A Simulated Annealing Algorithm for Joint Stratification and Sample Allocation Designs

Abstract

This study combined 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 stratification is a solution, 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 with 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 reduce the evaluation time.

A hybrid estimation of distribution algorithm for joint stratification and sample allocation

“…Here we are very close to a global minimum and we get there on the second step -without adjusting the probability of strata assignments. On a more general level however, the hybrid EDA uses mutation and add strata components (see (O'Luing et al, 2019)), as well as simulated annealing (see (O'Luing et al, 2020) which enable escape from this occurrence. The UMDA also has alternative approaches of avoiding 1, 0 probabilities (such as capping the probability interval to between 1 L and (1 − 1 L )) e.g.…”

“…This quality is evaluated by the Bethel-Chromy algorithm (Bethel, 1985;Chromy, 1987;Bethel, 1989) which is expensive (in computational terms). Previous contributions in this area includes work carried out by (Kozak et al, 2007;Keskintürk and Er, 2007;Benedetti et al, 2008;Rivest, 2009, 2011;Ballin and Barcaroli, 2013;O'Luing et al, 2019;Ballin and Barcaroli, 2020;O'Luing et al, 2020O'Luing et al, , 2021.…”

“…That has been our focus in earlier papers in which we presented evolutionary (a grouping genetic algorithm - (O'Luing et al, 2019)) and local search (simulated annealing algorithm - (O'Luing et al, 2020) algorithms and explored multi-stage combinations of clustering algorithms with a hill-climbing algorithm ((O'Luing et al, 2021)). We have evaluated the performance of these algorithms by the solution quality and computation time taken to find a local minimum.…”

“…We have evaluated the performance of these algorithms by the solution quality and computation time taken to find a local minimum. In (O'Luing et al, 2020) and (O'Luing et al, 2021) we also considered training times. The performance has varied according to each data stratification problem.…”

“…To expand on the details mentioned above, we explore a new paradigm of evolutionary algorithms named estimation of distribution algorithms (EDAs) (Baluja, 1994;Mühlenbein and Paaß, 1996;Larrañaga and Lozano, 2001;Pelikan et al, 2003) in the context of this problem. In particular, we consider the application of a hybridised version of an EDA and compare it against the best results achieved so far with the algorithms discussed in (O'Luing et al, 2019), (O'Luing et al, 2020) and (O'Luing et al, 2021).…”