Yeboon Yun

A generalized model for data envelopment analysis

Abstract Data envelopment analysis (DEA) is a method to estimate a relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models have been developed: The CCR model, the BCC model and the FDH model are well known as basic DEA models. These models based on the domination structure in primal form are characterized by how to determine the production possibility set from a viewpoint of dual form; the convex cone, the convex hull and the free disposable hull for the observed data, respectively. In this study, we suggest a model called generalized DEA (GDEA) model, which can treat the above stated basic DEA models in a unified way. In addition, by establishing the theoretical properties on relationships among the GDEA model and those DEA models, we prove that the GDEA model makes it possible to calculate the efficiency of DMU incorporating various preference structures of decision makers. Furthermore, we propose a dual approach to GDEA, GDEA D and also show that GDEA D can reveal domination relations among all DMUs.

Sequential Approximate Multiobjective Optimization Using Computational Intelligence

This book highlights a new direction of multiobjective optimzation, which has never been treated in previous publications. When the function form of objective functions is not known explicitly as encountered in many practical problems, sequential approximate optimization based on metamodels is an effective tool from a practical viewpoint. Several sophisticated methods for sequential approximate multiobjective optimization using computational intelligence are introduced along with real applications, mainly engineering problems, in this book.

Generation of efficient frontiers in multi-objective optimization problems by generalized data envelopment analysis

Abstract In many practical problems such as engineering design problems, criteria functions cannot be given explicitly in terms of design variables. Under this circumstance, values of criteria functions for given values of design variables are usually obtained by some analyses such as structural analysis, thermodynamical analysis or fluid mechanical analysis. These analyses require considerably much computation time. Therefore, it is not unrealistic to apply existing interactive optimization methods to those problems. On the other hand, there have been many trials using genetic algorithms (GA) for generating efficient frontiers in multi-objective optimization problems. This approach is effective in problems with two or three objective functions. However, these methods cannot usually provide a good approximation to the exact efficient frontiers within a small number of generations in spite of our time limitation. The present paper proposes a method combining generalized data envelopment analysis (GDEA) and GA for generating efficient frontiers in multi-objective optimization problems. GDEA removes dominated design alternatives faster than methods based on only GA. The proposed method can yield desirable efficient frontiers even in non-convex problems as well as convex problems. The effectiveness of the proposed method will be shown through several numerical examples.

Multiple criteria decision making with generalized DEA and an aspiration level method

In this paper, we suggest an aspiration level approach using generalized data envelopment analysis (GDEA) and genetic algorithms (GA) in multiple criteria decision making such as engineering design problems. It will be shown that several Pareto optimal solutions close to an aspiration level of decision maker can be listed up as candidates of a final decision making solution by the proposed method. Through the robust design problem, it will be proved also that the aspiration level method using GDEA is useful for supporting a decision making of complex system. 2003 Elsevier B.V. All rights reserved.

A role of total margin in support vector machines

The support vector algorithm has paid attention on maximizing the shortest distance between sample points and discrimination hyperplane. This paper suggests the total margin algorithm which considers the distance between all data points and the separating hyperplane. The method extends existing support vector machine algorithms. In addition, the method improves the generalization error bound. Numerical studies show that the total margin algorithm provides good performance, comparing with the previous methods.

Support Vector Regression Based on Goal Programming and Multi-objective Programming

Support vector machine (SVM) is gaining much popularity as a powerful machine learning technique. SVM was originally developed for pattern classification and later extended to regression. One of main features of SVM is that it generalizes the maximal margin linear classifiers into high dimensional feature spaces through nonlinear mappings defined implicitly by kernels in the Hilbert space so that it may produce nonlinear classifiers in the original data space. On the oilier hand, the authors developed a family of various SVMs using multi-objective programming and goal programming (MOP/GF) techniques. This paper extends the family of SVM for classification to regression, and discusses their performance through numerical experiments.

MOP/GP models for machine learning

Abstract Techniques for machine learning have been extensively studied in recent years as effective tools in data mining. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problems with two class sets, its idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. This task is performed by solving a quadratic programming problem in a traditional formulation, and can be reduced to solving a linear programming in another formulation. However, the idea of maximal margin separation is not quite new: in the 1960s the multi-surface method (MSM) was suggested by Mangasarian. In the 1980s, linear classifiers using goal programming were developed extensively. This paper presents an overview on how effectively MOP/GP techniques can be applied to machine learning such as SVM, and discusses their problems.

Multi-objective Model Predictive Control

For many real-world problems, true function form cannot be given a prior. Consequently, for example, engineering design requires experiments and/or numerical simulations to evaluate objective and constraint functions as function in terms of design variables. However, those experiments/simulations are computationally expensive. For alleviating this burden of function evaluations, model predictive optimization (or surrogate modelbased optimization depending on literatures) methods have been used extensively in recent years. As a result, constructing good surrogate model with as few function evaluations as possible is essential to finding an optimal solution for problems. This research considers model predictive optimization problems under a dynamic environment with multiple objectives. Some techniques using machine learning such as support vector regression or radial basis function networks are applied to the generation of surrogate model. Although they are effective for model prediction, their prediction abilities may become worse due to a long prediction period. In order to develop accurate and stable prediction in model predictive optimization under a dynamic environment with multiple objectives, we propose computational intelligence methods with predetermined model, and investigate its effectiveness through numerical examples.

On Efficiency of Data Envelopment Analysis

In this paper, we suggest a new concept of “Value Free Efficiency” which does not introduce any value judgment for outputs and inputs. That is, similarly to the usual multiple criteria decision analysis, a Decision Making Unit (DMU) is defined to be efficient if there is no unit that consumes less inputs and produces more outputs than the DMU. In addition, we propose a generalized DEA model for estimating value free efficiency, ratio value efficiency proposed by Charnes, Cooper and Rhodes [4], and sum value efficiency proposed by Belton [2] and Belton and Vickers [3] as special cases. An illustrative example compares these concepts of efficiency.

Modified Support Vector Regression in outlier detection

In order to construct approximation functions on real-life data, it is necessary to remove outliers from the measured raw data before modeling. Although the standard Support Vector Regression based outlier detection methods for non-linear function with multidimensional input have achieved good performance, they have practical issues in computational costs and parameter adjustment. In this paper we propose a practical approach to outlier detection using modified SVR, which reduces computational cost and defines outlier threshold appropriately. We apply this method to both test and industrial data sets for validation.