Solving land-use allocation problems can help us to deal with some of the most urgent global environmental issues. Since these problems are NP-hard, effective optimizers are needed to handle them. The knowledge about variable dependencies allows for proposing such tools. However, in this work, we consider a real-world multi-objective problem for which standard variable dependency discovery techniques are inapplicable. Therefore, using linkage-based variation operators is unreachable. To address this issue, we propose a definition of problem-dedicated variable dependency. On this base, we propose obtaining masks of dependent variables. Using them, we construct three novel crossover operators. The results concerning real-world test cases show that introducing our propositions into two well-known optimizers (NSGA-II, MOEA/D) dedicated to multi-objective optimization significantly improves their effectiveness.

ACCEPTED MARCH, 2025 1 Real-Time Shape Estimation of Tensegrity Structures Using Strut Inclination Angles Tufail Ahmad Bhat 1, Y uhei Y oshimitsu 1, Kazuki Wada 1, Shuhei Ikemoto 1 Abstract --T ensegrity structures are becoming widely used in robotics, such as continuously bending soft manipulators and mobile robots to explore unknown and uneven environments dynamically. Estimating their shape, which is the foundation of their state, is essential for establishing control. However, on-board sensor-based shape estimation remains difficult despite its importance, because tensegrity structures lack well-defined joint structures, which makes it challenging to use conventional angle sensors such as potentiometers or encoders for shape estimation. T o our knowledge, no existing work has successfully achieved shape estimation using only onboard sensors such as Inertial Measurement Units (IMUs). This study addresses this issue by proposing a novel approach that uses energy minimization to estimate the shape. We validated our method through experiments on a simple Class 1 tensegrity structure, and the results show that the proposed algorithm can estimate the real-time shape of the structure using onboard sensors, even in the presence of external disturbances. I NTRODUCTION T HE concept of "tensegrity" is coined by the iconoclastic architect R. Buckminster Fuller. It describes structures that achieve stability through a balance of forces: specific components, known as "cables" are always in tension, while others, known as "struts" are constantly under compression [1]. In tensegrity, the cables of the structure are always under continuous tension, a condition known as "prestress".

Gray-box optimization proposes effective and efficient optimizers of general use. To this end, it leverages information about variable dependencies and the subfunction-based problem representation. These approaches were already shown effective by enabling \textit{tunnelling} between local optima even if these moves require the modification of many dependent variables. Tunnelling is useful in solving the maximum satisfiability problem (MaxSat), which can be reformulated to Max3Sat. Since many real-world problems can be brought to solving the MaxSat/Max3Sat instances, it is important to solve them effectively and efficiently. Therefore, we focus on Max3Sat instances for which tunnelling fails to introduce improving moves between locally optimal high-quality solutions and the region of globally optimal solutions. We analyze the features of such instances on the ground of phase transitions. Based on these observations, we propose manipulating clause-satisfiability characteristics that allow connecting high-quality solutions distant in the solution space. We utilize multi-satisfiability characteristics in the optimizer built from typical gray-box mechanisms. The experimental study shows that the proposed optimizer can solve those Max3Sat instances that are out of the grasp of state-of-the-art gray-box optimizers. At the same time, it remains effective for instances that have already been successfully solved by gray-box.

Community detection, the unsupervised task of clustering nodes of a graph, finds applications across various fields. The common approaches for community detection involve optimizing an objective function to partition the nodes into communities at a single scale of granularity. However, the single-scale approaches often fall short of producing partitions that are robust and at a suitable scale. The existing algorithm, PyGenStability, returns multiple robust partitions for a network by optimizing the multi-scale Markov stability function. However, in cases where the suitable scale is not known or assumed by the user, there is no principled method to select a single robust partition at a suitable scale from the multiple partitions that PyGenStability produces. Our proposed method combines the Markov stability framework with a pre-trained machine learning model for scale selection to obtain one robust partition at a scale that is learned based on the graph structure. This automatic scale selection involves using a gradient boosting model pre-trained on hand-crafted and embedding-based network features from a labeled dataset of 10k benchmark networks. This model was trained to predicts the scale value that maximizes the similarity of the output partition to the planted partition of the benchmark network. Combining our scale selection algorithm with the PyGenStability algorithm results in PyGenStabilityOne (PO): a hyperparameter-free multi-scale community detection algorithm that returns one robust partition at a suitable scale without the need for any assumptions, input, or tweaking from the user. We compare the performance of PO against 29 algorithms and show that it outperforms 25 other algorithms by statistically meaningful margins. Our results facilitate choosing between community detection algorithms, among which PO stands out as the accurate, robust, and hyperparameter-free method.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, with their performance heavily dependent on the quality of input prompts. While prompt engineering has proven effective, it typically relies on manual adjustments, making it time-consuming and potentially suboptimal. This paper introduces GAAPO (Genetic Algorithm Applied to Prompt Optimization), a novel hybrid optimization framework that leverages genetic algorithm principles to evolve prompts through successive generations. Unlike traditional genetic approaches that rely solely on mutation and crossover operations, GAAPO integrates multiple specialized prompt generation strategies within its evolutionary framework. Through extensive experimentation on diverse datasets including ETHOS, MMLU-Pro, and GPQA, our analysis reveals several important point for the future development of automatic prompt optimization methods: importance of the tradeoff between the population size and the number of generations, effect of selection methods on stability results, capacity of different LLMs and especially reasoning models to be able to automatically generate prompts from similar queries... Furthermore, we provide insights into the relative effectiveness of different prompt generation strategies and their evolution across optimization phases. These findings contribute to both the theoretical understanding of prompt optimization and practical applications in improving LLM performance.

We propose a robust and scalable framework for variational Bayes (VB) that effectively handles outliers and contamination of arbitrary nature in large datasets. Our approach divides the dataset into disjoint subsets, computes the posterior for each subset, and applies VB approximation independently to these posteriors. The resulting variational posteriors with respect to the subsets are then aggregated using the geometric median of probability measures, computed with respect to the Wasserstein distance. This novel aggregation method yields the Variational Median Posterior (VM-Posterior) distribution. We rigorously demonstrate that the VM-Posterior preserves contraction properties akin to those of the true posterior, while accounting for approximation errors or the variational gap inherent in VB methods. We also provide provable robustness guarantee of the VM-Posterior. Furthermore, we establish a variational Bernstein-von Mises theorem for both multivariate Gaussian distributions with general covariance structures and the mean-field variational family. To facilitate practical implementation, we adapt existing algorithms for computing the VM-Posterior and evaluate its performance through extensive numerical experiments. The results highlight its robustness and scalability, making it a reliable tool for Bayesian inference in the presence of complex, contaminated datasets.

Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure to extract the distinct aspects called archetypes in observations with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data with wide applications throughout the sciences. However, AA also faces challenges, particularly as the associated optimization problem is non-convex. This survey provides researchers and data mining practitioners an overview of methodologies and opportunities that AA has to offer surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data using AA and limitations. The survey concludes by explaining important future research directions concerning AA.

In many optimization domains, there are multiple different solvers that contribute to the overall state-of-the-art, each performing better on some, and worse on other types of problem instances. Meta-algorithmic approaches, such as instance-based algorithm selection, configuration and scheduling, aim to close this gap by extracting the most performance possible from a set of (configurable) optimizers. In this context, the best performing individual algorithms are often hand-crafted hybrid heuristics which perform many restarts of fast local optimization approaches. However, data-driven techniques to create optimized restart schedules have not yet been extensively studied. Here, we present a simple scheduling approach that iteratively selects the algorithm performing best on the distribution of unsolved training problems at time of selection, resulting in a problem-independent solver schedule. We demonstrate our approach using well-known optimizers from numerical black-box optimization on the BBOB testbed, bridging much of the gap between single and virtual best solver from the original portfolio across various evaluation protocols. Our greedy restart schedule presents a powerful baseline for more complex dynamic algorithm selection models.

Risk-averse reinforcement learning (RARL) is critical for decision-making under uncertainty, which is especially valuable in high-stake applications. However, most existing works focus on risk measures, e.g., conditional value-at-risk (CVaR), while measures of variability remain underexplored. In this paper, we comprehensively study nine common measures of variability, namely Variance, Gini Deviation, Mean Deviation, Mean-Median Deviation, Standard Deviation, Inter-Quantile Range, CVaR Deviation, Semi_Variance, and Semi_Standard Deviation. Among them, four metrics have not been previously studied in RARL. We derive policy gradient formulas for these unstudied metrics, improve gradient estimation for Gini Deviation, analyze their gradient properties, and incorporate them with the REINFORCE and PPO frameworks to penalize the dispersion of returns. Our empirical study reveals that variance-based metrics lead to unstable policy updates. In contrast, CVaR Deviation and Gini Deviation show consistent performance across different randomness and evaluation domains, achieving high returns while effectively learning risk-averse policies. Mean Deviation and Semi_Standard Deviation are also competitive across different scenarios. This work provides a comprehensive overview of variability measures in RARL, offering practical insights for risk-aware decision-making and guiding future research on risk metrics and RARL algorithms.

Multi-objective preference alignment in language models often encounters a challenging trade-off: optimizing for one human preference (e.g., helpfulness) frequently compromises others (e.g., harmlessness) due to the inherent conflicts between competing objectives. While prior work mainly focuses on algorithmic solutions, we explore a novel data-driven approach to uncover the types of data that can effectively mitigate these conflicts. Specifically, we propose the concept of Reward Consistency (RC), which identifies samples that align with multiple preference objectives, thereby reducing conflicts during training. Through gradient-based analysis, we demonstrate that RC-compliant samples inherently constrain performance degradation during multi-objective optimization. Building on these insights, we further develop Reward Consistency Sampling, a framework that automatically constructs preference datasets that effectively mitigate conflicts during multi-objective alignment. Our generated data achieves an average improvement of 13.37% in both the harmless rate and helpfulness win rate when optimizing harmlessness and helpfulness, and can consistently resolve conflicts in varying multi-objective scenarios.