Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks

Existing neural solvers for vehicle routing problems (VRPs) are typically trained either in a one-off manner on a fixed set of pre-defined tasks or in a lifelong manner on several tasks arriving sequentially, assuming sufficient training on each task. Both settings overlook a common real-world property: problem patterns may drift continually over time, yielding massive tasks sequentially arising while offering only limited training resources per task. In this paper, we study a novel lifelong learning paradigm for neural VRP solvers under continually drifting tasks over learning time steps, where sufficient training for any given task at any time is not available. We propose Dual Replay with Experience Enhancement (DREE), a general framework to improve learning efficiency and mitigate catastrophic forgetting under such drift. Extensive experiments show that, under such continual drift, DREE effectively learns new tasks, preserves prior knowledge, improves generalization to unseen tasks, and can be applied to diverse existing neural solvers.

HEATACO: Heatmap-Guided Ant Colony Decoding for Large-Scale Travelling Salesman Problems

Heatmap-based non-autoregressive solvers for large-scale Travelling Salesman Problems output dense edge-probability scores, yet final performance largely hinges on the decoder that must satisfy degree-2 constraints and form a single Hamiltonian tour. Greedy commitment can cascade into irreparable mistakes at large $N$, whereas MCTS-guided local search is accurate but compute-heavy and highly engineered. We instead treat the heatmap as a soft edge prior and cast decoding as probabilistic tour construction under feasibility constraints, where the key is to correct local mis-rankings via inexpensive global coordination. Based on this view, we introduce HeatACO, a plug-and-play Max-Min Ant System decoder whose transition policy is softly biased by the heatmap while pheromone updates provide lightweight, instance-specific feedback to resolve global conflicts; optional 2-opt/3-opt post-processing further improves tour quality. On TSP500/1K/10K, using heatmaps produced by four pretrained predictors, HeatACO+2opt achieves gaps down to 0.11%/0.23%/1.15% with seconds-to-minutes CPU decoding for fixed heatmaps, offering a better quality--time trade-off than greedy decoding and published MCTS-based decoders. Finally, we find the gains track heatmap reliability: under distribution shift, miscalibration and confidence collapse bound decoding improvements, suggesting heatmap generalisation is a primary lever for further progress.

Investigation of the Generalisation Ability of Genetic Programming-evolved Scheduling Rules in Dynamic Flexible Job Shop Scheduling

Dynamic Flexible Job Shop Scheduling (DFJSS) is a complex combinatorial optimisation problem that requires simultaneous machine assignment and operation sequencing decisions in dynamic production environments. Genetic Programming (GP) has been widely applied to automatically evolve scheduling rules for DFJSS. However, existing studies typically train and test GP-evolved rules on DFJSS instances of the same type, which differ only by random seeds rather than by structural characteristics, leaving their cross-type generalisation ability largely unexplored. To address this gap, this paper systematically investigates the generalisation ability of GP-evolved scheduling rules under diverse DFJSS conditions. A series of experiments are conducted across multiple dimensions, including problem scale (i.e., the number of machines and jobs), key job shop parameters (e.g., utilisation level), and data distributions, to analyse how these factors influence GP performance on unseen instance types. The results show that good generalisation occurs when the training instances contain more jobs than the test instances while keeping the number of machines fixed, and when both training and test instances have similar scales or job shop parameters. Further analysis reveals that the number and distribution of decision points in DFJSS instances play a crucial role in explaining these performance differences. Similar decision point distributions lead to better generalisation, whereas significant discrepancies result in a marked degradation of performance. Overall, this study provides new insights into the generalisation ability of GP in DFJSS and highlights the necessity of evolving more generalisable GP rules capable of handling heterogeneous DFJSS instances effectively.

Scalable Knee-Point Guided Activity Group Selection in Multi-Tree Genetic Programming for Dynamic Multi-Mode Project Scheduling

The dynamic multi-mode resource-constrained project scheduling problem is a challenging scheduling problem that requires making decisions on both the execution order of activities and their corresponding execution modes. Genetic programming has been widely applied as a hyper-heuristic to evolve priority rules that guide the selection of activity-mode pairs from the current eligible set. Recently, an activity group selection strategy has been proposed to select a subset of activities rather than a single activity at each decision point, allowing for more effective scheduling by considering the interdependence between activities. Although effective in small-scale instances, this strategy suffers from scalability issues when applied to larger problems. In this work, we enhance the scalability of the group selection strategy by introducing a knee-point-based selection mechanism to identify a promising subset of activities before evaluating their combinations. An activity ordering rule is first used to rank all eligible activity-mode pairs, followed by a knee point selection to find the promising pairs. Then, a group selection rule selects the best activity combination. We develop a multi-tree GP framework to evolve both types of rules simultaneously. Experimental results demonstrate that our approach scales well to large instances and outperforms GP with sequential decision-making in most scenarios.

Overlooked Safety Vulnerability in LLMs: Malicious Intelligent Optimization Algorithm Request and its Jailbreak

The widespread deployment of large language models (LLMs) has raised growing concerns about their misuse risks and associated safety issues. While prior studies have examined the safety of LLMs in general usage, code generation, and agent-based applications, their vulnerabilities in automated algorithm design remain underexplored. To fill this gap, this study investigates this overlooked safety vulnerability, with a particular focus on intelligent optimization algorithm design, given its prevalent use in complex decision-making scenarios. We introduce MalOptBench, a benchmark consisting of 60 malicious optimization algorithm requests, and propose MOBjailbreak, a jailbreak method tailored for this scenario. Through extensive evaluation of 13 mainstream LLMs including the latest GPT-5 and DeepSeek-V3.1, we reveal that most models remain highly susceptible to such attacks, with an average attack success rate of 83.59% and an average harmfulness score of 4.28 out of 5 on original harmful prompts, and near-complete failure under MOBjailbreak. Furthermore, we assess state-of-the-art plug-and-play defenses that can be applied to closed-source models, and find that they are only marginally effective against MOBjailbreak and prone to exaggerated safety behaviors. These findings highlight the urgent need for stronger alignment techniques to safeguard LLMs against misuse in algorithm design.

GAMA: A Neural Neighborhood Search Method with Graph-aware Multi-modal Attention for Vehicle Routing Problem

Recent advances in neural neighborhood search methods have shown potential in tackling Vehicle Routing Problems (VRPs). However, most existing approaches rely on simplistic state representations and fuse heterogeneous information via naive concatenation, limiting their ability to capture rich structural and semantic context. To address these limitations, we propose GAMA, a neural neighborhood search method with Graph-aware Multi-modal Attention model in VRP. GAMA encodes the problem instance and its evolving solution as distinct modalities using graph neural networks, and models their intra- and inter-modal interactions through stacked self- and cross-attention layers. A gated fusion mechanism further integrates the multi-modal representations into a structured state, enabling the policy to make informed and generalizable operator selection decisions. Extensive experiments conducted across various synthetic and benchmark instances demonstrate that the proposed algorithm GAMA significantly outperforms the recent neural baselines. Further ablation studies confirm that both the multi-modal attention mechanism and the gated fusion design play a key role in achieving the observed performance gains.

SymLight: Exploring Interpretable and Deployable Symbolic Policies for Traffic Signal Control

Deep Reinforcement Learning have achieved significant success in automatically devising effective traffic signal control (TSC) policies. Neural policies, however, tend to be over-parameterized and non-transparent, hindering their interpretability and deployability on resource-limited edge devices. This work presents SymLight, a priority function search framework based on Monte Carlo Tree Search (MCTS) for discovering inherently interpretable and deployable symbolic priority functions to serve as the TSC policies. The priority function, in particular, accepts traffic features as input and then outputs a priority for each traffic signal phase, which subsequently directs the phase transition. For effective search, we propose a concise yet expressive priority function representation. This helps mitigate the combinatorial explosion of the action space in MCTS. Additionally, a probabilistic structural rollout strategy is introduced to leverage structural patterns from previously discovered high-quality priority functions, guiding the rollout process. Our experiments on real-world datasets demonstrate SymLight's superior performance across a range of baselines. A key advantage is SymLight's ability to produce interpretable and deployable TSC policies while maintaining excellent performance.

DyRo-MCTS: A Robust Monte Carlo Tree Search Approach to Dynamic Job Shop Scheduling

Dynamic job shop scheduling, a fundamental combinatorial optimisation problem in various industrial sectors, poses substantial challenges for effective scheduling due to frequent disruptions caused by the arrival of new jobs. State-of-the-art methods employ machine learning to learn scheduling policies offline, enabling rapid responses to dynamic events. However, these offline policies are often imperfect, necessitating the use of planning techniques such as Monte Carlo Tree Search (MCTS) to improve performance at online decision time. The unpredictability of new job arrivals complicates online planning, as decisions based on incomplete problem information are vulnerable to disturbances. To address this issue, we propose the Dynamic Robust MCTS (DyRo-MCTS) approach, which integrates action robustness estimation into MCTS. DyRo-MCTS guides the production environment toward states that not only yield good scheduling outcomes but are also easily adaptable to future job arrivals. Extensive experiments show that DyRo-MCTS significantly improves the performance of offline-learned policies with negligible additional online planning time. Moreover, DyRo-MCTS consistently outperforms vanilla MCTS across various scheduling scenarios. Further analysis reveals that its ability to make robust scheduling decisions leads to long-term, sustainable performance gains under disturbances.

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP

Genetic programming has undergone rapid development in recent years. However, theoretical studies of genetic programming are far behind. One of the major obstacles to theoretical studies is the challenge of developing a model to describe the relationship between fitness values and program genotypes. In this paper, we take linear genetic programming (LGP) as an example to study the fitness-to-genotype relationship. We find that the fitness expectation increases with fitness supremum over instruction editing distance, considering 1) the fitness supremum linearly increases with the instruction editing distance in LGP, 2) the fitness infimum is fixed, and 3) the fitness probabilities over different instruction editing distances are similar. We then extend these findings to explain the bloat effect and the minimum hitting time of LGP based on instruction editing distance. The bloat effect happens because it is more likely to produce better offspring by adding instructions than by removing them, given an instruction editing distance from the optimal program. The analysis of the minimum hitting time suggests that for a basic LGP genetic operator (i.e., freemut), maintaining a necessarily small program size and mutating multiple instructions each time can improve LGP performance. The reported empirical results verify our hypothesis.

LiBOG: Lifelong Learning for Black-Box Optimizer Generation

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.