The maximally diverse grouping problem (MDGP) seeks to partition the vertices of a complete graph into a fixed number of groups under capacity constraints, maximizing the sum of edge weights within each group. MDGP is an NP-hard combinatorial optimization problem and has wide real-world applications. In this paper, we propose an adaptive configuration-aware simulated annealing (ACSA) algorithm to solve MDGP. First, ACSA adopts a relaxation-based insertion strategy, which temporarily relaxes capacity constraints to expand the neighborhood and allow effective exploration of promising regions. Second, a memory-based swap mechanism is introduced to integrate high-potential suboptimal swap moves into the conventional best-swap operation, thereby achieving a better balance between diversification and intensification of the search. Finally, ACSA employs a vertex-wise sequential coordination strategy to dynamically organize the insertion and swap moves, which enhances the search flexibility. Experiments on 500 benchmark instances demonstrate the strong competitiveness of ACSA, as it improves the best results among the state-of-the-art algorithms on 460 instances and matches them on 39 instances.

The clique partitioning problem (CPP) aims to find a partition of vertices of a complete graph in order to maximize the sum of edge weights within each partition (clique), which has been proven to be NP-hard and has wide real-world applications. In this paper, we propose an elite-guided weighted simulated annealing algorithm called EWSA to solve the CPP. First, EWSA employs two specific configurations and alternates between them via an oscillation strategy, which balances the exploitation and exploration of the search. Second, a weighting strategy is introduced to improve the scoring function in traditional simulated annealing, which is able to guide the search to explore diverse solutions. Finally, a partition restriction strategy is adopted to reduce search space and increase the search efficiency. Experiments on 255 instances demonstrate the competitiveness of EWSA. For 130 open instances, EWSA discovers new upper bounds in 32 cases and matches the best known results for the others. For the remaining 125 closed instances, EWSA achieves the best known objective values within a short computational time.

Large Language Models (LLMs) have emerged as a promising technology for solving combinatorial optimization problems. However, their direct application to scheduling problems remains limited due to the inherent complexity of these problems. This paper proposes an LLMs-based neighborhood search method that leverages LLMs to tackle the job shop scheduling problem (JSP) and its variants. The main contributions of this work are threefold. First, we introduce a novel LLMs-guided neighborhood evaluation strategy that guides local search by dynamically adjusting operation weights. Second, we develop a verification evolution (VeEvo) framework to mitigate the hallucination effects of LLMs, enabling the generation of high-quality heuristics for weight updates. Third, we integrate this framework with the weighted neighborhood evaluation strategy to effectively guide the search towards promising regions. Extensive experiments are conducted on 349 benchmark instances across three classical scheduling problems. The results demonstrate that our algorithm significantly outperforms existing state-of-the-art methods. For JSP, our algorithm reduces the average optimality gap from 10.46% to 1.35% on Taillard's instances compared to reinforced adaptive staircase curriculum learning. For flexible JSP (FJSP), it reduces the gap from 13.24% to 0.05% on Brandimarte's instances compared to deep reinforcement learning methods. Furthermore, for FJSP with sequence dependent setup time, our algorithm updates 9 upper bounds for benchmark instances.

We present a unified heuristic solver for the PACE 2025 challenge, addressing both the dominating set and hitting set problems by reducing them to the unicost set covering problem. Our solver applies standard reduction rules, a multi-round frequency-based greedy initializer, and a local search guided by adaptive element weights. Additional techniques, such as component-level exact solving and swap restriction, further enhance performance. In the final official evaluation, our proposed solver achieved second place in the heuristic track for the dominating set problem of the PACE 2025 challenge, while securing first place in the heuristic track for the hitting set problem.

Multi-agent reinforcement learning system is used to solve the problem that agents achieve specific goals in the interaction with the environment through learning policies. Almost all existing multi-agent reinforcement learning methods assume that the observation of the agents is accurate during the training process. It does not take into account that the observation may be wrong due to the complexity of the actual environment or the existence of dishonest agents, which will make the agent training difficult to succeed. In this paper, considering the limitations of the traditional multi-agent algorithm framework in noisy environments, we propose a multi-agent fault-tolerant reinforcement learning (MAFTRL) algorithm. Our main idea is to establish the agent's own error detection mechanism and design the information communication medium between agents. The error detection mechanism is based on the autoencoder, which calculates the credibility of each agent's observation and effectively reduces the environmental noise. The communication medium based on the attention mechanism can significantly improve the ability of agents to extract effective information. Experimental results show that our approach accurately detects the error observation of the agent, which has good performance and strong robustness in both the traditional reliable environment and the noisy environment. Moreover, MAFTRL significantly outperforms the traditional methods in the noisy environment.