Dual Relaxation and Branch-and-Bound Techniques for Multiobjective Optimization

1984 ◽  
pp. 84-90
Author(s):  
Paolo Serafini
Keyword(s):  
Multiobjective Optimization ◽  
Branch And Bound ◽  
Dual Relaxation ◽  
Branch And Bound Techniques

Timetable-Based Transit Assignment Using Branch and Bound Techniques

2001 ◽  
Vol 1752 (1) ◽  
pp. 100-107 ◽  
Author(s):  
Markus Friedrich ◽  
Ingmar Hofsaess ◽  
Steffen Wekeck
Keyword(s):  
Branch And Bound ◽  
Transit Assignment ◽  
Branch And Bound Techniques

Branch-and-Bound Techniques

1990 ◽  
pp. 123-146
Author(s):  
J. M. Proth ◽  
H. P. Hillion
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Techniques

GLOBAL OPTIMIZATION USING THE BRANCH‐AND‐BOUND ALGORITHM WITH A COMBINATION OF LIPSCHITZ BOUNDS OVER SIMPLICES

2009 ◽  
Vol 15 (2) ◽  
pp. 310-325 ◽  
Author(s):  
Remigijus Paulavičius ◽  
Julius Žilinskas
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
The Other ◽  
Branch And Bound Algorithm ◽  
Global Optimization Algorithm ◽  
Lipschitz Optimization ◽  
Branch And Bound Algorithms ◽  
Simple Bounds ◽  
Branch And Bound Techniques

Many problems in economy may be formulated as global optimization problems. Most numerically promising methods for solution of multivariate unconstrained Lipschitz optimization problems of dimension greater than 2 use rectangular or simplicial branch‐and‐bound techniques with computationally cheap, but rather crude lower bounds. The proposed branch‐and‐bound algorithm with simplicial partitions for global optimization uses a combination of 2 types of Lipschitz bounds. One is an improved Lipschitz bound with the first norm. The other is a combination of simple bounds with different norms. The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well‐known algorithms. The proposed algorithm often outperforms the comparable branch‐and‐bound algorithms. Santrauka Daug įvairių ekonomikos uždavinių yra formuluojami kaip globaliojo optimizavimo uždaviniai. Didžioji dalis Lipšico globaliojo optimizavimo metodų, tinkamų spręsti didesnės dimensijos, t. y. n > 2, uždavinius, naudoja stačiakampį arba simpleksinį šakų ir rėžių metodus bei paprastesnius rėžius. Šiame darbe pasiūlytas simpleksinis šakų ir rėžių algoritmas, naudojantis dviejų tipų viršutinių rėžių junginį. Pirmasis yra pagerintas rėžis su pirmąja norma, kitas – trijų paprastesnių rėžių su skirtingomis normomis junginys. Gautieji eksperimentiniai pasiūlyto algoritmo rezultatai yra palyginti su kitų gerai žinomų Lipšico optimizavimo algoritmų rezultatais.

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