This article proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large-scale multiobjective and many-objective optimization problems (MaOPs). Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2–10 objectives and 200–1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large-scale multiobjective and MaOPs.

Model merging is an efficient empowerment technique in the machine learning community that does not require the collection of raw training data and does not require expensive computation. As model merging becomes increasingly prevalent across various fields, it is crucial to understand the available model merging techniques comprehensively. However, there is a significant gap in the literature regarding a systematic and thorough review of these techniques. This survey provides a comprehensive overview of model merging methods and theories, their applications in various domains and settings, and future research directions. Specifically, we first propose a new taxonomic approach that exhaustively discusses existing model merging methods. Secondly, we discuss the application of model merging techniques in large language models, multimodal large language models, and more than ten machine learning subfields, including continual learning, multi-task learning, few-shot learning, and so on. Finally, we highlight the remaining challenges of model merging and discuss future research directions. A comprehensive list of papers about model merging is available at https://github.com/EnnengYang/Awesome-Model-Merging-Methods-Theories-Applications .

The performance of decomposition-based algorithms is sensitive to the Pareto front shapes since their reference vectors preset in advance are not always adaptable to various problem characteristics with no a priori knowledge. For this issue, this article proposes an adaptive reference vector reinforcement learning (RVRL) approach to decomposition-based algorithms for industrial copper burdening optimization. The proposed approach involves two main operations, that is: 1) a reinforcement learning (RL) operation and 2) a reference point sampling operation. Given the fact that the states of reference vectors interact with the landscape environment (quite often), the RL operation treats the reference vector adaption process as an RL task, where each reference vector learns from the environmental feedback and selects optimal actions for gradually fitting the problem characteristics. Accordingly, the reference point sampling operation uses estimation-of-distribution learning models to sample new reference points. Finally, the resultant algorithm is applied to handle the proposed industrial copper burdening problem. For this problem, an adaptive penalty function and a soft constraint-based relaxing approach are used to handle complex constraints. Experimental results on both benchmark problems and real-world instances verify the competitiveness and effectiveness of the proposed algorithm.

Mobile edge computing (MEC) emerges as an appealing paradigm to provide time-sensitive computing services for industrial Internet of Things (IIoT) applications. How to guarantee truthfulness and budget-balance under locality constraints is an important issue to the allocation and pricing design of the MEC system. In this paper, we propose a truthful combinatorial double auction mechanism, which integrates the padding concept and the efficient pricing strategy to guarantee desirable properties in constrained MEC environments. This mechanism takes into account the locality characteristics of the MEC systems, where mobile devices (MDs) only offload tasks to edge servers (ESs) in the proximity with various requirements, and ESs only serve their neighboring MDs with limited resources. To be specific, for allocation, a linear programming (LP)-based padding method is used to obtain the near-optimal solution in the polynomial time. For pricing, a critical-value-based pricing strategy and a VCG-based pricing strategy are designed for MDs and ESs to achieve truthfulness and budget-balance. Our theoretical analysis confirms that TCDA is able to hold a set of desirable economic properties, including truthfulness, individual rationality, and budget-balance. Furthermore, simulation results validate the theoretical analysis, and verify the effectiveness and efficiency of TCDA.

Traditional routing algorithms cannot dynamically change network environments due to the limited information for routing decisions. Meanwhile, they are prone to performance bottlenecks in the face of increasingly complex business requirements. Some approaches, such as deep reinforcement learning (DRL) have been proposed to address the routing problems. However, they hardly utilize the information about the network environment fully. The Knowledge Defined Networking (KDN) architecture inspires us to develop new learning mechanisms adapted to the dynamic characteristics of the network topology. In this paper, we propose an effective scheme to solve the routing optimization problem by adding a graph neural network (GNN) structure to DRL, called Message Passing Deep Reinforcement Learning (MPDRL). MPDRL uses the characteristics of GNN to interact with the network topology environment and extracts exploitable knowledge through the message passing process of information between links in the topology. The goal is to achieve the load balance of network traffic and improve network performance. We have conducted experiments on three Internet Service Provider (ISP) network topologies. The evaluation results show that MPDRL obtains better network performance than the baseline algorithms.