Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function Export

@incollection{citeulike:4056838, abstract = {The performance of stochastic optimisers can be assessed experimentally on given problems by performing multiple optimisation runs, and analysing the results. Since an optimiser may be viewed as an estimator for the (Pareto) minimum of a (vector) function, stochastic optimiser performance is discussed in the light of the criteria applicable to more usual statistical estimators. Multiobjective optimisers are shown to deviate considerably from standard point estimators, and to require special statistical methodology. The attainment function is formulated, and related results from random closed-set theory are presented, which cast the attainment function as a mean-like measure for the outcomes of multiobjective optimisers. Finally, a covariance-measure is defined, which should bring additional insight into the stochastic behaviour of multiobjective optimisers. Computational issues and directions for further work are discussed at the end of the paper.}, author = {Grunert and Fonseca, Carlos and Hall, Andreia}, citeulike-article-id = {4056838}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/3-540-44719-9_15}, citeulike-linkout-1 = {http://www.springerlink.com/content/3lnrlh620y94d0n3}, doi = {10.1007/3-540-44719-9_15}, journal = {Evolutionary Multi-Criterion Optimization}, keywords = {attainment, metaheuristic, multi-objective, statistic, stochastic-local-search}, pages = {213--225}, posted-at = {2009-02-15 20:04:06}, priority = {5}, title = {Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function}, url = {http://dx.doi.org/10.1007/3-540-44719-9_15}, year = {2001} }

TY - CHAP ID - citeulike:4056838 L3 - citeulike-article-id:4056838 N2 - The performance of stochastic optimisers can be assessed experimentally on given problems by performing multiple optimisation runs, and analysing the results. Since an optimiser may be viewed as an estimator for the (Pareto) minimum of a (vector) function, stochastic optimiser performance is discussed in the light of the criteria applicable to more usual statistical estimators. Multiobjective optimisers are shown to deviate considerably from standard point estimators, and to require special statistical methodology. The attainment function is formulated, and related results from random closed-set theory are presented, which cast the attainment function as a mean-like measure for the outcomes of multiobjective optimisers. Finally, a covariance-measure is defined, which should bring additional insight into the stochastic behaviour of multiobjective optimisers. Computational issues and directions for further work are discussed at the end of the paper. JF - Evolutionary Multi-Criterion Optimization EP - 225 TI - Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function SP - 213 KW - attainment KW - metaheuristic KW - multi-objective KW - statistic KW - stochastic-local-search AU - Grunert AU - Fonseca, Carlos AU - Hall, Andreia PY - 2001/// UR - http://dx.doi.org/10.1007/3-540-44719-9_15 ER -