Global optimization via inverse distance weighting and radial basis functions

Abstract Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis.

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APLIKASI GEOSPASIAL MENGGUNAKAN ARCGIS 10.3 DALAM PEMBUATAN PETA DAYA HANTAR LISTRIK DI CEKUNGAN AIRTANAH SUMOWONO

Jurnal Presipitasi Media Komunikasi dan Pengembangan Teknik Lingkungan ◽

10.14710/presipitasi.v14i1.15-23 ◽

2017 ◽

Vol 14 (1) ◽

pp. 15

Author(s):

Thomas Triadi Putranto ◽

Kevin Alexander

Keyword(s):

Radial Basis Functions ◽

Basis Functions ◽

Inverse Distance Weighting ◽

Empirical Bayesian ◽

Bayesian Kriging ◽

Empirical Bayesian Kriging ◽

Distance Weighting ◽

Radial Basis ◽

Inverse Distance

Air tanah sebagai air bersih merupakan salah satu kebutuhan primer manusia yang dimanfaatkan dalam berbagai kepentingan manusia serta untuk air minum. Airtanah memiliki kualitas dimana salah satu parameter fisiknya adalah daya hantar listrik (DHL). Dalam suatu Cekungan Airtanah (CAT), airtanah memiliki keberagaman nilai daya hantar listrik yang dipengaruhi oleh faktor infiltrasi dan lingkungan. Nilai DHL dapat dijadikan suatu acuan mengenai kelayakan suatu airtanah sebagai air minum. Sebagai salah satu sumber yang paling diminati masyarakat, maka masyarakat juga perlu untuk mengetahui kualitas dari airtanah tersebut melalui parameter daya hantar listrik sehingga peta daya hantar listrik daerah CAT Sumowono dapat menjadi suatu informasi bagi masyarakat yang menggunakan airtanah dari CAT Sumowono tersebut. Maka dari itu perlu adanya pembuatan peta daya hantar listrik daerah CAT Sumowono agar masyarakat merasa nyaman dan aman dalam memanfaatkan airtanah. Metode interpolasi data DHL menggunakan analisis geostatistik yang terdapat pada perangkat lunak ArcGIS 10.3. Metode interpolasi yang digunakan adalah Inverse Distance Weighting (IDW), Radial Basis Functions (RBF) dan Empirical Bayesian Kriging (EBK). Dari keseluruhan data yang terinterpolasi, didapatkan dua kelas kualitas airtanah berdasarkan nilai DHL, yaitu Sangat Baik (<250 μS/cm) dan Baik (250-750 μS/cm). Metode interpolasi yang dinilai paling seimbang adalah metode RBF. Melalui peta DHL hasil interpolasi metode RBF diketahui persebaran daerah dengan kelas sangat baik pada daerah CAT Sumowono mencakup 52,8% dari luas CAT dan 47,2% masuk ke dalam kelas baik.

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Global optimization based on active preference learning with radial basis functions

Machine Learning ◽

10.1007/s10994-020-05935-y ◽

2020 ◽

Author(s):

Alberto Bemporad ◽

Dario Piga

Keyword(s):

Global Optimization ◽

Objective Function ◽

Decision Maker ◽

Optimization Problems ◽

Global Optimum ◽

Bayesian Optimization ◽

Preference Learning ◽

Global Optimizer ◽

Radial Basis ◽

Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

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