Combination of two underestimators for univariate global optimization

2018 ◽  
Vol 52 (1) ◽  
pp. 177-186
Author(s):  
Mohand Ouanes ◽  
Mohammed Chebbah ◽  
Ahmed Zidna
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Branch And Bound Algorithm ◽  
Test Problems

In this work, we propose a new underestimator in branch and bound algorithm for solving univariate global optimization problems. The new underestimator is a combination of two underestimators, the classical one used in αBB method (see Androulakis et al. [J. Glob. Optim. 7 (1995) 337–3637]) and the quadratic underestimator developed in Hoai An and Ouanes [RAIRO: OR 40 (2006) 285–302]. We show that the new underestimator is tighter than the two underestimators. A convex/concave test is used to accelerate the convergence of the proposed algorithm. The convergence of our algorithm is shown and a set of test problems given in Casado et al. [J. Glob. Optim. 25 (2003) 345–362] are solved efficiently.

scholarly journals INFLUENCE OF LIPSCHITZ BOUNDS ON THE SPEED OF GLOBAL OPTIMIZATION

2012 ◽  
Vol 18 (1) ◽  
pp. 54-66 ◽  
Author(s):  
Remigijus Paulavičius ◽  
Julius Žilinskas
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Lipschitz Function ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Branch And Bound Algorithm ◽  
Test Problems ◽  
Global Optimization Methods

Global optimization methods based on Lipschitz bounds have been analyzed and applied widely to solve various optimization problems. In this paper a bound for Lipschitz function is proposed, which is computed using function values at the vertices of a simplex and the radius of the circumscribed sphere. The efficiency of a branch and bound algorithm with proposed bound and combinations of bounds is evaluated experimentally while solving a number of multidimensional test problems for global optimization. The influence of different bounds on the performance of a branch and bound algorithm has been investigated.

AN IMPLEMENTATION OF A PARALLEL GENERALIZED BRANCH AND BOUND TEMPLATE

2007 ◽  
Vol 12 (3) ◽  
pp. 277-289 ◽  
Author(s):  
Milda Baravykaitė ◽  
Raimondas Čiegis
Keyword(s):  
Global Optimization ◽  
Load Balancing ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Test Problems ◽  
Search Spaces ◽  
Parallel Version ◽  
Derivative Free ◽  
Template Library ◽  
Selection Of

Branch and bound (BnB) is a general algorithm to solve optimization problems. We present a template implementation of the BnB paradigm. A BnB template is implemented using C++ object oriented paradigm. MPI is used for underlying communications. A paradigm of domain decomposition (data parallelization) is used to construct a parallel algorithm. To obtain a better load balancing, the BnB template has the load balancing module that allows the redistribution of search spaces among the processors at run time. A parallel version of user's algorithm is obtained automatically. A new derivative-free global optimization algorithm is proposed for solving nonlinear global optimization problems. It is based on the BnB algorithm and its implementation is done by using the developed BnB algorithm template library. The robustness of the new algorithm is demonstrated by solving a selection of test problems.

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.

A Two-Phase Complete Algorithm for Multi-Objective Distributed Constraint Optimization

2014 ◽  
Vol 18 (4) ◽  
pp. 573-580
Author(s):  
Alexandre Medi ◽  
◽  
Tenda Okimoto ◽  
Katsumi Inoue ◽  
◽  
...  
Keyword(s):  
Branch And Bound ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Branch And Bound Algorithm ◽  
Constraint Optimization ◽  
Distributed Constraint Optimization ◽  
Multi Objective ◽  
Multi Agent ◽  
Distributed Constraint Optimization Problem

A Distributed Constraint Optimization Problem (DCOP) is a fundamental problem that can formalize various applications related to multi-agent cooperation. Many application problems in multi-agent systems can be formalized as DCOPs. However, many real world optimization problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Distributed Constraint Optimization Problem (MO-DCOP) is an extension of a mono-objective DCOP. Compared to DCOPs, there exists few works on MO-DCOPs. In this paper, we develop a novel complete algorithm for solving an MO-DCOP. This algorithm utilizes a widely used method called Pareto Local Search (PLS) to generate an approximation of the Pareto front. Then, the obtained information is used to guide the search thresholds in a Branch and Bound algorithm. In the evaluations, we evaluate the runtime of our algorithm and show empirically that using a Pareto front approximation obtained by a PLS algorithm allows to significantly speed-up the search in a Branch and Bound algorithm.

scholarly journals Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Chun-Feng Wang ◽  
Yan-Qin Bai
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Linearization Method ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming ◽  
Pruning Techniques

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

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