摘要：Physics-informed neural networks (PINNs) are applied to facilitate incompressible two-phase bubble motion modeling by integrating governing equations and interface evolution equations. The loss function of PINNs consists of multiple loss terms, including initial and boundary conditions constraints, partial differential equations residuals, and volume fraction constraints. The performance of PINNs is influenced by the competing effects of these loss terms. Therefore, we introduce a heuristic adaptive weights approach to automatically adjust loss weights for each training point, avoiding manual tuning and improving the accuracy of PINNs. We investigate typical bubble motion cases, specifically focusing on bubble rising and breakup, to showcase the capabilities of the proposed method. We explore the impact of weights and present the results in comparison to the baselines...

摘要：We consider a novel variant of the three-dimensional bin packing problem (3DBPP) arising from a maritime shipping port. Unlike the classical bin packing problem, our 3DBPP requires all items to be stacked vertically during the packing process. To tackle this problem effectively, we divide it into two subproblems: the stack packing problem (SPP) and the two-dimensional bin packing problem (2DBPP). We first formulate the SPP as an integer programming model to minimize the total bottom area of the stacks, which is further solved by a branch-and-price method. Then, in the 2DBPP, to pack all stacks into a minimum number of bins, we follow the left-down most extreme point placement strategy. An encoder–decoder model was developed to optimize the packing sequence and orientation of the stacks simultaneously. Industrial instances from shipping ports were collected and extended. The computational results show that our two-stage algorithm performs well in solving the stacking-constrained 3DBPP.

摘要：Abstract: We revisit the classical online scheduling problem on parallel machines for minimizing total weighted completion time. In the problem, a set of independent jobs arriving online over time has to be scheduled on identical machines, where the information of each job including its processing time and weight is not known in advance. The goal is to minimize the total weighted completion time of the jobs. For this problem, we propose an improved 2: 11-competitive online algorithm based on a kind of waiting strategy.​