The recent developments in combinatorial optimization and multi-objective optimization have shown significant advancements, particularly in leveraging neural networks and adaptive search strategies. Key innovations include the integration of deep reinforcement learning with beam search strategies, which have demonstrated superior performance in combinatorial optimization tasks. Additionally, the introduction of novel algorithms for stochastic multi-armed bandit problems and the extension of regret analysis to include $p$-mean regret provide flexible frameworks for balancing fairness and efficiency in bandit algorithms. In the realm of multi-objective optimization, runtime analysis for evolutionary algorithms in unbounded integer spaces and improvements to the NSGA-II algorithm with tie-breaking rules have enhanced the efficiency and scalability of these methods. Notably, the application of neural combinatorial optimization to stochastic job shop scheduling problems and the development of adaptive large neighborhood search for mixed-integer programming problems highlight the growing trend of incorporating online learning capabilities to improve problem-solving strategies. These advancements collectively push the boundaries of what is achievable in optimization, offering new tools and methodologies for tackling complex, real-world problems.