An Implementation of a Parallel Generalized Branch and Bound Template

A branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n-dimensional pyramids and its maximum point is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally.

Section: Algorithmmentioning

confidence: 98%

Improved Lipschitz Bounds With the First Norm for Function Values Over Multidimensional Simplex

Paulavièius

Žilinskas

2008

“…A branch and bound template [2,3] may be used for implementation. Metaheuristic algorithms may be applied when problems are too large to be solved with guarantee.…”

Section: Multidimensional Scaling With City-block Distances Based On mentioning

confidence: 99%

Multidimensional Scaling With City‐block Distances Based on Combinatorial Optimization and Systems of Linear Equations

Žilinskas

2009

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. In this paper a two-level optimization based on combinatorial optimization and systems of linear equations is proposed exploiting piecewise quadratic structure of the objective function with city-block distances. The approach is tested experimentally and improvement directions are identified.

“…Third, we are not concentrated on finding the exact global minimum, it is sufficient to get a solution which improves the known engineering approximation. Thus in engineering applications, most popular optimization algorithms are based on specific classes of algorithms, such as the branch and bound (BB) strategy with simple heuristics for the definition of bounds (see, papers on implementations of parallel BB templates [3,4]), genetic, ant colony type algorithms [11,19] or the simulated annealing method [23]. If the dimension of a search space is small, then the Nelder-Mead simplex method can be used.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Solver for the Design of Oil Filters

Starikovičius

Čiegis

Iliev

2011

Self Cite

Nowadays, it is widely recognized that computer simulation plays a crucial role in designing oil filters used in the automotive industry. However, even a single direct simulation of the flow usually requires significant computational resources. Thus, it is obvious that solution of optimization problems is only feasible using parallel computers and algorithms.In this paper, we present a general master-slave parallel template, which was specially designed for the easy integration of direct parallel solvers into a parallel optimization tool. We show how an already existing direct solver for the 3D simulation of flow through the oil filter is integrated into our template to obtain a parallel optimization solver. Some capabilities and performance of this solver are demonstrated by solving geometry optimization problem of a filter element.