联合分层和样本分配设计的模拟退火算法
A Simulated Annealing Algorithm for Joint Stratification and Sample Allocation Designs
摘要：
本研究将模拟退火与delta评估结合，以解决联合分层与样本分配问题。在这个问题中，原子层被划分为相互排斥和集体穷举的层。原子层的每个分区是分层问题的可能解决方案，其质量由其成本来衡量。可能的解决方案的贝尔数是巨大的，即使是一个中等数量的原子层，并增加了一个额外的复杂性层与每个解决方案的评估时间。许多大规模的组合优化问题不能被解决到最优，因为搜索最优解需要大量的计算时间。一些局部搜索启发式算法已被设计用于这个问题，但这些可能会陷入局部极小值，防止任何进一步的改进。我们添加到现有的本地搜索算法套件，模拟退火算法，允许从局部极小值逃逸，并使用三角洲评估，利用连续的解决方案之间的相似性，从而减少了评估时间。我们比较了模拟退火算法与两个最近的算法。在这两种情况下，模拟退火算法在相当少的计算时间内获得了质量相当的解决方案。
英文摘要：
This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each partition of atomic strata is a possible solution to the stratification problem, the quality of which is measured by its cost. The Bell number of possible solutions is enormous, for even a moderate number of atomic strata, and an additional layer of complexity is added with the evaluation time of each solution. Many larger scale combinatorial optimisation problems cannot be solved to optimality, because the search for an optimum solution requires a prohibitive amount of computation time. A number of local search heuristic algorithms have been designed for this problem but these can become trapped in local minima preventing any further improvements. We add, to the existing suite of local search algorithms, a simulated annealing algorithm that allows for an escape from local minima and uses delta evaluation to exploit the similarity between consecutive solutions, and thereby reduces the evaluation time. We compared the simulated annealing algorithm with two recent algorithms. In both cases, the simulated annealing algorithm attained a solution of comparable quality in considerably less computation time.
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