arXiv subjects

Hisao Ishibuchi

Publications and source records attributed to Hisao Ishibuchi.

At least 19 recordsLinked to original sources

arXiv2026

PHIDA: Persistence-Guided Node-to-Cluster Mapping for Online Clustering

Online clustering methods that adaptively create and update nodes as data arrive often make node learning explicit, whereas the mapping from the learned node state to output clusters often remains implicit or simplified. Implicit mappings make output clusters sensitive to weak graph bridges or local relations based on distance in the graph over learned nodes, leaving no explicit constraint on which node groups remain intact during mapping. This paper addresses this gap by proposing PHIDA, a persistence-guided node-to-cluster mapping method for online clustering with learned nodes. PHIDA implements this mapping within Adaptive Resonance Theory (ART)-based online clustering by combining Inverse-Distance ART (IDA) node learning with node-to-cluster mapping constrained by Persistent Homology (PH). Experiments on 24 benchmark datasets show that PHIDA achieves the best average ranks in stationary comparisons that include the recent stationary-only clustering methods, while also improving aggregate performance in the nonstationary setting over the evaluated online methods that adaptively create and update nodes. Ablations and comparisons with conventional node-to-cluster mappings indicate that the observed gains are associated with PH-constrained mapping that preserves raw PH components, together with the use of the PH component view during node learning. Source code is available at https://github.com/Masuyama-lab/PHIDA

cs.LG↗

arXiv2026

A Parameter-free Adaptive Resonance Theory-based Topological Clustering Algorithm Capable of Continual Learning

In general, a similarity threshold (i.e., a vigilance parameter) for a node learning process in Adaptive Resonance Theory (ART)-based algorithms has a significant impact on clustering performance. In addition, an edge deletion threshold in a topological clustering algorithm plays an important role in adaptively generating well-separated clusters during a self-organizing process. In this paper, we propose an ART-based topological clustering algorithm that integrates parameter estimation methods for both the similarity threshold and the edge deletion threshold. The similarity threshold is estimated using a determinantal point process-based criterion, while the edge deletion threshold is defined based on the age of edges. Experimental results with synthetic and real-world datasets show that the proposed algorithm has superior clustering performance to state-of-the-art clustering algorithms without requiring parameter specifications specific to the datasets. Source code is available at https://github.com/Masuyama-lab/CAE

cs.NE↗

arXiv2026

An Efficient Evolutionary Algorithm for Few-for-Many Optimization

Few-for-many (F4M) optimization, recently introduced as a novel paradigm in multi-objective optimization, aims to find a small set of solutions that effectively handle a large number of conflicting objectives. Unlike traditional many-objective optimization methods, which typically attempt comprehensive coverage of the Pareto front, F4M optimization emphasizes finding a small representative solution set to efficiently address high-dimensional objective spaces. Motivated by the computational complexity and practical relevance of F4M optimization, this paper proposes a new evolutionary algorithm explicitly tailored for efficiently solving F4M optimization problems. Inspired by SMS-EMOA, our proposed approach employs a $(μ+1)$-evolution strategy guided by the objective of F4M optimization. Furthermore, to facilitate rigorous performance assessment, we propose a novel benchmark test suite specifically designed for F4M optimization by leveraging the similarity between the R2 indicator and F4M formulations. Our test suite is highly flexible, allowing any existing multi-objective optimization problem to be transformed into a corresponding F4M instance via scalarization using the weighted Tchebycheff function. Comprehensive experimental evaluations on benchmarks demonstrate the superior performance of our algorithm compared to existing state-of-the-art algorithms, especially on instances involving a large number of objectives. The source code of the proposed algorithm will be released publicly. Source code is available at https://github.com/MOL-SZU/SoM-EMOA.

cs.NE↗

arXiv2025

An Adaptive Resonance Theory-based Topological Clustering Algorithm with a Self-Adjusting Vigilance Parameter

Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT

cs.LG↗

arXiv2025

Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems

Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models through evolutionary processes. However, it is very difficult to choose an appropriate rule representation for each problem. Additionally, some problems benefit from using different representations for different subspaces within the input space. Thus, an adaptive mechanism is needed to choose an appropriate rule representation for each rule in LCSs. This article introduces a flexible rule representation using a four-parameter beta distribution and integrates it into a fuzzy-style LCS. The four-parameter beta distribution can form various function shapes, and this flexibility enables our LCS to automatically select appropriate representations for different subspaces. Our rule representation can represent crisp/fuzzy decision boundaries in various boundary shapes, such as rectangles and bells, by controlling four parameters, compared to the standard representations such as trapezoidal ones. Leveraging this flexibility, our LCS is designed to adapt the appropriate rule representation for each subspace. Moreover, our LCS incorporates a generalization bias favoring crisp rules where feasible, enhancing model interpretability without compromising accuracy. Experimental results on real-world classification tasks show that our LCS achieves significantly superior test accuracy and produces more compact rule sets. Our implementation is available at https://github.com/YNU-NakataLab/Beta4-UCS. An extended abstract related to this work is available at https://doi.org/10.36227/techrxiv.174900805.59801248/v1.

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arXiv2025

A Class Inference Scheme With Dempster-Shafer Theory for Learning Fuzzy-Classifier Systems

The decision-making process significantly influences the predictions of machine learning models. This is especially important in rule-based systems such as Learning Fuzzy-Classifier Systems (LFCSs) where the selection and application of rules directly determine prediction accuracy and reliability. LFCSs combine evolutionary algorithms with supervised learning to optimize fuzzy classification rules, offering enhanced interpretability and robustness. Despite these advantages, research on improving decision-making mechanisms (i.e., class inference schemes) in LFCSs remains limited. Most LFCSs use voting-based or single-winner-based inference schemes. These schemes rely on classification performance on training data and may not perform well on unseen data, risking overfitting. To address these limitations, this article introduces a novel class inference scheme for LFCSs based on the Dempster-Shafer Theory of Evidence (DS theory). The proposed scheme handles uncertainty well. By using the DS theory, the scheme calculates belief masses (i.e., measures of belief) for each specific class and the ``I don't know'' state from each fuzzy rule and infers a class from these belief masses. Unlike the conventional schemes, the proposed scheme also considers the ``I don't know'' state that reflects uncertainty, thereby improving the transparency and reliability of LFCSs. Applied to a variant of LFCS (i.e., Fuzzy-UCS), the proposed scheme demonstrates statistically significant improvements in terms of test macro F1 scores across 30 real-world datasets compared to conventional voting-based and single-winner-based fuzzy inference schemes. It forms smoother decision boundaries, provides reliable confidence measures, and enhances the robustness and generalizability of LFCSs in real-world applications. Our implementation is available at https://github.com/YNU-NakataLab/jUCS.

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arXiv2025

X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning

Function approximation is a critical task in various fields. However, existing neural network approaches struggle with locally complex or discontinuous functions due to their reliance on a single global model covering the entire problem space. We propose X-KAN, a novel method that optimizes multiple local Kolmogorov-Arnold Networks (KANs) through an evolutionary rule-based machine learning framework called XCSF. X-KAN combines KAN's high expressiveness with XCSF's adaptive partitioning capability by implementing local KAN models as rule consequents and defining local regions via rule antecedents. Our experimental results on artificial test functions and real-world datasets demonstrate that X-KAN significantly outperforms conventional methods, including XCSF, Multi-Layer Perceptron, and KAN, in terms of approximation accuracy. Notably, X-KAN effectively handles functions with locally complex or discontinuous structures that are challenging for conventional KAN, using a compact set of rules (average 7.2 $\pm$ 2.3 rules). These results validate the effectiveness of using KAN as a local model in XCSF, which evaluates the rule fitness based on both accuracy and generality. Our X-KAN implementation is available at https://github.com/YNU-NakataLab/X-KAN.

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arXiv2025

Optimal Distribution of Solutions for Crowding Distance on Linear Pareto Fronts of Two-Objective Optimization Problems

Characteristics of an evolutionary multi-objective optimization (EMO) algorithm can be explained using its best solution set. For example, the best solution set for SMS-EMOA is the same as the optimal distribution of solutions for hypervolume maximization. For NSGA-III, if the Pareto front has intersection points with all reference lines, all of those intersection points are the best solution set. For MOEA/D, the best solution set is the set of the optimal solution of each sub-problem. Whereas these EMO algorithms can be analyzed in this manner, the best solution set for the most well-known and frequently-used EMO algorithm NSGA-II has not been discussed in the literature. This is because NSGA-II is not based on any clear criterion to be optimized (e.g., hypervolume maximization, distance minimization to the nearest reference line). As the first step toward the best solution set analysis for NSGA-II, we discuss the optimal distribution of solutions for the crowding distance under the simplest setting: the maximization of the minimum crowding distance on linear Pareto fronts of two-objective optimization problems. That is, we discuss the optimal distribution of solutions on a straight line. Our theoretical analysis shows that the uniformly distributed solutions are not the best solution set. However, it is also shown by computational experiments that the uniformly distributed solutions (except for the duplicated two extreme solutions at each edge of the Pareto front) are obtained from a modified NSGA-II with the ($μ$ + 1) generation update scheme.

cs.NE↗

arXiv2025

When to Truncate the Archive? On the Effect of the Truncation Frequency in Multi-Objective Optimisation

Using an archive to store nondominated solutions found during the search of a multi-objective evolutionary algorithm (MOEA) is a useful practice. However, as nondominated solutions of a multi-objective optimisation problem can be enormous or infinitely many, it is desirable to provide the decision-maker with only a small, representative portion of all the nondominated solutions in the archive, thus entailing a truncation operation. Then, an important issue is when to truncate the archive. This can be done once a new solution generated, a batch of new solutions generated, or even using an unbounded archive to keep all nondominated solutions generated and truncate it later. Intuitively, the last approach may lead to a better result since we have all the information in hand before performing the truncation. In this paper, we study this issue and investigate the effect of the timing of truncating the archive. We apply well-established truncation criteria that are commonly used in the population maintenance procedure of MOEAs (e.g., crowding distance, hypervolume indicator, and decomposition). We show that, interestingly, truncating the archive once a new solution generated tends to be the best, whereas considering an unbounded archive is often the worst. We analyse and discuss this phenomenon. Our results highlight the importance of developing effective subset selection techniques (rather than employing the population maintenance methods in MOEAs) when using a large archive.

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arXiv2025

Large Language Model-Based Benchmarking Experiment Settings for Evolutionary Multi-Objective Optimization

When we manually design an evolutionary optimization algorithm, we implicitly or explicitly assume a set of target optimization problems. In the case of automated algorithm design, target optimization problems are usually explicitly shown. Recently, the use of large language models (LLMs) for the design of evolutionary multi-objective optimization (EMO) algorithms have been examined in some studies. In those studies, target multi-objective problems are not always explicitly shown. It is well known in the EMO community that the performance evaluation results of EMO algorithms depend on not only test problems but also many other factors such as performance indicators, reference point, termination condition, and population size. Thus, it is likely that the designed EMO algorithms by LLMs depends on those factors. In this paper, we try to examine the implicit assumption about the performance comparison of EMO algorithms in LLMs. For this purpose, we ask LLMs to design a benchmarking experiment of EMO algorithms. Our experiments show that LLMs often suggest classical benchmark settings: Performance examination of NSGA-II, MOEA/D and NSGA-III on ZDT, DTLZ and WFG by HV and IGD under the standard parameter specifications.

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arXiv2024

Pareto Front Shape-Agnostic Pareto Set Learning in Multi-Objective Optimization

Pareto set learning (PSL) is an emerging approach for acquiring the complete Pareto set of a multi-objective optimization problem. Existing methods primarily rely on the mapping of preference vectors in the objective space to Pareto optimal solutions in the decision space. However, the sampling of preference vectors theoretically requires prior knowledge of the Pareto front shape to ensure high performance of the PSL methods. Designing a sampling strategy of preference vectors is difficult since the Pareto front shape cannot be known in advance. To make Pareto set learning work effectively in any Pareto front shape, we propose a Pareto front shape-agnostic Pareto Set Learning (GPSL) that does not require the prior information about the Pareto front. The fundamental concept behind GPSL is to treat the learning of the Pareto set as a distribution transformation problem. Specifically, GPSL can transform an arbitrary distribution into the Pareto set distribution. We demonstrate that training a neural network by maximizing hypervolume enables the process of distribution transformation. Our proposed method can handle any shape of the Pareto front and learn the Pareto set without requiring prior knowledge. Experimental results show the high performance of our proposed method on diverse test problems compared with recent Pareto set learning algorithms.

cs.LG↗

arXiv2024

Learning Pareto Set for Multi-Objective Continuous Robot Control

For a control problem with multiple conflicting objectives, there exists a set of Pareto-optimal policies called the Pareto set instead of a single optimal policy. When a multi-objective control problem is continuous and complex, traditional multi-objective reinforcement learning (MORL) algorithms search for many Pareto-optimal deep policies to approximate the Pareto set, which is quite resource-consuming. In this paper, we propose a simple and resource-efficient MORL algorithm that learns a continuous representation of the Pareto set in a high-dimensional policy parameter space using a single hypernet. The learned hypernet can directly generate various well-trained policy networks for different user preferences. We compare our method with two state-of-the-art MORL algorithms on seven multi-objective continuous robot control problems. Experimental results show that our method achieves the best overall performance with the least training parameters. An interesting observation is that the Pareto set is well approximated by a curved line or surface in a high-dimensional parameter space. This observation will provide insight for researchers to design new MORL algorithms.

cs.AI↗

arXiv2024

Evolutionary Computation for the Design and Enrichment of General-Purpose Artificial Intelligence Systems: Survey and Prospects

In Artificial Intelligence, there is an increasing demand for adaptive models capable of dealing with a diverse spectrum of learning tasks, surpassing the limitations of systems devised to cope with a single task. The recent emergence of General-Purpose Artificial Intelligence Systems (GPAIS) poses model configuration and adaptability challenges at far greater complexity scales than the optimal design of traditional Machine Learning models. Evolutionary Computation (EC) has been a useful tool for both the design and optimization of Machine Learning models, endowing them with the capability to configure and/or adapt themselves to the task under consideration. Therefore, their application to GPAIS is a natural choice. This paper aims to analyze the role of EC in the field of GPAIS, exploring the use of EC for their design or enrichment. We also match GPAIS properties to Machine Learning areas in which EC has had a notable contribution, highlighting recent milestones of EC for GPAIS. Furthermore, we discuss the challenges of harnessing the benefits of EC for GPAIS, presenting different strategies to both design and improve GPAIS with EC, covering tangential areas, identifying research niches, and outlining potential research directions for EC and GPAIS.

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arXiv2024

Data-Driven Preference Sampling for Pareto Front Learning

Pareto front learning is a technique that introduces preference vectors in a neural network to approximate the Pareto front. Previous Pareto front learning methods have demonstrated high performance in approximating simple Pareto fronts. These methods often sample preference vectors from a fixed Dirichlet distribution. However, no fixed sampling distribution can be adapted to diverse Pareto fronts. Efficiently sampling preference vectors and accurately estimating the Pareto front is a challenge. To address this challenge, we propose a data-driven preference vector sampling framework for Pareto front learning. We utilize the posterior information of the objective functions to adjust the parameters of the sampling distribution flexibly. In this manner, the proposed method can sample preference vectors from the location of the Pareto front with a high probability. Moreover, we design the distribution of the preference vector as a mixture of Dirichlet distributions to improve the performance of the model in disconnected Pareto fronts. Extensive experiments validate the superiority of the proposed method compared with state-of-the-art algorithms.

cs.LG↗

arXiv2024

Evolutionary Preference Sampling for Pareto Set Learning

Recently, Pareto Set Learning (PSL) has been proposed for learning the entire Pareto set using a neural network. PSL employs preference vectors to scalarize multiple objectives, facilitating the learning of mappings from preference vectors to specific Pareto optimal solutions. Previous PSL methods have shown their effectiveness in solving artificial multi-objective optimization problems (MOPs) with uniform preference vector sampling. The quality of the learned Pareto set is influenced by the sampling strategy of the preference vector, and the sampling of the preference vector needs to be decided based on the Pareto front shape. However, a fixed preference sampling strategy cannot simultaneously adapt the Pareto front of multiple MOPs. To address this limitation, this paper proposes an Evolutionary Preference Sampling (EPS) strategy to efficiently sample preference vectors. Inspired by evolutionary algorithms, we consider preference sampling as an evolutionary process to generate preference vectors for neural network training. We integrate the EPS strategy into five advanced PSL methods. Extensive experiments demonstrate that our proposed method has a faster convergence speed than baseline algorithms on 7 testing problems. Our implementation is available at https://github.com/rG223/EPS.

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arXiv2024

Improving Critical Node Detection Using Neural Network-based Initialization in a Genetic Algorithm

The Critical Node Problem (CNP) is concerned with identifying the critical nodes in a complex network. These nodes play a significant role in maintaining the connectivity of the network, and removing them can negatively impact network performance. CNP has been studied extensively due to its numerous real-world applications. Among the different versions of CNP, CNP-1a has gained the most popularity. The primary objective of CNP-1a is to minimize the pair-wise connectivity in the remaining network after deleting a limited number of nodes from a network. Due to the NP-hard nature of CNP-1a, many heuristic/metaheuristic algorithms have been proposed to solve this problem. However, most existing algorithms start with a random initialization, leading to a high cost of obtaining an optimal solution. To improve the efficiency of solving CNP-1a, a knowledge-guided genetic algorithm named K2GA has been proposed. Unlike the standard genetic algorithm framework, K2GA has two main components: a pretrained neural network to obtain prior knowledge on possible critical nodes, and a hybrid genetic algorithm with local search for finding an optimal set of critical nodes based on the knowledge given by the trained neural network. The local search process utilizes a cut node-based greedy strategy. The effectiveness of the proposed knowledgeguided genetic algorithm is verified by experiments on 26 realworld instances of complex networks. Experimental results show that K2GA outperforms the state-of-the-art algorithms regarding the best, median, and average objective values, and improves the best upper bounds on the best objective values for eight realworld instances.

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arXiv2023

Privacy-preserving Continual Federated Clustering via Adaptive Resonance Theory

With the increasing importance of data privacy protection, various privacy-preserving machine learning methods have been proposed. In the clustering domain, various algorithms with a federated learning framework (i.e., federated clustering) have been actively studied and showed high clustering performance while preserving data privacy. However, most of the base clusterers (i.e., clustering algorithms) used in existing federated clustering algorithms need to specify the number of clusters in advance. These algorithms, therefore, are unable to deal with data whose distributions are unknown or continually changing. To tackle this problem, this paper proposes a privacy-preserving continual federated clustering algorithm. In the proposed algorithm, an adaptive resonance theory-based clustering algorithm capable of continual learning is used as a base clusterer. Therefore, the proposed algorithm inherits the ability of continual learning. Experimental results with synthetic and real-world datasets show that the proposed algorithm has superior clustering performance to state-of-the-art federated clustering algorithms while realizing data privacy protection and continual learning ability. The source code is available at \url{https://github.com/Masuyama-lab/FCAC}.

cs.LG↗

arXiv2022

Effects of Archive Size on Computation Time and Solution Quality for Multi-Objective Optimization

An unbounded external archive has been used to store all nondominated solutions found by an evolutionary multi-objective optimization algorithm in some studies. It has been shown that a selected solution subset from the stored solutions is often better than the final population. However, the use of the unbounded archive is not always realistic. When the number of examined solutions is huge, we must pre-specify the archive size. In this study, we examine the effects of the archive size on three aspects: (i) the quality of the selected final solution set, (ii) the total computation time for the archive maintenance and the final solution set selection, and (iii) the required memory size. Unsurprisingly, the increase of the archive size improves the final solution set quality. Interestingly, the total computation time of a medium-size archive is much larger than that of a small-size archive and a huge-size archive (e.g., an unbounded archive). To decrease the computation time, we examine two ideas: periodical archive update and archiving only in later generations. Compared with updating the archive at every generation, the first idea can obtain almost the same final solution set quality using a much shorter computation time at the cost of a slight increase of the memory size. The second idea drastically decreases the computation time at the cost of a slight deterioration of the final solution set quality. Based on our experimental results, some suggestions are given about how to appropriately choose an archiving strategy and an archive size.

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