A Simulated Annealing Algorithm for Joint Stratification and Sample Allocation Designs

TL;DR

This paper introduces a simulated annealing algorithm combined with delta evaluation to efficiently solve the complex joint stratification and sample allocation problem, outperforming existing local search heuristics in solution quality and computation time.

Contribution

The paper presents a novel simulated annealing approach with delta evaluation for joint stratification and sample allocation, improving solution efficiency and escaping local minima.

Findings

Simulated annealing achieved comparable solution quality faster.

Delta evaluation significantly reduced computation time.

Outperformed existing local search algorithms in experiments.

Abstract

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.