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Combination of Machine Learning and Kriging for Spatial Estimation of Geological Attributes

NATURAL RESOURCES RESEARCH 2022年第1期31卷 191-213页

作者： Erdogan Erten, Gamze Yavuz, Mahmut Deutsch, Clayton V. Eskisehir Osmangazi Univ Dept Min Engn TR-26040 Eskisehir Turkey Univ Alberta Ctr Computat Geostat Donadeo Innovat Ctr Engn 6 2 9211-116 St Edmonton AB T6G 1H9 Canada

A growing number of studies in the spatial estimation of geological features use machine learning (ML) models, as these models promise to provide efficient solutions for estimation especially in non-Gaussian, non-stationary and complex cases. However, these models have two major limitations: (1) the data are considered to be independent and identically distributed (or spatially uncorrelated), and (2) the data are not reproduced at their locations. Kriging, on the other hand, has a long history of generating unbiased estimates with minimum error variance at unsampled locations. Kriging assumes stationarity and linearity. This study proposes a methodology that combines kriging and ML models to mitigate the disadvantages of each method and obtain more accurate estimates. In the proposed methodology, a stacked ensemble model, which is also referred to as the super learner (SL) model, is applied for ML modeling. We have shown how the estimates generated by the SL model and estimates obtained from kriging can be combined through a weighting function based on a kriging variance. The weights are optimized using the sequential quadratic programming. The proposed methodology is demonstrated in two synthetic case studies containing data with non-stationarity and non-Gaussian features;a real case study using a dataset from an oilsands deposit is also presented. The performance of the combined model is compared with the SL model and kriging using the coefficient of determination (R-squared), root mean squared error, and mean absolute error criteria. The combined model appears to yield more accurate estimates than the ones generated by SL model and kriging in all cases.

关键词： Spatial estimation Kriging Machine learning Super learner Combination sequential quadratic programming

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Computation of the empirical likelihood ratio from censored data

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2007年第11-12期77卷 1103-1112页

作者： Chen, Kun Zhou, Mai Univ Kentucky Dept Stat Lexington KY 40506 USA Bayer Pharmaceut W Haven West Haven CT 06516 USA

The empirical likelihood ratio method is a general nonparametric inference procedure that has many desirable properties. Recently, the procedure has been generalized to several settings including testing of weighted means with right-censored data. However, the computation of the empirical likelihood ratio with censored data and other complex settings is often nontrivial. We propose to use a sequential quadratic programming (SQP) method to solve the computational problem. We introduce several auxiliary variables so that the computation of SQP is greatly simplified. Examples of the computation with null hypothesis concerning the weighted mean are presented for right- and interval-censored data.

关键词： sequential quadratic programming maximization constraints Wilks' theorem

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An SQP method for general nonlinear programs using only equality constrained subproblems

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MATHEMATICAL programming 1998年第3期82卷 413-448页

作者： Spellucci, P Tech Univ Darmstadt Dept Math D-64289 Darmstadt Germany

In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [P. Spellucci, Han's method without solving QP, in: A. Auslender, W. Oettli, J. Steer (Eds), Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, vol. 30, Springer, Berlin, 1981, pp. 123-141.] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SOP-methods, as demonstrated by extensive numerical tests. (C) 1998 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.

关键词： sequential quadratic programming SQP method nonlinear programming

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Hybrid of comprehensive learning particle swarm optimization and SQP algorithm for large scale economic load dispatch optimization of power system

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Science China(Information Sciences) 2010年第8期53卷 1566-1573页

作者： WANG Yu , LI Bin & YUAN Bo Department of Electronic Science and Technology, School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China 1. Department of Electronic Science and Technology School of Information Science and Technology University of Science and Technology of China Hefei 230027 China

Economic load dispatch (ELD) is an important optimization task in power systems. In the previous works, various researchers attempted to address this problem by both mathmatical and heuristic optimization algorithms. However, there are still two practically important issues that have not attracted sufficient attention: 1) the stability of these algorithms cannot be effectively ensured; 2) the performance of these algorithms on large scale ELD optimization tasks remains to be unsatisfactory. CLPSO is an effective global optimization algorithm. To strengthen the convergence ability of CLPSO, the sequential quadratic programming (SQP) is introduced into it. This results in a new algorithm hybrid of comprehensive learning particle swarm optimization and sequential quadratic programming (SQP-CLPSO). To assess the performance of SQP-CLPSO, it is compared with several state-of-the-art evolutionary algorithms (EAs) on the classical ELD optimization problems. Experimental results show that SQP-CLPSO has very good abilities of convergence, diversity maintainence and scalability, which make it suitable for complex ELD problems.

关键词： particle swarm optimization comprehensive learning particle swarm optimization sequential quadratic programming local search power systems economic load dispatch

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A new approach for process optimization of a METVC desalination system

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DESALINATION AND WATER TREATMENT 2012年第1-3期37卷 84-96页

作者： Shakib, Seyed Ehsan Amidpour, Majid Aghanajafi, Cyrus KN Toosi Univ Technol Fac Mech Engn Tehran Iran

Making potable water through desalination plants is a very important process in areas where clean water is highly required. One of the most common and acceptable desalination processes is multiple effect evaporation desalination (MED) process. The main objective of this paper is optimization of MED desalination with thermal vapor compression (METVC) from economical and thermodynamic point of view. Hence, first, a comprehensive thermodynamic model for METVC is developed and then the effect of operating parameters on thermal performance of the system is analyzed. Since the values of operating parameters have a great effect on both thermal performance and cost of the plant, the optimization of these parameters is very important. In this regard, some researchers have focused on improving the economical or thermodynamic aspect of the system. However, in practice it is reasonable to optimize both these criteria simultaneously. Based on this, in order to optimize the process of METVC and show influence of objective function on optimization results, four objective functions are chosen as four cases for optimization. These cases include 1) minimizing specific heat transfer area, 2) maximizing exergy efficiency, 3) maximizing performance ratio (PR) and 4) minimizing specific heat transfer area and maximizing PR. In fact, cases 1 to 3 are single objective problem while case 4 is a multi objective problem. All of the optimization problems are solved by a heuristic optimization problem, namely, Genetic Algorithm (GA). From optimization study, it can be seen that the results of multi objective problem are perfect and more reasonable than other cases. In other words, the results of cases 1 to 3 demonstrate some improvement in either thermodynamic or economical aspects of the system although multi objective optimization satisfy both thermodynamic and economical aspects of METVC and exhibit a rational system that could be applied for a real design approach.

关键词： Multi effect thermal vapor compression desalination Thermodynamic model Exergy analysis Genetic algorithm sequential quadratic programming Optimization

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An SQP algorithm for finely discretized continuous minimax problems and other minimax problems with many objective functions

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SIAM JOURNAL ON OPTIMIZATION 1996年第2期6卷 461-487页

作者： Zhou, JL Tits, AL UNIV MARYLAND SYST RES INSTCOLLEGE PKMD 20742 UNIV MARYLAND DEPT ELECT ENGNCOLLEGE PKMD 20742

A common strategy for achieving global convergence in the solution of semi-infinite programming (SIP) problems, and in particular continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with progressively finer discretization meshes. Finely discretized minimax and SIP problems, as well as other problems with many more objectives/constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the objectives/constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, a sequential quadratic programming (SQP)-type algorithm is proposed that incorporates this idea in the particular case of minimax problems. The general case will be considered in a separate paper. The quadratic programming subproblem that yields the search direction involves only a small subset of the objective functions. This subset is updated at each iteration in such a way that global convergence is ensured. Heuristics are suggested that take advantage of a possible close relationship between ''adjacent'' objective functions. Numerical results demonstrate the efficiency of the proposed algorithm.

关键词： continuous minimax semi-infinite programming many constraints sequential quadratic programming discretization global convergence

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Supercalm multifunctions for convergence analysis

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SET-VALUED ANALYSIS 2006年第3期14卷 249-261页

作者： Levy, Adam B. Bowdoin Coll Dept Math Brunswick ME 04011 USA

Calmness of multifunctions is a well-studied concept of generalized continuity in which single-valued selections from the image sets of the multifunction exhibit a restricted type of local Lipschitz continuity where the base point is fixed as one point of comparison. Generalized continuity properties of multifunctions like calmness can be applied to convergence analysis when the multifunction appropriately represents the iterates generated by some algorithm. Since it involves an essentially linear relationship between input and output, calmness gives essentially linear convergence results when it is applied directly to convergence analysis. We introduce a new continuity concept called 'supercalmness' where arbitrarily small calmness constants can be obtained near the base point, which leads to essentially superlinear convergence results. We also explore partial supercalmness and use a well-known generalized derivative to characterize both when a multifunction is supercalm and when it is partially supercalm. To illustrate the value of such characterizations, we explore in detail a new example of a general primal sequential quadratic programming method for nonlinear programming and obtain verifiable conditions to ensure convergence at a superlinear rate.

关键词： calmness multifunctions generalized continuity variational analysis convergence analysis sequential quadratic programming

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Optimal chiller loading for energy conservation using a hybrid whale optimization algorithm based on population membrane systems

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INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION 2022年第1期42卷 101-116页

作者： Mohammadbeigi, Amir Maroosi, Ali Hemmati, Mohammad Univ Torbat Heydarieh Dept Elect Engn Torbat Heydarieh Iran Univ Torbat Heydarieh Dept Comp Engn Torbat Heydarieh Iran

The optimal chiller loading (OCL) is one of the most essential issues for saving energy and costs. Because of the pervasive use of chiller systems in the world, even saving a small amount of energy consumption in a chiller system can be significant. This study introduces a hybrid algorithm that could achieve similar or better results than those presented in previous studies for OCL problem. The whale optimization algorithm (WOA) is a recent promising algorithm for solving optimization problems with the small number of tuning parameters. However, it suffers from its inefficient exploitation around the best solution. To address this shortcoming, WOA-SQP was introduced that uses a sequential quadratic programming (SQP) method to exploit efficiently the search space around the best solution obtained by WOA. Although, WOA-SQP could achieve good results, but the variance of its solutions is high for different runs on the same problem. The non-deterministic distributed parallel framework of the population P system (PPS) enhances the diversity of WOA-SQP to minimize the variance of the solutions that shows the stability of the algorithm. Simulation results of the proposed algorithm on several case studies show the better performance of the proposed algorithm in comparison with the recent approaches.

关键词： Whale Optimization Algorithm sequential quadratic programming population membrane systems optimal Chiller Loading

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Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem

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ANNALS OF OPERATIONS RESEARCH 2006年第1期148卷 81-94页

作者： Carlsson, Fredrik Forsgren, Anders Rehbinder, Henrik Eriksson, Kjell Royal Inst Technol KTH Dept Math SE-10044 Stockholm Sweden RaySearch Labs SE-11134 Stockholm Sweden

Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition.

关键词： IMRT optimization sequential quadratic programming quasi-Newton method

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A TANDEM APPROACH TO SELECTION OF MACHINABILITY DATA

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 1995年第2期10卷 79-86页

作者： YEO, SH RAHMAN, M WONG, YS NATL UNIV SINGAPORE DEPT MECH & PROD ENGN SINGAPORE 0511 SINGAPORE

One drawback of current machinability data systems is the inability to accommodate technological changes. Existing schemes to optimise machinability data are too specific and rigid. This paper describes the development of a methodology For a more effective selection of machinability data. The methodology incorporates various techniques, such as expert systems and mathematical programming. The unique feature of this system is the way machinability data are handled to arrive at the most suitable solution. The system accepts a wide range of data, from the very complete and specific to the very general. The more detailed and specific the data set is, the more credible the results will be. The machinability data in the data banks are easily updated and improved using feedback data from current shop floor production. The process of obtaining solutions from these banks is regarded as flexible optimisation. This paper reports on the optimisation methodology for multipass turning operations. Longitudinal turning, facing, taper turning and contour turning have been considered.

关键词： MACHINABILITY DATA MULTIPASS OPTIMIZATION sequential quadratic programming

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