김광수 (Kim, Kwangsoo)

곽취 (Guo, Cui)

안극동 (Yan, Kedong)

마정유 (Ma, Zhengyu)

장인용 (Jang, In-Yong)

김학영 (Kim, Hak-Young)

김동섭 (Kim, Dong-Sup)

곽재옥 (Kwak, Jae-Ok)

김제훈 (Kim, Je-Hun)

조결영 (Zhao, Jieying)

크말라 페브리하디니 (Kemala, Febrihadini)

노상균 (Noh, Sangkyun)

The Mathematical Optimization & Operations Research Lab, affiliated with the Department of Industrial Management Engineering at Korea University, focuses on developing mathematical models to address real-world problems. The lab's research encompasses global optimization, combinatorial optimization, and nonlinear programming, with the goal of creating efficient and accurate solutions for complex problems. Key research areas include Boolean Logical Data Analytics and Mathematical Data Analysis, utilizing mathematical optimization techniques for data classification and analysis.

고려대학교 산업경영공학부 정보학연구실에서는 실제 문제 해결을 위한 수리 모형 개발을 수행한다. 주요 연구 분야는 다음과 같다. 전역 최적화(조합 최적화 및 비선형 계획법) 이론과 알고리즘 개발, Boolean Logical Data Analytics, 수리 최적화 기법을 활용한 데이터 분류 및 분석 연구를 진행한다.

Nonlinear separation of data via mixed 0-1 integer and linear programming

A compact mean-variance-skewness model for large-scale portfolio optimization and its application to the NYSE Market

Global Optimization of Multiplicative Programs

Analysis of Bounds for Multilinear Functions

A Branch-and-Reduce Approach to Global Optimization

Graph, Clique and Facet of Boolean Logical Polytope

Strong Valid Inequalities for Boolean Logical Pattern Generation

0-1 Multilinear Programming as a Unifying Theory for LAD Pattern Generation

MILP Approach to Pattern Generation in Logical Analysis of Data

A LAD-based method for selecting short oligo probes for genotyping applications

Comments on "An Efficient Algorithm for Solving Generalized Linear Multiplicative Programming" by S. Liu and Y. Zhao

On Pareto-Optimal Boolean Logical Patterns for Numerical Data

Spherical Classification of Data; a New Rule-Based Learning Method

A Multi-Term, Polyhedral Relaxation of a 0-1 Multilinear Function for Boolean Logical Pattern Generation

Compact MILP Models for Optimal and Pareto-Optimal LAD Patterns

General Set Covering for Feature Selection in Data Mining

Biomedical Informatics and OR

Data separation via a finite number of discriminant functions: a global optimization approach

Pattern classification via k-piecewise linear discriminants

A Simulation-Based Heuristic Procedure for Analyzing Human Postural Balance

Robust metaheuristic algorithm for redundancy optimization in large-scale complex systems

Global Optimization of Nonconvex NLPs and MINLPs with Applications in Process Design

Generating Interpretable Patterns for Biomedical Image Classification

Analysis of Brain fMRI Data via Topological Data Clustering Method IoPS

Identifying Combinatorial Significance for Classification of Alzheimer’s Disease Proteomics Expression with Logical Analysis of Data

Cliques for Multi-Term Linearization of 0–1 Multilinear Program for Boolean Logical Pattern Generation

A heuristic method for selecting support features from large datasets

Selecting genotyping oligo prbes via logical analysis of data

Efficient Tabu Search-Based Procedure for Optimal Redundancy Allocation in Complex System Reliability

제한된 데이터 환경에서의 반도체 설비 유지보수 전략: 생존 분석 기반 정비 데이터 분석

경영과학 방법론을 통한 사회정치적 의사결정 및 쟁점 이해:조합최적화 기반 신고리 5·6호기 원전공론화 위원회 설문 데이터 분석

단기 항공수요 예측을 위한 경제지표의 LAD 분석

Short Note on Optimizing Feature Selection to Improve Medical Diagnosis

Set Covering 기반의 대용량 오믹스데이터 특징변수 추출기법

SPC 차트를 이용한 포트폴리오 관리

목표계획법을 이용한 경계부대 근무편성에 관한 연구

최적화에 기반을 둔 LAD의 패턴 생성 기법

혼합정수 선형계획법 기반의 비선형 패턴 분류 기법

An Online Framework for Logical Analysis of Data with Dynamic Cutpoint Generation and Incremental Pattern Refinement

Efficient and Stable Pallet Loading via Semi-Online 3D Bin Packing: A Case Study in E-Commerce

Overcoming Spatial Feature Limitations in Image Classification through Convolutional Logical Analysis of Data

Data Classification and hypergraph -Part I

Bipartite Graphs for Boolean Pattern Recognition

Finding Locally Maximal Boolean Patterns from Numerical Data

Maximul Independent Set for Boolean Pattern Recognition

Graph Reduction & Row Generation Schemes for Finding Maximum Independent Set

B-D Rates of Simplices for Persistent Homology of Point Cloud Data

Hypergraph and Strong Valid Inequalities for Boolean Logical Pattern Generation

Property of n-Simplex Coveredness and n-Spherical Complex for Topological Data Clustering

위상학적 의료영상 데이터의 분석을 위한 호몰로지의 불변구간 정의

데이터 분류에 관한 다중선형 함수의 하이퍼그래프 분석

Topological Clustering Method Based on Newly Defined Persistency using Simplex Coveredness and
n-Space Complex

Logical Analysis of Sociological Data: Case Study of 'Participatory Surveys for Public Deliberation on Shin-Gori Nuclear Reactors No. 5 & 6'

Boolean logic pattern analysis of social phenomena via mathematical data analysis

위상학적 클러스터링 방법론: 단체덮힘성과
n-공간복합체를 이용한 불변성의 새로운 정의

불변구조 탐색을 통한 뇌 fMRI 데이터의 위상학적 분석

불변호몰로지에 기반한 불린로직패턴 확장기법 연구

불린로직 패턴 생성을 위한 위상적 데이터 융합･선택

위상학적 데이터 지도학습 기법: 불변구간 결정 이론과 순도복합체

수리적 데이터분석을 통한 사회현상의 패턴분석 및 의사결정의 유용성

Strong Polyhedral Relaxation of a 0-1 Multilinear Program via Hypergraph

수리적 데이터 분석의 사회과학적 유용성

Mathematical Data Analysis: an OR Perspective

Hypergraph Theoretic Polyhedral Relaxation of a Class of 0-1 Polynomial Program

On Upper Bounding of 0-1 Multilinear Function for Boolean Logical Pattern Generation

Rule-based Learning via Spherical Classification of Data

Free Disposal Hull 분석을 통한 공공기관 예산의 최적 편성

Global Optimization Approach to Implementing an Optimal Boolean Logic Data Classifier

Portfolio Selection and Management via Statistical Analysis of Economic Indicators

A Rectified LAD for Numerical Data

Compact 0-1 Linearization of 0-1 Multilinear Program in Data Mining

0-1 Multilinear Programming & LAD Patterns

Compact MILP models for optimal and Pareto-optimal LAD patterns

Meta-heuristic procedure for finding optimal LAD patterns

MILP approach to separation of nonconvex data

An Implementation of LAD for Large-scale Datasets

A Tabu-Search Algorithm for Finding Efficient Solutions to an MILP Model for Separation of Data

An MILP-based methodology for data classification

A Heuristic Method for Selecting Support Features from Large Datasets

Selecting Genotyping Oligo Probes via Logical Analysis of Data

Separation of data via concurrently determined discriminant functions

SPC 기법에 기반을 둔 포트폴리오 관리

An MILP Approach to Binary Classification by Generalized Piecewise Nonlinear and Nonconvex Discriminant Functions

최적화에 근거한 LAD의 패턴생성 기법

혼합정수 선형계획법 기반의 비선형, 비볼록 패턴 분류 기법

Wisconsin Breast Cancer Diagnosis via Global Optimization

MILP Approach for Pattern Generation in Logical Analysis of Data

New MILP Formulation for Pattern Generation in LAD

Binary Classification via k-Piecewise Linear Discriminants

RYOO, Hong Seo

This paper presents an algorithm for finding global solutions of nonconvex nonlinear programs (NLPs) and mixed-integer nonlinear programs (MINLPs). The approach is based on the solution of a sequence of convex underestimating subproblems generated by evolutionary subdivision of the search region. The key components of the algorithm are new optimality-based and feasibility-based range reduction tests. The former use known feasible solutions and perturbation results to exclude inferior parts of the search region from consideration, while the latter analyze constraints to obtain valid inequalities. Furthermore, the algorithm integrates these devices with an efficient local search heuristic. Computational results demonstrate that the algorithm compares very favorably to several other current approaches when applied to a large collection of global optimization and process design problems. It is typically faster …

Global optimization of nonconvex NLPs and MINLPs with applications in process design

This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of these techniques, we incorporate them within the branch-and-bound framework. This results in a branch-and-reduce global optimization algorithm. A detailed discussion of the algorithm components and theoretical properties are provided. Specialized algorithms for polynomial and multiplicative programs are developed. Extensive computational results are presented for engineering design problems, standard global optimization test problems, univariate polynomial programs, linear multiplicative programs, mixed-integer nonlinear programs and concave quadratic programs. For the problems solved, the computer implementation of the proposed algorithm provides very accurate solutions in modest …

A branch-and-reduce approach to global optimization

This paper develops global optimization algorithms for linear multiplicative and generalized linear multiplicative programs based upon the lower bounding procedure of Ryoo and Sahinidis [30] and new greedy branching schemes that are applicable in the context of any rectangular branch-and-bound algorithm. Extensive computational results are presented on a wide range of problems from the literature, including quadratic and bilinear programs, and randomly generated large-scale multiplicative programs. It is shown that our algorithms make possible for the first time the solution of large and complex multiplicative programs to global optimality.

Global optimization of multiplicative programs

We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave envelope for the product of p variables over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}_{^ + }^p $$ \end{document}.

Analysis of bounds for multilinear functions

Pattern generation methods for the Logical Analysis of Data (LAD) have been term-enumerative in nature. In this paper, we present a Mixed 0–1 Integer and Linear Programming (MILP) approach that can identify LAD patterns that are optimal with respect to various previously studied and new pattern selection preferences. Via art of formulation, the MILP-based method can generate optimal patterns that also satisfy user-specified requirements on prevalence, homogeneity and complexity. Considering that MILP problems with hundreds of 0–1 variables are easily solved nowadays, the proposed method presents an efficient way of generating useful patterns for LAD. With extensive experiments on benchmark datasets, we demonstrate the utility of the MILP-based pattern generation.

Milp approach to pattern generation in logical analysis of data

This paper develops MILP models for various optimal and Pareto-optimal LAD patterns that involve at most 2n 0–1 decision variables, where n is the number of support features for the data under analysis, which usually is small. Noting that the previous MILP pattern generation models are defined in 2n+m 0–1 variables, where m is the number of observations in the dataset with m≫n in general, the new models are expected to generate useful LAD patterns more efficiently. With experiments on six well-studied machine learning datasets, we first demonstrate the efficiency of the new MILP models and next use them to show different utilities of strong prime patterns and strong spanned patterns in enhancing the overall classification accuracy of a LAD decision theory.

This paper develops a portfolio optimization model that uses the first three moments of the distribution of the rate of return on investment in selecting portfolios. An alternative measure of skewness is designed for the purpose, and, in the grand scheme of compact factorization, the proposed model is transformed to an equivalent quadratic program with a quadratic constraint with 2 T nonlinear variables and terms, where usually T ⩽50. Extensive computational results are obtained on a real-world dataset of the returns of about 3500 stocks that were traded in the NYSE from 3 January to 17 September 2002. In summary, the portfolios built by the proposed model gave the average return on investment of 66.85% over the course of 150 trading days, a period in time when US economy and stock markets suffered tremendously after the tragic events of September 2001.

A compact mean-variance-skewness model for large-scale portfolio optimization and its application to the NYSE market

Specializing a general framework of logical analysis of data for efficiently handling large-scale genomic data, we develop in this paper a probe design method for selecting short oligo probes for genotyping applications. When tested on genomic sequences obtained from the National Center of Biotechnology Information in various monospecific and polyspecific in silico experiments, the proposed probe design method was able to select a small number of oligo probes of length 7 or 8 nucleotides that perfectly classified all unseen testing sequences. These results demonstrate the efficacy of the proposed probe design method and illustrate the usefulness and potential a well-designed optimization-based probe selection method has in genotyping applications.

This paper revisits the Boolean logical requirement of a pattern and develops 0-1 multilinear programming (MP) models for (Pareto-)optimal patterns for logical analysis of data (LAD). We show that all existing and also new pattern generation models can naturally be obtained from the MP models via linearization techniques for 0-1 multilinear functions. Furthermore, 0-1 MP provides an insight for understanding how different and independently developed models for a particular type of pattern are inter-related. These show that 0-1 MP presents a unifying theory for pattern generation in LAD.

0-1 multilinear programming as a unifying theory for LAD pattern generation

0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.

Strong valid inequalities for Boolean logical pattern generation

Portfolio management deals with decision making on'when'and'how'to revise an existing portfolio. In this paper, we show that a classical statistical process control (SPC) chart for normal data, a wellestablished tool in quality engineering, can effectively be used for signaling times for revising a portfolio. Noting that the day-to-day performance of a portfolio may be auto-correlated, we use the exponentially weighted moving average center-line chart to develop an automatic portfolio management procedure. The portfolio management procedure is extensively tested on historical data of equities traded in the Korea Exchange (KRX), the American Stock Exchange (AMEX), and the New York Stock Exchange (NYSE). In comparison with the performances of the KOSPI, XAX, and NYA indices during the same time periods, results from these experiments show that SPC chart-based portfolio revision presents itself a convenient and reliable method for optimally managing portfolios.

Portfolio management using statistical process control chart

Based upon the general tabu search methodology, this paper develops a robust metaheuristic algorithm for the redundancy optimization in large-scale complex system reliability that performs a rigorous search of the “attractive” feasible space and is capable of escaping from a local solution. An illustrative example is provided and extensive computational results are reported on two test problems from the literature (Aggarwal, 1976; Shi, 1987) and also on randomly generated large-scale instances of complex systems with up to 200 components. The computational results indicate that the proposed metaheuristic algorithm possesses a superior robustness and efficiency for solving the class of hard optimization problems studied in this paper.

This paper clarifies the difference between intrinsically 0–1 data and binarized numerical data for Boolean logical patterns and strengthens mathematical results and methods from the literature on Pareto-optimal LAD patterns. Toward this end, we select suitable pattern definitions from the literature and adapt them with attention given to unique characteristics of individual patterns and the disparate natures of Boolean and numerical data. Next, we propose a set of revised criteria and definitions by which useful LAD patterns are clearly characterized for both 0–1 and real-valued data. Furthermore, we fortify recent pattern generation optimization models and demonstrate how earlier results on Pareto-optimal patterns can be adapted in accordance with revised pattern definitions. A numerical study validates practical benefits of the results of this paper through optimization-based pattern generation experiments.

On Pareto-optimal Boolean logical patterns for numerical data

0–1 multilinear program (MP) holds a unifying theory to LAD pattern generation. This paper studies a multi-term relaxation of the objective function of the pattern generation MP for a tight polyhedral relaxation in terms of a small number of stronger 0–1 linear inequalities. Toward this goal, we analyze data in a graph to discover useful neighborhood properties among a set of objective terms around a single constraint term. In brief, they yield a set of facet-defining inequalities for the 0–1 multilinear polytope associated with the McCormick inequalities that they replace. The construction and practical utility of the new inequalities are illustrated on a small example and thoroughly demonstrated through numerical experiments with 12 public machine learning datasets.

A multi-term, polyhedral relaxation of a 0–1 multilinear function for Boolean logical pattern generation

This paper develops a new methodology for pattern classification by concurrently determined k piecewise linear and convex discriminant functions. Toward the end, we design a new l 1 -norm distance metric for measuring misclassification errors and use it to develop a mixed 0–1 integer and linear program (MILP) for the k piecewise linear and convex separation of data. The proposed model is meritorious in that it considers the synergy as well as the individual role of the k hyperplanes in constructing a decision surface and exploits the advances in theory and algorithms and the advent of powerful softwares for MILP for its solution. With artificially created data, we illustrate pros and cons of pattern classification by the proposed methodology. With six benchmark classification datasets, we demonstrate that the proposed approach is effective and competitive with well-established learning methods. In summary, the …

Pattern classification by concurrently determined piecewise linear and convex discriminant functions

This paper presents a new mathematical programming-based learning methodology for separation of two types of data. Specifically, we develop a new l 1 -norm error distance metric and use it to develop a Mixed 0–1 Integer and Linear Programming (MILP) model that optimizes the interplay of user-provided discriminant functions, including kernel functions for support vector machines, to implement a nonlinear, nonconvex and/or disjoint decision boundary for the best separation of data at hand. With the concurrent optimization of discriminant functions, the MILP-based learning can be used for finding the optimal and least complex classification rule for noise-free data and for implementing a most robust classification rule for real-life data with noise. With extensive experiments on separation of two dimensional artificial datasets that are clean and noisy, we graphically illustrate the aforementioned advantages of the …

Nonlinear separation of data via Mixed 0–1 Integer and Linear Programming

This paper presents a mixed 0–1 integer and linear programming (MILP) model for separation of data via a finite number of non-linear and non-convex discriminant functions. The MILP model concurrently optimizes the parameters of the user-provided individual discriminant functions to implement a decision boundary for an optimal separation of data under analysis. The performance of the MILP-based classification of data is illustrated on randomly generated two dimensional datasets and extensively tested on six well-studied datasets in data mining research, in comparison with three well-established supervised learning methodologies, namely, the multisurface method, the logical analysis of data and the support vector machines. Numerical results from these experiments show that the new MILP-based classification of data is an effective and useful methodology for supervised learning.

In this paper, we develop clinical Alzheimer’s Disease pattern as a combination of protein expression quantity using logical analysis of data on ROSMAP brain samples [1]. As a result, 14 transcripts are selected as support markers and compose interpretable patterns. These patterns show far statistical significance than any individual transcripts. In addition, patterns also indicate novel combinations of transcripts that have a little relation on the STRING network. Our result demonstrates a possible novel approach on analyzing interconnected transcripts, expecting a full pathology of the Alzheimer’s Disease.

Identifying combinatorial significance for classification of alzheimer’s disease proteomics expression with logical analysis of data

0–1 multilinear program (MP) holds a unifying theory to Boolean logical pattern generation. For a tighter polyhedral relaxation of MP, this note exploits cliques in the graph representation of data under analysis to generate valid inequalities for MP that subsume all previous results and, collectively, provide a much stronger relaxation of MP. A preliminary numerical study demonstrates strength and practical benefits of the new results.

Cliques for multi-term linearization of 0–1 multilinear program for Boolean logical pattern generation

Logical analysis of data (LAD) discovers useful knowledge from a set of data in the form of a Boolean pattern for classifying future data. Generating a pattern has been shown to be equivalent to solving a 0–1 multilinear program (MP). Thus, the success of LAD is tightly related to how efficiently practical instances of pattern generation MP’s can be solved. For a polyhedral relaxation of LAD pattern generation MP, this paper introduces a new notion of similarity among data that allows for simultaneously relaxing multiple terms of the objective function of MP into a single valid inequality for the Boolean MP polytope. Specifically, we present a framework for constructing three types of strong valid inequalities from cliques in multiple graph representations of data that collectively yield a tight polyhedral relaxation of MP. Furthermore, we specify conditions under which each type of the new inequalities defines a facet of the MP …

정보학연구실

교수님 소개

류홍서

연구실 소개

연구실 키워드

알럼나이가 간 회사

연구실 지원 방법

대우 조건

연도별 논문 인용수

저널 & 학회 논문 출판 수

연구실 논문 목록

제한된 데이터 환경에서의 반도체 설비 유지보수 전략: 생존 분석 기반 정비 데이터 분석

An Online Framework for Logical Analysis of Data with Dynamic Cutpoint Generation and Incremental Pattern Refinement

Efficient and Stable Pallet Loading via Semi-Online 3D Bin Packing: A Case Study in E-Commerce

연구실 보유 특허

대학별 입시끈

우리 연구실 모집

교수님 소개

류홍서

연구실 키워드

알럼나이가 간 회사

연구실 지원 방법

대우 조건

연도별 논문 인용수

저널 & 학회 논문 출판 수

연구실 논문 목록

제한된 데이터 환경에서의 반도체 설비 유지보수 전략: 생존 분석 기반 정비 데이터 분석

An Online Framework for Logical Analysis of Data with Dynamic Cutpoint Generation and Incremental Pattern Refinement

Efficient and Stable Pallet Loading via Semi-Online 3D Bin Packing: A Case Study in E-Commerce

연구실 보유 특허

최근 3년간 연구실적 높은 연구실

대학별 입시끈

우리 연구실 모집