Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS research.

A core challenge of Monte Carlo Tree Search (MCTS) is its sample efficiency, which can be improved by grouping state-action pairs and using their aggregate statistics instead of single-node statistics. On the Go Abstractions in Upper Confidence bounds applied to Trees (OGA-UCT) is the state-of-the-art MCTS abstraction algorithm for deterministic environments that builds its abstraction using the Abstractions of State-Action Pairs (ASAP) framework, which aims to detect states and state-action pairs with the same value under optimal play by analysing the search graph. ASAP, however, requires two state-action pairs to have the same immediate reward, which is a rigid condition that limits the number of abstractions that can be found and thereby the sample efficiency. In this paper, we break with the paradigm of grouping value-equivalent states or state-action pairs and instead group states and state-action pairs with possibly different values as long as the difference between their values can be inferred. We call this abstraction framework Known Value Difference Abstractions (KVDA), which infers the value differences by analysis of the immediate rewards and modifies OGA-UCT to use this framework instead. The modification is called KVDA-UCT, which detects significantly more abstractions than OGA-UCT, introduces no additional parameter, and outperforms OGA-UCT on a variety of deterministic environments and parameter settings.

Frequent natural disasters cause significant losses to human society, and timely, efficient collection of post-disaster environmental information is the foundation for effective rescue operations. Due to the extreme complexity of post-disaster environments, existing sensing technologies such as mobile crowdsensing suffer from weak environmental adaptability, insufficient professional sensing capabilities, and poor practicality of sensing solutions. Therefore, this paper explores a heterogeneous multi-agent online collaborative scheduling algorithm, HoCs-MPQ, to achieve efficient collection of post-disaster environmental information. HoCs-MPQ models collaboration and conflict relationships among multiple elements through weighted undirected graph construction, and iteratively solves the maximum weight independent set based on multi-priority queues, ultimately achieving collaborative sensing scheduling of time-dependent UA Vs, vehicles, and workers. Specifically, (1) HoCs-MPQ constructs weighted undirected graph nodes based on collaborative relationships among multiple elements and quantifies their weights, then models the weighted undirected graph based on conflict relationships between nodes; (2) HoCs-MPQ solves the maximum weight independent set based on iterated local search, and accelerates the solution process using multi-priority queues. Finally, we conducted detailed experiments based on extensive real-world and simulated data. The experiments show that, compared to baseline methods (e.g., HoCs-GREEDY, HoCs-K-WTA, HoCs-MADL, and HoCs-MARL), HoCs-MPQ improves task completion rates by an average of 54.13%, 23.82%, 14.12%, and 12.89% respectively, with computation time for single online autonomous scheduling decisions not exceeding 3 seconds.

Machine learning models increasingly map biological sequence-fitness landscapes to predict mutational effects. Effective evaluation of these models requires benchmarks curated from empirical data. Despite their impressive scales, existing benchmarks lack topographical information regarding the underlying fitness landscapes, which hampers interpretation and comparison of model performance beyond averaged scores. Here, we introduce GraphFLA, a Python framework that constructs and analyzes fitness landscapes from mutagensis data in diverse modalities (e.g., DNA, RNA, protein, and beyond) with up to millions of mutants. GraphFLA calculates 20 biologically relevant features that characterize 4 fundamental aspects of landscape topography. By applying GraphFLA to over 5,300 landscapes from ProteinGym, RNAGym, and CIS-BP, we demonstrate its utility in interpreting and comparing the performance of dozens of fitness prediction models, highlighting factors influencing model accuracy and respective advantages of different models. In addition, we release 155 combinatorially complete empirical fitness landscapes, encompassing over 2.2 million sequences across various modalities. All the codes and datasets are available at https://github.com/COLA-Laboratory/GraphFLA.

Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable when continuous, large-scale data are involved. Naively binarizing continuous features sacrifices global optimality and often yields needlessly deep trees. We recast the optimal regression-tree training as a two-stage optimization problem and propose Reduced-Space Optimal Regression Trees (RS-ORT) - a specialized branch-and-bound (BB) algorithm that branches exclusively on tree-structural variables. This design guarantees the algorithm's convergence and its independence from the number of training samples. Leveraging the model's structure, we introduce several bound tightening techniques - closed-form leaf prediction, empirical threshold discretization, and exact depth-1 subtree parsing - that combine with decomposable upper and lower bounding strategies to accelerate the training. The BB node-wise decomposition enables trivial parallel execution, further alleviating the computational intractability even for million-size datasets. Based on the empirical studies on several regression benchmarks containing both binary and continuous features, RS-ORT also delivers superior training and testing performance than state-of-the-art methods. Notably, on datasets with up to 2,000,000 samples with continuous features, RS-ORT can obtain guaranteed training performance with a simpler tree structure and a better generalization ability in four hours.

Make-on-demand combinatorial synthesis libraries (CSLs) like Enamine REAL have significantly enabled drug discovery efforts. However, their large size presents a challenge for virtual screening, where the goal is to identify the top compounds in a library according to a computational objective (e.g., optimizing docking score) subject to computational constraints under a limited computational budget. For current library sizes -- numbering in the tens of billions of compounds -- and scoring functions of interest, a routine virtual screening campaign may be limited to scoring fewer than 0.1% of the available compounds, leaving potentially many high scoring compounds undiscovered. Furthermore, as constraints (and sometimes objectives) change during the course of a virtual screening campaign, existing virtual screening algorithms typically offer little room for amortization. We propose the approximate-but-exhaustive search protocol for CSLs, or APEX. APEX utilizes a neural network surrogate that exploits the structure of CSLs in the prediction of objectives and constraints to make full enumeration on a consumer GPU possible in under a minute, allowing for exact retrieval of approximate top-$k$ sets. To demonstrate APEX's capabilities, we develop a benchmark CSL comprised of more than 10 million compounds, all of which have been annotated with their docking scores on five medically relevant targets along with physicohemical properties measured with RDKit such that, for any objective and set of constraints, the ground truth top-$k$ compounds can be identified and compared against the retrievals from any virtual screening algorithm. We show APEX's consistently strong performance both in retrieval accuracy and runtime compared to alternative methods.

Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary classification framework. Our proposed method EDC finds analytical functions of manageable size that specify the location and shape of the decision boundary. In extensive experiments on artificial and real-life data, we demonstrate how EDC is able to discover both the structure of the target equation as well as the value of its parameters, outperforming the current state-of-the-art ED-based classification methods in binary classification and achieving performance comparable to the state of the art in binary classification. We suggest a grammar of modest complexity that appears to work well on the tested datasets but argue that the exact grammar -- and thus the complexity of the models -- is configurable, and especially domain-specific expressions can be included in the pattern language, where that is required. The presented grammar consists of a series of summands (additive terms) that include linear, quadratic and exponential terms, as well as products of two features (producing hyperbolic curves ideal for capturing XOR-like dependencies). The experiments demonstrate that this grammar allows fairly flexible decision boundaries while not so rich to cause overfitting.

One weakness of Monte Carlo Tree Search (MCTS) is its sample efficiency which can be addressed by building and using state and/or action abstractions in parallel to the tree search such that information can be shared among nodes of the same layer. The primary usage of abstractions for MCTS is to enhance the Upper Confidence Bound (UCB) value during the tree policy by aggregating visits and returns of an abstract node. However, this direct usage of abstractions does not take the case into account where multiple actions with the same parent might be in the same abstract node, as these would then all have the same UCB value, thus requiring a tiebreak rule. In state-of-the-art abstraction algorithms such as pruned On the Go Abstractions (pruned OGA), this case has not been noticed, and a random tiebreak rule was implicitly chosen. In this paper, we propose and empirically evaluate several alternative intra-abstraction policies, several of which outperform the random policy across a majority of environments and parameter settings.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

Recent advances have demonstrated the effectiveness of graph-based learning on relational databases (RDBs) for predictive tasks. Such approaches require transforming RDBs into graphs, a process we refer to as RDB-to-graph modeling, where rows of tables are represented as nodes and foreign-key relationships as edges. Yet, effective modeling of RDBs into graphs remains challenging. Specifically, there exist numerous ways to model RDBs into graphs, and performance on predictive tasks varies significantly depending on the chosen graph model of RDBs. In our analysis, we find that the best-performing graph model can yield up to a 10% higher performance compared to the common heuristic rule for graph modeling, which remains non-trivial to identify. To foster research on intelligent RDB-to-graph modeling, we introduce RDB2G-Bench, the first benchmark framework for evaluating such methods. We construct extensive datasets covering 5 real-world RDBs and 12 predictive tasks, resulting in around 50k graph model-performance pairs for efficient and reproducible evaluations. Thanks to our precomputed datasets, we were able to benchmark 10 automatic RDB-to-graph modeling methods on the 12 tasks about 380x faster than on-the-fly evaluation, which requires repeated GNN training. Our analysis of the datasets and benchmark results reveals key structural patterns affecting graph model effectiveness, along with practical implications for effective graph modeling. Our datasets and code are available at https://github.com/chlehdwon/RDB2G-Bench.