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Near-Tight Runtime Guarantees for Many-Objective evolutionary algorithms

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arXiv 2024年

作者： Wietheger, Simon Doerr, Benjamin Algorithms and Complexity Group Technische Universität Wien Vienna Austria CNRS École Polytechnique Institut Polytechnique de Paris Palaiseau France

Despite significant progress in the field of mathematical runtime analysis of multi-objective evolutionary algorithms (MOEAs), the performance of MOEAs on discrete many-objective problems is little understood. In particular, the few existing bounds for the SEMO, global SEMO, and SMS-EMOA algorithms on classic benchmarks are all roughly quadratic in the size of the Pareto front. In this work, we prove near-tight runtime guarantees for these three algorithms on the four most common benchmark problems OneMinMax, CountingOnesCountingZeros, LeadingOnesTrailingZeros, and OneJumpZeroJump, and this for arbitrary numbers of objectives. Our bounds depend only linearly on the Pareto front size, showing that these MOEAs on these benchmarks cope much better with many objectives than what previous works suggested. Our bounds are tight apart from small polynomial factors in the number of objectives and length of bitstrings. This is the first time that such tight bounds are proven for many-objective uses of these MOEAs. While it is known that such results cannot hold for the NSGA-II, we do show that our bounds, via a recent structural result, transfer to the NSGA-III algorithm. Copyright © 2024, The Authors. All rights reserved.

关键词： evolutionary algorithms

A Hybrid Intelligent Framework for Maximising Sag Mill Throughput: An Integration of Expert Knowledge, Machine Learning and evolutionary algorithms for Parameter Optimisation

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SSRN

SSRN 2024年

作者： Ghasemi, Zahra Neshat, Mehdi Aldrich, Chris Karageorgos, John Zanin, Max Neumann, Frank Chen, Lei School of Electrical and Mechanical Engineering The University of Adelaide North Terrace AdelaideSA5005 Australia Centre for Artificial Intelligence Research & Optimisation Torrens University Australia Brisbane4006 Australia Western Australian School of Mines Curtin University PerthWA6845 Australia Manta Controls Pty Ltd 1 Sharon Pl GrangeSA5022 Australia School of Chemical Engineering The University of Adelaide North Terrace AdelaideSA5005 Australia School of Civil Environmental and Mining Engineering The University of South Australia AdelaideSA5095 Australia School of Computer and Mathematical Sciences The University of Adelaide North Terrace AdelaideSA5005 Australia Faculty of Engineering and Information Technology The University of Technology Sydney UltimoNSW2007 Australia

In mineral processing plants, grinding is a crucial step, accounting for approximately 50% of the total mineral processing costs. Semi-autogenous grinding (SAG) mills are extensively employed in the grinding circuit of mineral processing plants. Maximising SAG mill throughput is of significant importance considering its profound financial outcomes. However, the optimum process parameter setting aimed at achieving maximum mill throughput remains an uninvestigated domain in prior research. This study introduces a hybrid intelligent framework leveraging expert knowledge, machine learning techniques and evolutionary algorithms to address this research need. In this study, we utilise an extensive industrial dataset comprising 36,743 records and select relevant features based on the insights of industry experts. Following the removal of erroneous data, a comprehensive evaluation of 17 diverse machine learning models is undertaken to identify the most accurate predictive model. To improve the model’s performance, feature selection and outlier detection are executed. The resultant optimal model, trained with refined features, serves as the objective function within three distinct evolutionary algorithms. These algorithms are employed to identify parameter configurations that maximise SAG mill throughput while adhering to the working limits of input parameters as constraints. Notably, our analysis revealed that CatBoost, as an ensemble model, stands out as the most accurate predictor. Furthermore, differential evolution emerges as the preferred optimisation algorithm, exhibiting superior performance in both achieving the highest mill throughput predictions and ensuring robustness in predictions, surpassing alternative methods. © 2024, The Authors. All rights reserved.

关键词： evolutionary algorithms

A First Look at Kolmogorov-Arnold Networks in Surrogate-assisted evolutionary algorithms

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arXiv 2024年

作者： Hao, Hao Zhang, Xiaoqun Li, Bingdong Zhou, Aimin The Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China The Shanghai Institute of AI for Education The School of Computer Science and Technology East China Normal University Shanghai200062 China

Surrogate-assisted evolutionary Algorithm (SAEA) is an essential method for solving expensive expensive problems. Utilizing surrogate models to substitute the optimization function can significantly reduce reliance on the function evaluations during the search process, thereby lowering the optimization costs. The construction of surrogate models is a critical component in SAEAs, with numerous machine learning algorithms playing a pivotal role in the model-building phase. This paper introduces Kolmogorov-Arnold Networks (KANs) as surrogate models within SAEAs, examining their application and effectiveness. We employ KANs for regression and classification tasks, focusing on the selection of promising solutions during the search process, which consequently reduces the number of expensive function evaluations. Experimental results indicate that KANs demonstrate commendable performance within SAEAs, effectively decreasing the number of function calls and enhancing the optimization efficiency. The relevant code is publicly accessible and can be found in the GitHub repository. © 2024, CC BY.

关键词： evolutionary algorithms

Optimized Drug Design using Multi-Objective evolutionary algorithms with SELFIES

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arXiv 2024年

作者： Hömberg, Tomoya Mostaghim, Sanaz Hiwa, Satoru Hiroyasu, Tomoyuki Department of Computational Intelligence Otto-von-Guericke University Magdeburg Germany Faculty of Life and Medical Sciences Doshisha University Kyoto Japan

Computer aided drug design is a promising approach to reduce the tremendous costs, i.e. time and resources, for developing new medicinal drugs. It finds application in aiding the traversal of the vast chemical space of potentially useful compounds. In this paper, we deploy multi-objective evolutionary algorithms, namely NSGA-II, NSGA-III, and MOEA/D, for this purpose. At the same time, we used the SELFIES string representation method. In addition to the QED and SA score, we optimize compounds using the GuacaMol benchmark multi-objective task sets. Our results indicate that all three algorithms show converging behavior and successfully optimize the defined criteria whilst differing mainly in the number of potential solutions found. We observe that novel and promising candidates for synthesis are discovered among obtained compounds in the Pareto-sets. Copyright © 2024, The Authors. All rights reserved.

关键词： evolutionary algorithms

Theoretical Advantage of Multiobjective evolutionary algorithms for Problems with Different Degrees of Conflict

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arXiv 2024年

作者： Zheng, Weijie School of Computer Science and Technology International Research Institute for Artificial Intelligence Harbin Institute of Technology Shenzhen China

The field of multiobjective evolutionary algorithms (MOEAs) often emphasizes its popularity for optimization problems with conflicting objectives. However, it is still theoretically unknown how MOEAs perform for different degrees of conflict, even for no conflicts, compared with typical approaches outside this field. As the first step to tackle this question, we propose the OneMaxMink benchmark class with the degree of the conflict k ∈ [0..n], a generalized variant of COCZ and OneMinMax. Two typical non-MOEA approaches, scalarization (weighted-sum approach) and Ε−constraint approach, are considered. We prove that for any set of weights, the set of optima (one optimum corresponds to one constructed single-objective problem) found by scalarization approach cannot cover the full Pareto front of OneMaxMink. Although the set of the optima of constrained problems constructed via Ε−constraint approach can cover the full Pareto front, the general used ways (via exterior or nonparameter penalty functions) to solve such constrained problems encountered difficulties. The nonparameter penalty function way cannot construct the set of optima whose function values are the Pareto front, and the exterior way helps (with expected runtime of O(n ln n) for the randomized local search algorithm for reaching any Pareto front point) but with careful settings of Ε and r (r > 1/(Ε + 1 − ⌈Ε⌉)). In constrast, the generally analyzed MOEAs can efficiently solve OneMaxMink without above careful designs. We prove that (G)SEMO, MOEA/D, NSGA-II, and SMS-EMOA can cover the full Pareto front in O(max{k, 1}n ln n) expected number of function evaluations, which is the same asymptotic runtime as the exterior way in Ε-constraint approach with careful settings. As a side result, our results also give the performance analysis of solving a constrained problem via multiobjective way. Copyright © 2024, The Authors. All rights reserved.

关键词： evolutionary algorithms

Comparative analysis of various evolutionary algorithms: Past three decades

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EAI ENDORSED TRANSACTIONS ON SCALABLE INFORMATION SYSTEMS 2024年第4期11卷

作者： Srikumar, A. Pande, Sagar Dhanraj VIT AP Univ Sch Comp Sci & Engn Amaravati Andhra Pradesh India

INTRODUCTION: The evolutionary algorithms created back in 1953, have gone through various phases of development over the years. It has been put to use to solve various problems in different domains including complex problems such as the infamous problem of Travelling Salesperson (TSP). OBJECTIVES: The main objective of this research is to find out the advancements in evolutionary algorithms and to check whether it is still relevant in 2023. METHODS: To give an overview of the related concepts, subdomains, pros, and cons, the historical and recent developments are discussed and critiqued to provide insights into the results and a better conception of the trends in the domain. RESULTS: For a better perception of the development of evolutionary algorithms over the years, decade-wise trend analysis has been done for the past three decades. CONCLUSION: Scope of research in the domain is ever expanding and to name a few EAs for Data mining, Hybrid EAs are still under development.

关键词： optimization evolutionary algorithms Genetic algorithms Trend Analysis of Genetic algorithms

Performance Comparison of Surrogate-Assisted evolutionary algorithms on Computational Fluid Dynamics Problems

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arXiv 2024年

作者： Kůdela, Jakub Dobrovský, Ladislav Institute of Automation and Computer Science Faculty of Mechanical Engineering Brno University of Technology Czech Republic

Surrogate-assisted evolutionary algorithms (SAEAs) are recently among the most widely studied methods for their capability to solve expensive real-world optimization problems. However, the development of new methods and benchmarking with other techniques still relies almost exclusively on artificially created problems. In this paper, we use two real-world computational fluid dynamics problems to compare the performance of eleven state-of-the-art single-objective SAEAs. We analyze the performance by investigating the quality and robustness of the obtained solutions and the convergence properties of the selected methods. Our findings suggest that the more recently published methods, as well as the techniques that utilize differential evolution as one of their optimization mechanisms, perform significantly better than the other considered methods. © 2024, CC BY.

关键词： evolutionary algorithms

evolutionary algorithms with Self-adjusting Asymmetric Mutation 16th

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Evolutionary Algorithms with Self-adjusting Asymmetric Mutat...

16th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

ISBN: (纸本)9783030581114;9783030581121

evolutionary algorithms (EAs) and other randomized search heuristics are often considered as unbiased algorithms that are invariant with respect to different transformations of the underlying search space. However, if a certain amount of domain knowledge is available the use of biased search operators in EAs becomes viable. We consider a simple (1+1) EA for binary search spaces and analyze an asymmetric mutation operator that can treat zero- and one-bits differently. This operator extends previous work by Jansen and Sudholt (ECJ 18(1), 2010) by allowing the operator asymmetry to vary according to the success rate of the algorithm. Using a self-adjusting scheme that learns an appropriate degree of asymmetry, we show improved runtime results on the class of functions OneMaxa describing the number of matching bits with a fixed target alpha is an element of{0, 1}(n).

关键词： evolutionary algorithms Runtime analysis Self-adjusting algorithms Parameter control Asymmetric mutations

Self-Adjusting evolutionary algorithms Are Slow on Multimodal Landscapes

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arXiv 2024年

作者： Lengler, Johannes Sturm, Konstantin Department of Computer Science ETH Zürich Zürich Switzerland

The one-fifth rule and its generalizations are a classical parameter control mechanism in discrete domains. They have also been transferred to control the offspring population size of the (1, λ)-EA. This has been shown to work very well for hill-climbing, and combined with a restart mechanism it was recently shown by Hevia Fajardo and Sudholt to improve performance on the multi-modal problem Cliff drastically. In this work we show that the positive results do not extend to other types of local optima. On the distorted OneMax benchmark, the self-adjusting (1, λ)-EA is slowed down just as elitist algorithms because self-adaptation prevents the algorithm from escaping from local optima. This makes the self-adaptive algorithm considerably worse than good static parameter choices, which do allow to escape from local optima efficiently. We show this theoretically and complement the result with empirical runtime results. © 2024, CC BY.

关键词： evolutionary algorithms