problems: the symmetric and nonsymmetric traveling salesperson problem and the linear ordering problem. This transformation allows us to gain a better understanding of the intersection between the problems, as well as to bound their intrinsic dimension.
比较组合优化问题是一项艰巨的任务。它们使用不同的标准和术语来定义:重量、流量、距离等。尽管存在这种明显的差异,但在许多情况下,它们往往会产生具有类似性质的问题实例。比较不同问题的一种方法是将它们投射到同一空间,以获得齐次表示。在一个统一的框架中表达问题也可能导致发现理论性质或设计新的算法。本文提出使用对称群上的傅里叶变换作为工具,将不同的基于排列的组合优化问题投影到同一空间上。基于先前的研究(Kondor, 2010),该研究表征了二次分配问题的傅里叶系数,我们描述了其他三个著名问题的傅里叶系数:对称和非对称旅行销售人员问题以及线性排序问题。这种转换使我们能够更好地理解问题之间的交集,并限定它们的内在维度。
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引用次数: 1
Evolutionary and Estimation of Distribution Algorithms for Unconstrained, Constrained, and Multiobjective Noisy Combinatorial Optimisation Problems 无约束、约束和多目标噪声组合优化问题的分布算法的进化和估计
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00320
Aishwaryaprajna;Jonathan E. Rowe
We present an empirical study of a range of evolutionary algorithms applied to various noisy combinatorial optimisation problems. There are three sets of experiments. The first looks at several toy problems, such as OneMax and other linear problems. We find that UMDA and the Paired-Crossover Evolutionary Algorithm (PCEA) are the only ones able to cope robustly with noise, within a reasonable fixed time budget. In the second stage, UMDA and PCEA are then tested on more complex noisy problems: SubsetSum, Knapsack, and SetCover. Both perform well under increasing levels of noise, with UMDA being the better of the two. In the third stage, we consider two noisy multiobjective problems (CountingOnesCountingZeros and a multiobjective formulation of SetCover). We compare several adaptations of UMDA for multiobjective problems with the Simple Evolutionary Multiobjective Optimiser (SEMO) and NSGA-II. We conclude that UMDA, and its variants, can be highly effective on a variety of noisy combinatorial optimisation, outperforming many other evolutionary algorithms.
我们提出了一系列应用于各种噪声组合优化问题的进化算法的实证研究。有三组实验。首先看几个玩具问题,如OneMax和其他线性问题。我们发现UMDA和配对交叉进化算法(PCEA)是唯一能够在合理的固定时间预算内鲁棒地处理噪声的算法。在第二阶段,UMDA和PCEA然后在更复杂的噪声问题上进行测试:SubsetSum, backpack和SetCover。两者在噪声水平增加的情况下都表现良好,其中UMDA表现较好。在第三阶段,我们考虑了两个有噪声的多目标问题(CountingOnesCountingZeros和SetCover的多目标公式)。我们比较了UMDA与简单进化多目标优化器(SEMO)和NSGA-II在多目标问题上的几种适应性。我们得出结论,UMDA及其变体可以在各种噪声组合优化中非常有效,优于许多其他进化算法。
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引用次数: 1
Contributions to Dynamic Analysis of Differential Evolution Algorithms 差分进化算法动态分析的贡献
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-09-01 DOI: 10.1162/evco_a_00318
Lucas Resende;Ricardo H. C. Takahashi
The Differential Evolution (DE) algorithm is one of the most successful evolutionary computation techniques. However, its structure is not trivially translatable in terms of mathematical transformations that describe its population dynamics. In this work, analytical expressions are developed for the probability of enhancement of individuals after each application of a mutation operator followed by a crossover operation, assuming a population distributed radially around the optimum for the sphere objective function, considering the DE/rand/1/bin and the DE/rand/1/exp algorithm versions. These expressions are validated by numerical experiments. Considering quadratic functions given by f(x)=xTDTDx and populations distributed according to the linear transformation D-1 of a radially distributed population, it is also shown that the expressions still hold in the cases when f(x) is separable (D is diagonal) and when D is any nonsingular matrix and the crossover rate is Cr=1.0. The expressions are employed for the analysis of DE population dynamics. The analysis is extended to more complex situations, reaching rather precise predictions of the effect of problem dimension and of the choice of algorithm parameters.
差分进化(DE)算法是最成功的进化计算技术之一。然而,它的结构在描述其人口动态的数学转换方面并不是简单的可翻译的。在这项工作中,考虑到DE/rand/1/bin和DE/rand/1/exp算法版本,假设种群分布在球体目标函数的最优点周围,在每次应用突变算子和交叉操作后,开发了个体增强概率的解析表达式。数值实验验证了这些表达式的正确性。考虑由f(x)=xTDTDx给出的二次函数和根据径向分布总体的线性变换D-1分布的总体,还证明了当f(x)可分(D为对角)和D为任意非奇异矩阵且交叉率为Cr=1.0时,表达式仍然成立。这些表达式用于DE种群动态分析。将分析扩展到更复杂的情况,对问题维数和算法参数选择的影响进行了相当精确的预测。
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引用次数: 0
A Personal Perspective on Evolutionary Computation: A 35-Year Journey 个人对进化计算的看法:35年的历程
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-06-01 DOI: 10.1162/evco_a_00323
Zbigniew Michalewicz
This paper presents a personal account of the author's 35 years “adventure” with Evolutionary Computation—from the first encounter in 1988 and many years of academic research through to working full-time in business—successfully implementing evolutionary algorithms for some of the world's largest corporations. The paper concludes with some observations and insights.
本文介绍了作者在进化计算领域35年的个人经历——从1988年第一次接触到多年的学术研究,一直到在商业领域全职工作——成功地为一些世界上最大的公司实现了进化算法。文章最后提出了一些观察和见解。
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引用次数: 2
Evolutionary Algorithms for Parameter Optimization—Thirty Years Later 参数优化的进化算法-三十年后
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-06-01 DOI: 10.1162/evco_a_00325
Thomas H. W. Bäck;Anna V. Kononova;Bas van Stein;Hao Wang;Kirill A. Antonov;Roman T. Kalkreuth;Jacob de Nobel;Diederick Vermetten;Roy de Winter;Furong Ye
Thirty years, 1993–2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30 years. These include the covariance matrix adaptation evolution strategy and some fast-growing fields such as multimodal optimization, surrogate-assisted optimization, multiobjective optimization, and automated algorithm design. Moreover, we also discuss particle swarm optimization and differential evolution, which did not exist 30 years ago, either. One of the key arguments made in the paper is that we need fewer algorithms, not more, which, however, is the current trend through continuously claiming paradigms from nature that are suggested to be useful as new optimization algorithms. Moreover, we argue that we need proper benchmarking procedures to sort out whether a newly proposed algorithm is useful or not. We also briefly discuss automated algorithm design approaches, including configurable algorithm design frameworks, as the proposed next step toward designing optimization algorithms automatically, rather than by hand.
从1993年到2023年的30年,在科学上是一个很长的时间框架。我们讨论了进化算法领域的一些主要发展,以及在参数优化方面的应用,在这30年里。其中包括协方差矩阵自适应进化策略以及多模态优化、代理辅助优化、多目标优化和自动化算法设计等一些快速发展的领域。此外,我们还讨论了30年前不存在的粒子群优化和差分进化。论文中提出的一个关键论点是,我们需要更少的算法,而不是更多的算法,然而,这是当前的趋势,通过不断地从自然界中获得范式,这些范式被认为是有用的新优化算法。此外,我们认为,我们需要适当的基准程序来整理新提出的算法是否有用。我们还简要讨论了自动算法设计方法,包括可配置算法设计框架,作为自动设计优化算法的下一步,而不是手工设计。
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引用次数: 2
Editorial: Reflecting on Thirty Years of ECJ 社论:欧洲法院三十年的反思
IF 6.8 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2023-06-01 DOI: 10.1162/evco_e_00324
Kenneth De Jong;Emma Hart
We reflect on 30 years of the journal Evolutionary Computation. Taking the papers published in the first volume in 1993 as a springboard, as the founding and current Editors-in-Chief, we comment on the beginnings of the field, evaluate the extent to which the field has both grown and itself evolved, and provide our own perpectives on where the future lies.
我们回顾了《进化计算》杂志30年的历史。以1993年第一卷中发表的论文为跳板,作为创始和现任主编,我们评论了该领域的开端,评估了该领域的发展和自身演变的程度,并就未来的方向提供了我们自己的观点。
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引用次数: 0
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Evolutionary Computation
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