Emergency rescue operations play a vital role in alleviating human suffering, reducing casualties, and cutting down economic losses. One key aspect in the management of these operations is the rational allocation of emergency relief materials, where the allocation is continuous, dynamic, and concurrent. This allocation should be made not only to minimize the emergency rescue losses, but also to reduce the cost of emergency rescue work. A reasonable and effective allocation scheme for emergency relief materials can be established to adapt to the continuity, dynamics, and concurrency of material distribution. In this work, we propose a multiobjective optimization model of emergency material allocation with continuous time-varying supply and demand constraints, where the objective is to minimize the losses and the economic cost incurred by the emergency rescue operations. The constrained optimization problem is handled through sequential unconstrained minimization techniques, and the multiobjective optimization is carried out by the fast nondominated sorting genetic algorithm (NSGA-II) with an elite strategy to obtain a Pareto solution set with fairness and balance of loss and cost. The loss and cost associated with the Pareto frontier are employed to find an appropriate noninferior solution and its corresponding material allocation scheme. We verify through several simulations the model feasibility and the effectiveness of the proposed method, which can provide decision support for continuous material allocation in emergency rescue operations.

To further elucidate the relationship between the growth stress and cracking of KDP (KH₂PO₄, potassium dihydrogen phosphate) crystals of different sizes, a three-dimensional finite element calculation was conducted to analyze the growth stress of KDP single crystals grown from Z-plate seeds with varying cooling rates. The mismatch in the coefficient of thermal expansion (CTE), between the cap region and its close vicinity, and among the transparent region, was taken into account. The results indicate that when the cap region is a solid region (when the seed was regenerated with a cooling rate of 0.1 °C/day), the difference in material properties between the cap region and its close vicinity, especially the CTE mismatch along the a-axis, is the main reason of the high stresses. When the cap region is a box-like structure filled with solution (when the seed was regenerated with a cooling rate of 0.3 °C/day), the calculated stress is in proportion to the CTE gradient of the transparent region. Under both models, the stresses induced from an incremental CTE value (from the cap region to the growth front) are greater than those calculated from a diminishing CTE value, implying that the impurities reduce the CTE of KDP crystals, causing the crystals to crack more easily. Despite the maximum stresses inside the crystals changing slightly with an increase in crystal size, the decreased fracture stress of large brittle crystals leads to a higher cracking risk in a large-sized crystal.