A genetic algorithm applied to optimal allocation in stratified sampling

References

• Ali, I., Y. S. Raghav, and A. Bari. 2013. Compromise allocation in multivariate stratified surveys with stochastic quadratic cost function. Journal of Statistical Computation and Simulation 83 (5):962–76.
   Web of Science ®Google Scholar
• Ansari, A. H., R. Varshney, and M. J. Ahsan. 2018. Compromise mixed allocation in multivariate stratified sampling using dynamic programming technique. Journal of Advanced Statistics 3 (4):71–9. doi:https://doi.org/10.22606/jas.2018.34003.
   Google Scholar
• Bakhshi, Z. 2018. Stochastic optimization in multivariate stratified double sampling. International Journal of Engineering Technologies and Management Research 5 (1):115–22.
   Google Scholar
• Ballin, M., and G. Barcaroli. 2008. Optimal stratification of sampling frames in a multivariate and multidomain sample design. Contributi ISTAT.
   Google Scholar
• Barcaroli, G. 2014. SamplingStrata: An R package for the optimization of stratied sampling. Journal of Statistical Software 61 (4):1–24.
   Web of Science ®Google Scholar
• Bazaraa, M. S., H. D. Sherali, and C. M. Shetty. 2006. Nonlinear programming: Theory and algorithms. 3rd ed. New York: Wiley.
   Google Scholar
• Bean, J. C. 1994. Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing 6 (2):154–60. doi:https://doi.org/10.1287/ijoc.6.2.154.
   Google Scholar
• Bethel, J. 1985. An optimum allocation algorithm for multivariate surveys. Proceedings of the Survey Research Methods Section of the American Statistical Association, 209–12.
   Google Scholar
• Bethel, J. 1989. Sample allocation in multivariate surveys. Survey Methodology 15 (1):47–57.
   Google Scholar
• Brito, J. A. M., P. L. N. Silva, G. S. Semaan, and N. Maculan. 2015. Integer programming formulations applied to optimal allocation in stratified sampling. Survey Methodology 41 (2):427–42.
   Web of Science ®Google Scholar
• Chromy, J. 1987. Design optimization with multiple objectives. Proceedings of the Survey Research Methods Section of the American Statistical Association, 194–9.
   Google Scholar
• Cochran, W. G. 1977. Sampling techniques. 3rd ed. New York: Wiley.
   Google Scholar
• Day, C. D. 2010. A multi-objective evolutionary algorithm for multivariate optimal allocation. Proceedings of the Survey Research Methods Section of the American Statistical Association, 3351–8.
   Google Scholar
• Folks, J. L., and C. E. Antle. 1965. Optimum Allocation of sampling units to strata when there are R responses of interest. Journal of the American Statistical Association 60 (309):225–33. doi:https://doi.org/10.2307/2283148.
   Google Scholar
• Garciá, J. A. D., and L. U. Cortez. 2006. Optimum allocation in multivariate stratified sampling: multi-objective programming. Comunicaciones Del Cimat, no I-06-07/28-03-2006.
   Google Scholar
• Gonçalves, J. R., and M. G. C. Resende. 2011. Biased random-key genetic algorithms for combinatorial optimization. Journal of Heuristics 17 (5):487–525. doi:https://doi.org/10.1007/s10732-010-9143-1.
   Web of Science ®Google Scholar
• Gonçalves, J. R., and M. G. C. Resende. 2015. A biased random-key genetic algorithm for the unequal area facility layout problem. European Journal of Operational Research 246 (1):86–107. doi:https://doi.org/10.1016/j.ejor.2015.04.029.
   Web of Science ®Google Scholar
• Haseen, S., I. Ali, and A. Bari. 2016. Multiobjective stochastic multivariate stratified sampling in presence of nonresponse. Communications in Statistics—Simulation and Computation 45 (8):2810–26. doi:https://doi.org/10.1080/03610918.2014.926173.
   Web of Science ®Google Scholar
• Huddleston, H. F., P. L. Claypool, and R. R. Hocking. 1970. Optimal sample allocation to strata using convex programming. Journal of the Royal Statistical Society, Series C 19 (3):273–8.
   Google Scholar
• Ismail, M. V., K. Nasser, and Q. S. Ahmad. 2011. Solution of a multivariate stratified sampling problem through Chebyshevs goal programming. Pakistan Journal of Statistics and Operation Research 1:101–8. doi:https://doi.org/10.18187/pjsor.v7i1.172.
   Google Scholar
• Khan, M. F., I. Ali, and Q. S. Ahmad. 2011. Chebyshev approximate solution to allocation problem in multiple objective surveys with random costs. American Journal of Computational Mathematics 01 (04):247–51. doi:https://doi.org/10.4236/ajcm.2011.14029.
   Google Scholar
• Khan, M. F., I. Ali, Y. S. Raghav, and A. Bari. 2012. Allocation in multivariate stratified surveys with non-linear random cost function. American Journal of Operations Research 02 (01):100–5.
   Google Scholar
• Khan, M. G. M., and M. J. Ahsan. 2003. A note on optimum allocation in multivariate stratified sampling. The South Pacific Journal of Natural and Applied Sciences 21 (1):91–5. doi:https://doi.org/10.1071/SP03017.
   Google Scholar
• Khan, M. G. M., M. J. Ahsan, and N. Jahan. 1997. Compromise allocation in multivariate stratified sampling: An integer solution. Naval Research Logistics 44 (1):69–79. doi:https://doi.org/10.1002/(SICI)1520-6750(199702)44:1<69::AID-NAV4>3.0.CO;2-K.
   Web of Science ®Google Scholar
• Kish, L. 1976. Optima and proxima in linear sample designs. Journal of the Royal Statistical Society, Series A 139 (1):80–95. doi:https://doi.org/10.2307/2344384.
   Google Scholar
• Kokan, A. R. 1963. Optimum allocation in multivariate surveys. Journal of the Royal Statistical Society, Series A 126 (4):557–65. doi:https://doi.org/10.2307/2982579.
   Google Scholar
• Kokan, A. R., and S. Khan. 1967. Optimum allocation in multivariate surveys: An analytical solution. Journal of the Royal Statistical Society: Series B (Methodological) 29 (1):115–25. doi:https://doi.org/10.1111/j.2517-6161.1967.tb00679.x.
   Google Scholar
• Kozak, M. 2006. Multivariate sample allocation: Application of random search method. Statistics in Transition 7 (4):889–900.
   Google Scholar
• Land, A. H., and A. G. Doig. 1960. An Automatic method for solving discrete programming problems. Econometrica 28 (3):497–520. doi:https://doi.org/10.2307/1910129.
   Web of Science ®Google Scholar
• Lohr, S. L. 2010. Sampling: Design and analysis, 2nd ed. Cengage Learning: Brooks/Cole.
   Google Scholar
• Luenberger, D. G., and Y. Ye. 2008. Linear and non-linear programming, 3rd ed. Cham: Springer.
   Google Scholar
• Neyman, J. 1934. On the two different aspects of the representative method: The method of representative sampling and the method of purposive sampling. Journal of the Royal Statistical Society 97 (4):558–625. doi:https://doi.org/10.2307/2342192.
   Google Scholar
• Raghav, Y. S., I. Ali, and A. Bari. 2014. Multi-objective nonlinear programming problem approach in multivariate stratified sample surveys in the case of non-response. Journal of Statistical Computation and Simulation 84 (1):22–36.
   Web of Science ®Google Scholar
• Ruiz, E., and S. Voβ. 2015. A biased random-key genetic algorithm for the multiple Knapsack assignment problem. Series lecture notes in computer science. In International Conference on Learning and Intelligent Optimization, 218–22. Cham: Springer.
   Google Scholar
• Ruiz, E., M. A. Sambola, E. Fernández, and M. G. C. Resende. 2015. A biased random-key genetic algorithm for the capacitated minimum spanning tree problem. Computers & Operations Research 57:95–108. doi:https://doi.org/10.1016/j.cor.2014.11.011.
   Web of Science ®Google Scholar
• Spears, W. M., and K. A. DeJong. 1991. On the virtues of parameterized uniform crossover. Proceedings of the Fourth International Conference on Genetic Algorithms, 230–6.
   Google Scholar
• Sukhatme, P. V., B. V. Sukhatme, S. Sukhatme, and C. Asok. 1984. Sampling theory of surveys with applications. 3rd ed. Iowa: Iowa State University Press.
   Google Scholar
• Valliant, R., and J. E. Gentle. 1997. An application of mathematical programming to sample allocation. Computational Statistics & Data Analysis 25:337–60. doi:https://doi.org/10.1016/S0167-9473(97)00007-8.
   Google Scholar
• Varshney, R. M. 2019. Optimum allocation in multivariate stratified sampling design in the presence of nonresponse with Gamma cost function. Journal of Statistical Computation and Simulation 89 (13):2454–67. doi:https://doi.org/10.1080/00949655.2019.1620747.
   Web of Science ®Google Scholar
• Varshney, R., M. G. M. Khan, U. Fatima, and M. J. Ahsan. 2015. Integer compromise allocation in multivariate stratified surveys. Annals of Operations Research 226 (1):659–68. doi:https://doi.org/10.1007/s10479-014-1734-z.
   Web of Science ®Google Scholar
• Wolsey, L. A. 1998. Integer programming. Hoboken, NJ: Wiley-Interscience Series in Discrete Mathematics and Optimization.
   Google Scholar
• Wolsey, L. A., and G. L. Nemhauser. 1999. Integer and combinatorial optimization. Hoboken, NJ: Wiley-Interscience Series in Discrete Mathematics and Optimization.
   Google Scholar