SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems

This paper introduces a surrogate model based algorithm for computationally expensive mixed-integer black-box global optimization problems with both binary and non-binary integer variables that may have computationally expensive constraints. The goal is to find accurate solutions with relatively few...

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Bibliographic Details
Published in:Computers & operations research Vol. 40; no. 5; pp. 1383 - 1400
Main Authors: Müller, Juliane, Shoemaker, Christine A., Piché, Robert
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2013
Elsevier
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Black-box
Comparative analysis
Computation
Derivative-free
Exact sciences and technology
Experimental design
Fundamental areas of phenomenology (including applications)
Global optimization
Integer programming
Integers
Mathematical analysis
Mathematical models
Mathematical problems
Mathematical programming
Mathematics
Mixed-integer optimization
Multimodal
Nonlinear
Nonlinearity
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Parametric inference
Physics
Probability and statistics
Radial basis functions
Sciences and techniques of general use
Searching
Solid mechanics
Static elasticity (thermoelasticity...)
Statistics
Structural and continuum mechanics
Studies
Surrogate model
Nonlinear
Global optimization
Radial basis functions
Surrogate model
Multimodal
Black-box
Mixed-integer optimization
Derivative-free
Black box
Adaptive method
Optimization
Optimal design
Function evaluation
Nonsmooth analysis
Response surface
Metamodel
Branch and bound method
Global optimum
Mixed integer programming
Search algorithm
Radial basis function
Genetic algorithm
Implicit enumeration method
Mixed problem
Objective function
Reliability
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:This paper introduces a surrogate model based algorithm for computationally expensive mixed-integer black-box global optimization problems with both binary and non-binary integer variables that may have computationally expensive constraints. The goal is to find accurate solutions with relatively few function evaluations. A radial basis function surrogate model (response surface) is used to select candidates for integer and continuous decision variable points at which the computationally expensive objective and constraint functions are to be evaluated. In every iteration multiple new points are selected based on different methods, and the function evaluations are done in parallel. The algorithm converges to the global optimum almost surely. The performance of this new algorithm, SO-MI, is compared to a branch and bound algorithm for nonlinear problems, a genetic algorithm, and the NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search) algorithm for mixed-integer problems on 16 test problems from the literature (constrained, unconstrained, unimodal and multimodal problems), as well as on two application problems arising from structural optimization, and three application problems from optimal reliability design. The numerical experiments show that SO-MI reaches significantly better results than the other algorithms when the number of function evaluations is very restricted (200–300 evaluations).
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2012.08.022