The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using transition probabilities between fitness levels. However, the lower bound generated by this method is often loose. An open question regarding the fitness level method is what are the tightest lower and upper time bounds that can be constructed based on transition probabilities between fitness levels. To answer this question, we combine drift analysis with fitness levels and define the tightest bound problem as a constrained multi-objective optimization problem subject to fitness levels. The tightest metric bounds by fitness levels are constructed and proven for the first time. Then linear bounds are derived from metric bounds and a framework is established that can be used to develop different fitness level methods for different types of linear bounds. The framework is generic and promising, as it can be used to draw tight time bounds on both fitness landscapes with and without shortcuts. This is demonstrated in the example of the (1+1) EA maximizing the TwoMax1 function.
适应度方法是分析精英进化算法命中时间的常用工具。其原理是将搜索空间划分为多个适合度等级,并利用适合度等级之间的过渡概率估算出命中时间的下限和上限。然而,这种方法产生的下限往往比较宽松。关于适合度方法的一个悬而未决的问题是,根据适合度之间的过渡概率,可以构建出最严格的时间下限和上限。为了回答这个问题,我们将漂移分析与适应度水平相结合,并将最严格约束问题定义为受限于适应度水平的多目标优化问题。我们首次构建并证明了适应度水平的最严格度量边界。然后,从度量约束推导出线性约束,并建立了一个框架,可用于为不同类型的线性约束开发不同的适度水平方法。该框架具有通用性和广阔前景,因为它既可以用于绘制有捷径的适度景观,也可以用于绘制无捷径的适度景观。(1+1) EA 最大化 TwoMax1 函数的例子就证明了这一点。
{"title":"Drift Analysis with Fitness Levels for Elitist Evolutionary Algorithms.","authors":"Jun He, Yuren Zhou","doi":"10.1162/evco_a_00349","DOIUrl":"https://doi.org/10.1162/evco_a_00349","url":null,"abstract":"<p><p>The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using transition probabilities between fitness levels. However, the lower bound generated by this method is often loose. An open question regarding the fitness level method is what are the tightest lower and upper time bounds that can be constructed based on transition probabilities between fitness levels. To answer this question, we combine drift analysis with fitness levels and define the tightest bound problem as a constrained multi-objective optimization problem subject to fitness levels. The tightest metric bounds by fitness levels are constructed and proven for the first time. Then linear bounds are derived from metric bounds and a framework is established that can be used to develop different fitness level methods for different types of linear bounds. The framework is generic and promising, as it can be used to draw tight time bounds on both fitness landscapes with and without shortcuts. This is demonstrated in the example of the (1+1) EA maximizing the TwoMax1 function.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140295207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial for the Special Issue on Reproducibility.","authors":"Manuel López-Ibáñez, Luís Paquete, Mike Preuss","doi":"10.1162/evco_e_00344","DOIUrl":"10.1162/evco_e_00344","url":null,"abstract":"","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139998205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raúl Martín-Santamaría, Sergio Cavero, Alberto Herrán, Abraham Duarte, J Manuel Colmenar
Reproducibility of experiments is a complex task in stochastic methods such as evolutionary algorithms or metaheuristics in general. Many works from the literature give general guidelines to favor reproducibility. However, none of them provide both a practical set of steps or software tools to help in this process. In this article, we propose a practical methodology to favor reproducibility in optimization problems tackled with stochastic methods. This methodology is divided into three main steps, where the researcher is assisted by software tools which implement state-of-the-art techniques related to this process. The methodology has been applied to study the double-row facility layout problem (DRFLP) where we propose a new algorithm able to obtain better results than the state-of-the-art methods. To this aim, we have also replicated the previous methods in order to complete the study with a new set of larger instances. All the produced artifacts related to the methodology and the study of the target problem are available in Zenodo.
{"title":"A Practical Methodology for Reproducible Experimentation: An Application to the Double-Row Facility Layout Problem.","authors":"Raúl Martín-Santamaría, Sergio Cavero, Alberto Herrán, Abraham Duarte, J Manuel Colmenar","doi":"10.1162/evco_a_00317","DOIUrl":"10.1162/evco_a_00317","url":null,"abstract":"<p><p>Reproducibility of experiments is a complex task in stochastic methods such as evolutionary algorithms or metaheuristics in general. Many works from the literature give general guidelines to favor reproducibility. However, none of them provide both a practical set of steps or software tools to help in this process. In this article, we propose a practical methodology to favor reproducibility in optimization problems tackled with stochastic methods. This methodology is divided into three main steps, where the researcher is assisted by software tools which implement state-of-the-art techniques related to this process. The methodology has been applied to study the double-row facility layout problem (DRFLP) where we propose a new algorithm able to obtain better results than the state-of-the-art methods. To this aim, we have also replicated the previous methods in order to complete the study with a new set of larger instances. All the produced artifacts related to the methodology and the study of the target problem are available in Zenodo.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40695126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna V Kononova, Diederick Vermetten, Fabio Caraffini, Madalina-A Mitran, Daniela Zaharie
We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple bound constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours in terms of performance, disruptiveness, and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants, on a special test function and the BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem dimensionality. Differential Evolution is not at all special in this regard-there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the heuristic optimisation community to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we refer to as the strategy of dealing with infeasible solutions. This component needs to be consistently: (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on an algorithm's performance in a wider sense (i.e., convergence time, robustness, etc.), and (c) included in the (automatic) design of algorithms. All of these should be done even for problems with bound constraints.
{"title":"The Importance of Being Constrained: Dealing with Infeasible Solutions in Differential Evolution and Beyond.","authors":"Anna V Kononova, Diederick Vermetten, Fabio Caraffini, Madalina-A Mitran, Daniela Zaharie","doi":"10.1162/evco_a_00333","DOIUrl":"10.1162/evco_a_00333","url":null,"abstract":"<p><p>We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple bound constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours in terms of performance, disruptiveness, and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants, on a special test function and the BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem dimensionality. Differential Evolution is not at all special in this regard-there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the heuristic optimisation community to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we refer to as the strategy of dealing with infeasible solutions. This component needs to be consistently: (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on an algorithm's performance in a wider sense (i.e., convergence time, robustness, etc.), and (c) included in the (automatic) design of algorithms. All of these should be done even for problems with bound constraints.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9474478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reproducibility is important for having confidence in evolutionary machine learning algorithms. Although the focus of reproducibility is usually to recreate an aggregate prediction error score using fixed random seeds, this is not sufficient. Firstly, multiple runs of an algorithm, without a fixed random seed, should ideally return statistically equivalent results. Secondly, it should be confirmed whether the expected behaviour of an algorithm matches its actual behaviour, in terms of how an algorithm targets a reduction in prediction error. Confirming the behaviour of an algorithm is not possible when using a total error aggregate score. Using an error decomposition framework as a methodology for improving the reproducibility of results in evolutionary computation addresses both of these factors. By estimating decomposed error using multiple runs of an algorithm and multiple training sets, the framework provides a greater degree of certainty about the prediction error. Also, decomposing error into bias, variance due to the algorithm (internal variance), and variance due to the training data (external variance) more fully characterises evolutionary algorithms. This allows the behaviour of an algorithm to be confirmed. Applying the framework to a number of evolutionary algorithms shows that their expected behaviour can be different to their actual behaviour. Identifying a behaviour mismatch is important in terms of understanding how to further refine an algorithm as well as how to effectively apply an algorithm to a problem.
{"title":"Using Decomposed Error for Reproducing Implicit Understanding of Algorithms.","authors":"Caitlin A Owen, Grant Dick, Peter A Whigham","doi":"10.1162/evco_a_00321","DOIUrl":"10.1162/evco_a_00321","url":null,"abstract":"<p><p>Reproducibility is important for having confidence in evolutionary machine learning algorithms. Although the focus of reproducibility is usually to recreate an aggregate prediction error score using fixed random seeds, this is not sufficient. Firstly, multiple runs of an algorithm, without a fixed random seed, should ideally return statistically equivalent results. Secondly, it should be confirmed whether the expected behaviour of an algorithm matches its actual behaviour, in terms of how an algorithm targets a reduction in prediction error. Confirming the behaviour of an algorithm is not possible when using a total error aggregate score. Using an error decomposition framework as a methodology for improving the reproducibility of results in evolutionary computation addresses both of these factors. By estimating decomposed error using multiple runs of an algorithm and multiple training sets, the framework provides a greater degree of certainty about the prediction error. Also, decomposing error into bias, variance due to the algorithm (internal variance), and variance due to the training data (external variance) more fully characterises evolutionary algorithms. This allows the behaviour of an algorithm to be confirmed. Applying the framework to a number of evolutionary algorithms shows that their expected behaviour can be different to their actual behaviour. Identifying a behaviour mismatch is important in terms of understanding how to further refine an algorithm as well as how to effectively apply an algorithm to a problem.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9084698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Describing the properties of complex systems that evolve over time is a crucial requirement for monitoring and understanding them. Signal Temporal Logic (STL) is a framework that proved to be effective for this aim because it is expressive and allows state properties as human-readable formulae. Crafting STL formulae that fit a particular system is, however, a difficult task. For this reason, a few approaches have been proposed recently for the automatic learning of STL formulae starting from observations of the system. In this paper, we propose BUSTLE (Bi-level Universal STL Evolver), an approach based on evolutionary computation for learning STL formulae from data. BUSTLE advances the state-of-the-art because it (i) applies to a broader class of problems, in terms of what is known about the state of the system during its observation, and (ii) generates both the structure and the values of the parameters of the formulae employing a bi-level search mechanism (global for the structure, local for the parameters). We consider two cases where (a) observations of the system in both anomalous and regular state are available, or (b) only observations of regular state are available. We experimentally evaluate BUSTLE on problem instances corresponding to the two cases and compare it against previous approaches. We show that the evolved STL formulae are effective and human-readable: the versatility of BUSTLE does not come at the cost of lower effectiveness.
{"title":"BUSTLE: a Versatile Tool for the Evolutionary Learning of STL Specifications from Data.","authors":"Federico Pigozzi, Laura Nenzi, Eric Medvet","doi":"10.1162/evco_a_00347","DOIUrl":"https://doi.org/10.1162/evco_a_00347","url":null,"abstract":"<p><p>Describing the properties of complex systems that evolve over time is a crucial requirement for monitoring and understanding them. Signal Temporal Logic (STL) is a framework that proved to be effective for this aim because it is expressive and allows state properties as human-readable formulae. Crafting STL formulae that fit a particular system is, however, a difficult task. For this reason, a few approaches have been proposed recently for the automatic learning of STL formulae starting from observations of the system. In this paper, we propose BUSTLE (Bi-level Universal STL Evolver), an approach based on evolutionary computation for learning STL formulae from data. BUSTLE advances the state-of-the-art because it (i) applies to a broader class of problems, in terms of what is known about the state of the system during its observation, and (ii) generates both the structure and the values of the parameters of the formulae employing a bi-level search mechanism (global for the structure, local for the parameters). We consider two cases where (a) observations of the system in both anomalous and regular state are available, or (b) only observations of regular state are available. We experimentally evaluate BUSTLE on problem instances corresponding to the two cases and compare it against previous approaches. We show that the evolved STL formulae are effective and human-readable: the versatility of BUSTLE does not come at the cost of lower effectiveness.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139913984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ryan Boldi, Martin Briesch, Dominik Sobania, Alexander Lalejini, Thomas Helmuth, Franz Rothlauf, Charles Ofria, Lee Spector
Genetic Programming (GP) often uses large training sets and requires all individuals to be evaluated on all training cases during selection. Random down-sampled lexicase selection evaluates individuals on only a random subset of the training cases allowing for more individuals to be explored with the same amount of program executions. However, sampling randomly can exclude important cases from the down-sample for a number of generations, while cases that measure the same behavior (synonymous cases) may be overused. In this work, we introduce Informed Down-Sampled Lexicase Selection. This method leverages population statistics to build down-samples that contain more distinct and therefore informative training cases. Through an empirical investigation across two different GP systems (PushGP and Grammar-Guided GP), we find that informed down-sampling significantly outperforms random down-sampling on a set of contemporary program synthesis benchmark problems. Through an analysis of the created down-samples, we find that important training cases are included in the down-sample consistently across independent evolutionary runs and systems. We hypothesize that this improvement can be attributed to the ability of Informed Down-Sampled Lexicase Selection to maintain more specialist individuals over the course of evolution, while still benefiting from reduced per-evaluation costs.
{"title":"Informed Down-Sampled Lexicase Selection: Identifying productive training cases for efficient problem solving.","authors":"Ryan Boldi, Martin Briesch, Dominik Sobania, Alexander Lalejini, Thomas Helmuth, Franz Rothlauf, Charles Ofria, Lee Spector","doi":"10.1162/evco_a_00346","DOIUrl":"https://doi.org/10.1162/evco_a_00346","url":null,"abstract":"<p><p>Genetic Programming (GP) often uses large training sets and requires all individuals to be evaluated on all training cases during selection. Random down-sampled lexicase selection evaluates individuals on only a random subset of the training cases allowing for more individuals to be explored with the same amount of program executions. However, sampling randomly can exclude important cases from the down-sample for a number of generations, while cases that measure the same behavior (synonymous cases) may be overused. In this work, we introduce Informed Down-Sampled Lexicase Selection. This method leverages population statistics to build down-samples that contain more distinct and therefore informative training cases. Through an empirical investigation across two different GP systems (PushGP and Grammar-Guided GP), we find that informed down-sampling significantly outperforms random down-sampling on a set of contemporary program synthesis benchmark problems. Through an analysis of the created down-samples, we find that important training cases are included in the down-sample consistently across independent evolutionary runs and systems. We hypothesize that this improvement can be attributed to the ability of Informed Down-Sampled Lexicase Selection to maintain more specialist individuals over the course of evolution, while still benefiting from reduced per-evaluation costs.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139562620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pablo Ramos Criado, D Barrios Rolanía, David de la Hoz, Daniel Manrique
Genetic variation operators in grammar-guided genetic programming are fundamental to guide the evolutionary process in search and optimization problems. However, they show some limitations, mainly derived from an unbalanced exploration and local-search trade-off. This article presents an estimation of distribution algorithm for grammar-guided genetic programming to overcome this difficulty and thus increase the performance of the evolutionary algorithm. Our proposal employs an extended dynamic stochastic context-free grammar to encode and calculate the estimation of the distribution of the search space from some promising individuals in the population. Unlike traditional estimation of distribution algorithms, the proposed approach improves exploratory behavior by smoothing the estimated distribution model. Therefore, this algorithm is referred to as SEDA, smoothed estimation of distribution algorithm. Experiments have been conducted to compare overall performance using a typical genetic programming crossover operator, an incremental estimation of distribution algorithm, and the proposed approach after tuning their hyperparameters. These experiments involve challenging problems to test the local search and exploration features of the three evolutionary systems. The results show that grammar-guided genetic programming with SEDA achieves the most accurate solutions with an intermediate convergence speed.
语法引导遗传编程中的遗传变异算子是引导搜索和优化问题进化过程的基础。然而,它们也存在一些局限性,主要是探索和局部搜索权衡不平衡。本文提出了一种语法引导遗传编程的分布估计算法,以克服这一困难,从而提高进化算法的性能。我们的建议采用一种扩展的动态随机无上下文语法来编码和计算种群中一些有希望的个体对搜索空间分布的估计。与传统的分布估计算法不同,我们提出的方法通过平滑估计分布模型来改善探索行为。因此,这种算法被称为 SEDA,即平滑估计分布算法。通过实验,比较了使用典型遗传编程交叉算子、增量估计分布算法和调整超参数后的拟议方法的整体性能。这些实验涉及具有挑战性的问题,以测试这三种进化系统的局部搜索和探索功能。结果表明,语法引导的遗传编程与 SEDA 以中等收敛速度获得了最准确的解决方案。
{"title":"Estimation of Distribution Algorithm for Grammar-Guided Genetic Programming.","authors":"Pablo Ramos Criado, D Barrios Rolanía, David de la Hoz, Daniel Manrique","doi":"10.1162/evco_a_00345","DOIUrl":"https://doi.org/10.1162/evco_a_00345","url":null,"abstract":"<p><p>Genetic variation operators in grammar-guided genetic programming are fundamental to guide the evolutionary process in search and optimization problems. However, they show some limitations, mainly derived from an unbalanced exploration and local-search trade-off. This article presents an estimation of distribution algorithm for grammar-guided genetic programming to overcome this difficulty and thus increase the performance of the evolutionary algorithm. Our proposal employs an extended dynamic stochastic context-free grammar to encode and calculate the estimation of the distribution of the search space from some promising individuals in the population. Unlike traditional estimation of distribution algorithms, the proposed approach improves exploratory behavior by smoothing the estimated distribution model. Therefore, this algorithm is referred to as SEDA, smoothed estimation of distribution algorithm. Experiments have been conducted to compare overall performance using a typical genetic programming crossover operator, an incremental estimation of distribution algorithm, and the proposed approach after tuning their hyperparameters. These experiments involve challenging problems to test the local search and exploration features of the three evolutionary systems. The results show that grammar-guided genetic programming with SEDA achieves the most accurate solutions with an intermediate convergence speed.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139565374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Existing work on offline data-driven optimization mainly focuses on problems in static environments, and little attention has been paid to problems in dynamic environments. Offline data-driven optimization in dynamic environments is a challenging problem because the distribution of collected data varies over time, requiring surrogate models and optimal solutions tracking with time. This paper proposes a knowledge-transfer-based data-driven optimization algorithm to address these issues. First, an ensemble learning method is adopted to train surrogate models to leverage the knowledge of data in historical environments as well as adapt to new environments. Specifically, given data in a new environment, a model is constructed with the new data, and the preserved models of historical environments are further trained with the new data. Then, these models are considered to be base learners and combined as an ensemble surrogate model. After that, all base learners and the ensemble surrogate model are simultaneously optimized in a multitask environment for finding optimal solutions for real fitness functions. In this way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the ensemble model is the most accurate surrogate, we assign more individuals to the ensemble surrogate than its base learners. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art offline data-driven optimization algorithms. Code is available at https://github.com/Peacefulyang/DSE_MFS.git.
{"title":"A Data Stream Ensemble Assisted Multifactorial Evolutionary Algorithm for Offline Data-Driven Dynamic Optimization.","authors":"Cuie Yang, Jinliang Ding, Yaochu Jin, Tianyou Chai","doi":"10.1162/evco_a_00332","DOIUrl":"10.1162/evco_a_00332","url":null,"abstract":"<p><p>Existing work on offline data-driven optimization mainly focuses on problems in static environments, and little attention has been paid to problems in dynamic environments. Offline data-driven optimization in dynamic environments is a challenging problem because the distribution of collected data varies over time, requiring surrogate models and optimal solutions tracking with time. This paper proposes a knowledge-transfer-based data-driven optimization algorithm to address these issues. First, an ensemble learning method is adopted to train surrogate models to leverage the knowledge of data in historical environments as well as adapt to new environments. Specifically, given data in a new environment, a model is constructed with the new data, and the preserved models of historical environments are further trained with the new data. Then, these models are considered to be base learners and combined as an ensemble surrogate model. After that, all base learners and the ensemble surrogate model are simultaneously optimized in a multitask environment for finding optimal solutions for real fitness functions. In this way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the ensemble model is the most accurate surrogate, we assign more individuals to the ensemble surrogate than its base learners. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art offline data-driven optimization algorithms. Code is available at https://github.com/Peacefulyang/DSE_MFS.git.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9424656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multiobjective evolutionary algorithms are successfully applied in many real-world multiobjective optimization problems. As for many other AI methods, the theoretical understanding of these algorithms is lagging far behind their success in practice. In particular, previous theory work considers mostly easy problems that are composed of unimodal objectives. As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OneJumpZeroJump problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark. We prove that the simple evolutionary multiobjective optimizer (SEMO) with probability one does not compute the full Pareto front, regardless of the runtime. In contrast, for all problem sizes n and all jump sizes k∈[4..n2-1], the global SEMO (GSEMO) covers the Pareto front in an expected number of Θ((n-2k)nk) iterations. For k=o(n), we also show the tighter bound 32enk+1±o(nk+1), which might be the first runtime bound for an MOEA that is tight apart from lower-order terms. We also combine the GSEMO with two approaches that showed advantages in single-objective multimodal problems. When using the GSEMO with a heavy-tailed mutation operator, the expected runtime improves by a factor of at least kΩ(k). When adapting the recent stagnation-detection strategy of Rajabi and Witt (2022) to the GSEMO, the expected runtime also improves by a factor of at least kΩ(k) and surpasses the heavy-tailed GSEMO by a small polynomial factor in k. Via an experimental analysis, we show that these asymptotic differences are visible already for small problem sizes: A factor-5 speed-up from heavy-tailed mutation and a factor-10 speed-up from stagnation detection can be observed already for jump size 4 and problem sizes between 10 and 50. Overall, our results show that the ideas recently developed to aid single-objective evolutionary algorithms to cope with local optima can be effectively employed also in multiobjective optimization.
{"title":"Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives.","authors":"Weijie Zheng, Benjamin Doerr","doi":"10.1162/evco_a_00328","DOIUrl":"10.1162/evco_a_00328","url":null,"abstract":"<p><p>Multiobjective evolutionary algorithms are successfully applied in many real-world multiobjective optimization problems. As for many other AI methods, the theoretical understanding of these algorithms is lagging far behind their success in practice. In particular, previous theory work considers mostly easy problems that are composed of unimodal objectives. As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OneJumpZeroJump problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark. We prove that the simple evolutionary multiobjective optimizer (SEMO) with probability one does not compute the full Pareto front, regardless of the runtime. In contrast, for all problem sizes n and all jump sizes k∈[4..n2-1], the global SEMO (GSEMO) covers the Pareto front in an expected number of Θ((n-2k)nk) iterations. For k=o(n), we also show the tighter bound 32enk+1±o(nk+1), which might be the first runtime bound for an MOEA that is tight apart from lower-order terms. We also combine the GSEMO with two approaches that showed advantages in single-objective multimodal problems. When using the GSEMO with a heavy-tailed mutation operator, the expected runtime improves by a factor of at least kΩ(k). When adapting the recent stagnation-detection strategy of Rajabi and Witt (2022) to the GSEMO, the expected runtime also improves by a factor of at least kΩ(k) and surpasses the heavy-tailed GSEMO by a small polynomial factor in k. Via an experimental analysis, we show that these asymptotic differences are visible already for small problem sizes: A factor-5 speed-up from heavy-tailed mutation and a factor-10 speed-up from stagnation detection can be observed already for jump size 4 and problem sizes between 10 and 50. Overall, our results show that the ideas recently developed to aid single-objective evolutionary algorithms to cope with local optima can be effectively employed also in multiobjective optimization.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":null,"pages":null},"PeriodicalIF":6.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9250961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}