Heuristic approach applied to the optimum stratification problem

Brito, José André de Moura; Lima, Leonardo de; González, Pedro Henrique; Oliveira, Breno C.; Maculan, Nelson

doi:10.1051/ro/2021051

Cited by 7 publications

(12 citation statements)

References 25 publications

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“…In complex mathematical models, the strategy for cost minimization and profit maximization is usually analyzed by computational experimental methods. Inspired by literatures [27][28][29][30][31], this study will find the optimal solution, perform parameter analysis and stability analysis through mathematical calculation software Matlab.…”

Section: The Stability Of the Modelmentioning

confidence: 99%

The complex evolution of information quality improvement in competitive market

Liu

2023

RAIRO-Oper. Res.

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Abstract. Information is important market resource. High-quality information is beneficial to increase enterprise’s reputation and reduce consumer’s verification cost. This paper constructs a two-layer dynamic model, in which enterprises simultaneously conduct price and information game. The goal of profit maximization integrates two types of games into one system. The complex evolution of the two-layer system are studied by equilibrium analysis, stability analysis, bifurcation diagram, entropy and Lyapunov exponent. It is found that improving the information quality through regulations will increase involution and reduce stability of the market. Then, the block chain technology is introduced into the model for improving information quality of the market. It is found that increasing enterprises’ willingness to adopt block chain can improve the information quality quickly and effectively, and that is verified by entropy value. Therefore, the application and promotion of new technologies are more effective than exogenous regulations for improving information quality in market .

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Section: The Stability Of the Modelmentioning

confidence: 99%

The complex evolution of information quality improvement in competitive market

Liu

2023

RAIRO-Oper. Res.

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“…According to several approaches in the literature proposed for solving (I) and (II), after determining the strata, it is common to apply the Neyman allocation (12) [40] to determine the sample sizes of the Problem (I). The equation (13) used in Problem (II) is obtained from the substitution of (12) in the term on the left side of equation ( 9) and algebraic manipulations.…”

Section: Univariate Stratification Problemmentioning

confidence: 99%

“…In [39], an algorithm is proposed that solves the multivariate stratification problem and uses a penalized objective function, which is optimized by applying the Simulated Annealing method. In [12], the authors propose a brute force algorithm, limited to small populations (𝑁 value), and an algorithm based on the VNS (Variable Neighborhood Search) method, where, in the sample allocation step, both do use of the exact method proposed by Brito et al [9]. As a result of this method, the authors developed the R package stratvns.…”

Section: Literature Reviewmentioning

confidence: 99%

Heuristic algorithm for univariate stratification problem

Brito,

Semaan,

de Lima

et al. 2023

RAIRO-Oper. Res.

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In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article proposes a heuristic to solve the univariate stratification problem - widely studied in the literature. One of its versions sets the number of strata and the precision level and seeks to determine the limits that define such strata to minimize the sample size allocated to the strata. A heuristic-based on a stochastic optimization method and an exact optimization method was developed to achieve this goal. The performance of this heuristic was evaluated through computational experiments, considering its application in various populations used in other works in the literature, based on 20 scenarios that combine different numbers of strata and levels of precision. From the analysis of the obtained results, it is possible to verify that the heuristic had a performance superior to four algorithms in the literature in more than 94\% of the cases, particularly concerning the known algorithm of Lavallé-Hidiroglou.

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“…Over the past few decades, methods have been categorized predominantly as approximation or optimization techniques [15]. Notably, an exact technique for resource allocation was presented in [17], utilized by the BRKGA (Biassed Random Key Genetic Algorithm) and GRASP (Greedy Randomised Adaptive Search Procedure) algorithms outlined in [16]. Additionally, [18] employed a dynamic programming method to calculate stratification points for two related variables.…”

Section: Introductionmentioning

confidence: 99%

Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach

Danish

2024

Preprint

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The study examines the determination of stratification points for two study variables within the framework of simple random sampling, particularly focusing on calculating the population mean using a closely associated variable. Utilizing a superpopulation model, the investigation seeks to derive minimal equations by minimizing aggregated variance with the assistance of the variables under scrutiny. In order to improve the accuracy of estimating population parameters within a stratified sampling framework, it is suggested in the article to establish optimal strata boundaries (OSB) instead of categorizing variables, the study focuses on continuous variables for analysis. The creation of homogeneous units within each stratum, facilitated by optimally constructed OSB, leads to more effective sample sizes (SS) and consequently enhances precision in estimation. However, it's noted that the OSB and SS may not remain optimal in cases where a fixed total sample size is mandated, particularly in survey designs constrained by a fixed budget. To address this challenge, the article outlines a methodology for calculating the OSB and SS under the condition that the survey's per-unit stratum measurement costs or its probability density function is understood. An empirical demonstration of a design-based stratification approach is showcased using breast cancer data, where the mean perimeter is estimated based on mean radius and mean texture. Furthermore, numerical examples are provided for hypothetical study variables following Cauchy and standard power distributions. The novel approach has been integrated into the revised stratifyR package and LINGO software. The research outcomes indicate that the newly introduced method demonstrates superior efficiency or comparable performance when aiming to refine the precision of population parameter estimations.

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Heuristic approach applied to the optimum stratification problem

Cited by 7 publications

References 25 publications

The complex evolution of information quality improvement in competitive market

The complex evolution of information quality improvement in competitive market

Heuristic algorithm for univariate stratification problem

Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach

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