A Brief History of Heuristics: from Bounded Rationality to Intractability

Semaan, Gustavo Silva; Brito, José André de Moura; Coelho, Igor Machado; Silva, Edelberto Franco; Fadel, Augusto; Ochi, Luiz Satoru; Maculan, Nelson

doi:10.1109/tla.2020.9398639

Cited by 6 publications

(2 citation statements)

References 89 publications

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“…However, according to [12], even considering all the computational apparatus currently available, the BFA has its application restricted to cases where TS ≤ 10 7 , a limit that is exceeded for small values, such as 𝑁 = 160 and 𝐿 = 3, for example. It is the main focus of the Computational Intractability theme, as exposed in [46].…”

Section: Discretizationmentioning

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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Section: Discretizationmentioning

confidence: 99%

Heuristic algorithm for univariate stratification problem

Brito,

Semaan,

de Lima

et al. 2023

RAIRO-Oper. Res.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addressing inconsistencies between the stratification variable and a study variable, [14] proposed a method utilizing two models. 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].…”

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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The effective BRKGA algorithm for the k-medoids clustering problem

Brito¹,

Semaan

Fadel

2022

RAIRO-Oper. Res.

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This paper presents a biased random-key genetic algorithm for k-medoids clustering problem. A novel heuristic operator was implemented and combined with a parallelized local search procedure. Experiments were carried out with fifty literature data sets with small, medium, and large sizes, considering several numbers of clusters, showed that the proposed algorithm outperformed eight other algorithms, for example, the classics PAM and CLARA algorithms. Furthermore, with the results of a linear integer programming formulation, we found that our algorithm obtained the global optimal solutions for most cases and, despite its stochastic nature, presented stability in terms of quality of the solutions obtained and the number of generations required to produce such solutions. In addition, considering the solutions (clusterings) produced by the algorithms, a relative validation index (average silhouette) was applied, where, again, was observed that our method performed well, producing cluster with a good structure.

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A Brief History of Heuristics: from Bounded Rationality to Intractability

Cited by 6 publications

References 89 publications

Heuristic algorithm for univariate stratification problem

Heuristic algorithm for univariate stratification problem

Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach

The effective BRKGA algorithm for the k-medoids clustering problem

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