Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-processing to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

In the last few decades, Machine Learning (ML) has achieved significant success across domains ranging from healthcare, sustainability, and the social sciences, to criminal justice and finance. But its deployment in increasingly sophisticated, critical, and sensitive areas affecting individuals, the groups they belong to, and society as a whole raises critical concerns around fairness, transparency, robustness, and privacy, among others. As the complexity and scale of ML systems and of the settings in which they are deployed grow, so does the need for responsible ML methods that address these challenges while providing guaranteed performance in deployment. Mixed-integer optimization (MIO) offers a powerful framework for embedding responsible ML considerations directly into the learning process while maintaining performance. For example, it enables learning of inherently transparent models that can conveniently incorporate fairness or other domain specific constraints. This tutorial paper provides an accessible and comprehensive introduction to this topic discussing both theoretical and practical aspects. It outlines some of the core principles of responsible ML, their importance in applications, and the practical utility of MIO for building ML models that align with these principles. Through examples and mathematical formulations, it illustrates practical strategies and available tools for efficiently solving MIO problems for responsible ML. It concludes with a discussion on current limitations and open research questions, providing suggestions for future work.

Large Language Models (LLMs) have unveiled remarkable capabilities in understanding and generating both natural language and code, but LLM reasoning is prone to hallucination and struggle with complex, novel scenarios, often getting stuck on partial or incorrect solutions. However, the inherent ability of Evolutionary Algorithms (EAs) to explore extensive and complex search spaces makes them particularly effective in scenarios where traditional optimization methodologies may falter. However, EAs explore a vast search space when applied to complex problems. To address the computational bottleneck of evaluating large populations, particularly crucial for complex evolutionary tasks, we introduce a highly efficient evaluation framework. This implementation maintains compatibility with existing primitive definitions, ensuring the generation of valid individuals. Using LLMs, we propose an enhanced evolutionary search strategy that enables a more focused exploration of expansive solution spaces. LLMs facilitate the generation of superior candidate solutions, as evidenced by empirical results demonstrating their efficacy in producing improved outcomes.

The layout of analog ICs requires making complex trade-offs, while addressing device physics and variability of the circuits. This makes full automation with learning-based solutions hard to achieve. However, reinforcement learning (RL) has recently reached significant results, particularly in solving the floorplanning problem. This paper presents a hybrid method that combines RL with a beam (BS) strategy. The BS algorithm enhances the agent's inference process, allowing for the generation of flexible floorplans by accomodating various objective weightings, and addressing congestion without without the need for policy retraining or fine-tuning. Moreover, the RL agent's generalization ability stays intact, along with its efficient handling of circuit features and constraints. Experimental results show approx. 5-85% improvement in area, dead space and half-perimeter wire length compared to a standard RL application, along with higher rewards for the agent. Moreover, performance and efficiency align closely with those of existing state-of-the-art techniques.

While Artificial intelligence (AI), including Generative AI, are effective at generating high-quality traffic data and optimization solutions in intelligent transportation systems (ITSs), these techniques often demand significant training time and computational resources, especially in large-scale and complex scenarios. To address this, we introduce a novel and efficient algorithm for solving the maximum weighted independent set (MWIS) problem, which can be used to model many ITSs applications, such as traffic signal control and vehicle routing. Given the NP-hard nature of the MWIS problem, our proposed algorithm, DynLS, incorporates three key innovations to solve it effectively. First, it uses a scores-based adaptive vertex perturbation (SAVP) technique to accelerate convergence, particularly in sparse graphs. Second, it includes a region location mechanism (RLM) to help escape local optima by dynamically adjusting the search space. Finally, it employs a novel variable neighborhood descent strategy, ComLS, which combines vertex exchange strategies with a reward mechanism to guide the search toward high-quality solutions. Our experimental results demonstrate DynLS's superior performance, consistently delivering high-quality solutions within 1000 seconds. DynLS outperformed five leading algorithms across 360 test instances, achieving the best solution for 350 instances and surpassing the second-best algorithm, Cyclic-Fast, by 177 instances. Moreover, DynLS matched Cyclic-Fast's convergence speed, highlighting its efficiency and practicality. This research represents a significant advancement in heuristic algorithms for the MWIS problem, offering a promising approach to aid AI techniques in optimizing intelligent transportation systems.

This paper presents the first experimental evaluation of four previously untested modifications of Unbounded Best-First Minimax algorithm. This algorithm explores the game tree by iteratively expanding the most promising sequences of actions based on the current partial game tree. We first evaluate the use of transposition tables, which convert the game tree into a directed acyclic graph by merging duplicate states. Second, we compare the original algorithm by Korf & Chickering with the variant proposed by Cohen-Solal, which differs in its backpropagation strategy: instead of stopping when a stable value is encountered, it updates values up to the root. This change slightly improves performance when value ties or transposition tables are involved. Third, we assess replacing the exact terminal evaluation function with the learned heuristic function. While beneficial when exact evaluations are costly, this modification reduces performance in inexpensive settings. Finally, we examine the impact of the completion technique that prioritizes resolved winning states and avoids resolved losing states. This technique also improves performance. Overall, our findings highlight how targeted modifications can enhance the efficiency of Unbounded Best-First Minimax.

Machine Ethics decisions should consider the implications of uncertainty over decisions. Decisions should be made over sequences of actions to reach preferable outcomes long term. The evaluation of outcomes, however, may invoke one or more moral theories, which might have conflicting judgements. Each theory will require differing representations of the ethical situation. For example, Utilitarianism measures numerical values, Deontology analyses duties, and Virtue Ethics emphasises moral character. While balancing potentially conflicting moral considerations, decisions may need to be made, for example, to achieve morally neutral goals with minimal costs. In this paper, we formalise the problem as a Multi-Moral Markov Decision Process and a Multi-Moral Stochastic Shortest Path Problem. We develop a heuristic algorithm based on Multi-Objective AO*, utilising Sven-Ove Hansson's Hypothetical Retrospection procedure for ethical reasoning under uncertainty. Our approach is validated by a case study from Machine Ethics literature: the problem of whether to steal insulin for someone who needs it.

Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this work, we present an updated version of SRBench. Our benchmark expands the previous one by nearly doubling the number of evaluated methods, refining evaluation metrics, and using improved visualizations of the results to understand the performances. Additionally, we analyze trade-offs between model complexity, accuracy, and energy consumption. Our results show that no single algorithm dominates across all datasets. We propose a call for action from SR community in maintaining and evolving SRBench as a living benchmark that reflects the state-of-the-art in symbolic regression, by standardizing hyperparameter tuning, execution constraints, and computational resource allocation. We also propose deprecation criteria to maintain the benchmark's relevance and discuss best practices for improving SR algorithms, such as adaptive hyperparameter tuning and energy-efficient implementations.

This study proposes a novel artificial protozoa optimizer (APO) that is inspired by protozoa in nature. The APO mimics the survival mechanisms of protozoa by simulating their foraging, dormancy, and reproductive behaviors. The APO was mathematically modeled and implemented to perform the optimization processes of metaheuristic algorithms. The performance of the APO was verified via experimental simulations and compared with 32 state-of-the-art algorithms. Wilcoxon signed-rank test was performed for pairwise comparisons of the proposed APO with the state-of-the-art algorithms, and Friedman test was used for multiple comparisons. First, the APO was tested using 12 functions of the 2022 IEEE Congress on Evolutionary Computation benchmark. Considering practicality, the proposed APO was used to solve five popular engineering design problems in a continuous space with constraints. Moreover, the APO was applied to solve a multilevel image segmentation task in a discrete space with constraints. The experiments confirmed that the APO could provide highly competitive results for optimization problems. The source codes of Artificial Protozoa Optimizer are publicly available at https://seyedalimirjalili.com/projects and https://ww2.mathworks.cn/matlabcentral/fileexchange/162656-artificial-protozoa-optimizer.

Multimodal deep learning harnesses diverse imaging modalities, such as MRI sequences, to enhance diagnostic accuracy in medical imaging. A key challenge is determining the optimal timing for integrating these modalities-specifically, identifying the network layers where fusion modules should be inserted. Current approaches often rely on manual tuning or exhaustive search, which are computationally expensive without any guarantee of converging to optimal results. We propose a sequential forward search algorithm that incrementally activates and evaluates candidate fusion modules at different layers of a multimodal network. At each step, the algorithm retrains from previously learned weights and compares validation loss to identify the best-performing configuration. This process systematically reduces the search space, enabling efficient identification of the optimal fusion timing without exhaustively testing all possible module placements. The approach is validated on two multimodal MRI datasets, each addressing different classification tasks. Our algorithm consistently identified configurations that outperformed unimodal baselines, late fusion, and a brute-force ensemble of all potential fusion placements. These architectures demonstrated superior accuracy, F-score, and specificity while maintaining competitive or improved AUC values. Furthermore, the sequential nature of the search significantly reduced computational overhead, making the optimization process more practical. By systematically determining the optimal timing to fuse imaging modalities, our method advances multimodal deep learning for medical imaging. It provides an efficient and robust framework for fusion optimization, paving the way for improved clinical decision-making and more adaptable, scalable architectures in medical AI applications.