Global optimization of non-convex piecewise linear regression splines

被引：8

作者：

Martinez, Nadia ^{[1
]}

Anahideh, Hadis ^{[2
]}

Rosenberger, Jay M. ^{[2
]}

Martinez, Diana ^{[3
]}

Chen, Victoria C. P. ^{[2
]}

Wang, Bo Ping ^{[4
]}

机构：

[1] Amer Airlines Inc, 4333 Amon Carter Blvd,HDQ1 MD 5358, Ft Worth, TX 76155 USA

[2] Univ Texas Arlington, Dept Ind & Mfg Syst Engn, Arlington, TX 76019 USA

[3] TMAC, 202 E Border St,Ste 323, Arlington, TX 76010 USA

[4] Univ Texas Arlington, Dept Mech & Aerosp Engn, Arlington, TX 76019 USA

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2017年 / 68卷 / 03期

基金：

美国国家科学基金会;

关键词：

Global optimization; Branch and bound; Surrogate methods; Multivariate adaptive regression splines; Crashworthiness; Genetic algorithms; DESIGN; ALGORITHM; CRASHWORTHINESS;

D O I：

10.1007/s10898-016-0494-5

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Multivariate adaptive regression spline (MARS) is a statistical modeling method used to represent a complex system. More recently, a version of MARS was modified to be piecewise linear. This paper presents a mixed integer linear program, called MARSOPT, that optimizes a non-convex piecewise linear MARS model subject to constraints that include both linear regression models and piecewise linear MARS models. MARSOPT is customized for an automotive crash safety system design problem for a major US automaker and solved using branch and bound. The solutions from MARSOPT are compared with those from customized genetic algorithms.

引用

页码：563 / 586

页数：24

共 50 条

[31] An Optimization Problem with a Separable Non-Convex Objective Function and a Linear Constraint
Djangir A. Babayev
George I. Bell
Journal of Heuristics, 2001, 7 : 169 - 184
[32] An optimization problem with a separable non-convex objective function and a linear constraint
Babayev, DA
Bell, GI
JOURNAL OF HEURISTICS, 2001, 7 (02) : 169 - 184
[33] DYNAMIC OPTIMIZATION WITH A NON-CONVEX TECHNOLOGY - THE CASE OF A LINEAR OBJECTIVE FUNCTION
MAJUMDAR, M
MITRA, T
REVIEW OF ECONOMIC STUDIES, 1983, 50 (01): : 143 - 151
[34] Parallel Global Optimization for Non-convex Mixed-Integer Problems
Barkalov, Konstantin
Lebedev, Ilya
SUPERCOMPUTING (RUSCDAYS 2019), 2019, 1129 : 98 - 109
[35] Global optimization of general non-convex problems with intermediate bilinear substructures
Zorn, Keith
Sahinidis, Nikolaos V.
OPTIMIZATION METHODS & SOFTWARE, 2014, 29 (03): : 442 - 462
[36] Trajectory planning based on non-convex global optimization for serial manipulators
Zhang, Shiyu
Dai, Shuling
Zanchettin, Andrea Maria
Villa, Renzo
APPLIED MATHEMATICAL MODELLING, 2020, 84 : 89 - 105
[37] Smoothing of piecewise linear splines and the application to piecewise linear fat splines
Department of Computer Science, University of Calgary, Calgary, Alta., Canada
不详
CAD Comput Aided Des, 6-7 (439-449):
[38] Natasha: Faster Non-Convex Stochastic Optimization via Strongly Non-Convex Parameter
Allen-Zhu, Zeyuan
INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 70, 2017, 70
[39] Smoothing of piecewise linear splines and the application to piecewise linear fat splines
Lin, Q
Rokne, JG
COMPUTER-AIDED DESIGN, 1996, 28 (6-7) : 439 - 449
[40] Nonparametric instrumental regression with non-convex constraints
Grasmair, M.
Scherzer, O.
Vanhems, A.
INVERSE PROBLEMS, 2013, 29 (03)

← 1 2 3 4 5 →