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

Speed and memory requirements of branch and bound algorithms depend on the selection strategy of which candidate node to process next. The goal of this paper is to experimentally investigate this influence to the performance of sequential and parallel branch and bound algorithms. The experiments have been performed solving a number of multidimensional test problems for global optimization. Branch and bound algorithm using simplicial partitions and combination of Lipschitz bounds has been investigated. Similar results may be expected for other branch and bound algorithms.

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“…However the first norm does not always give the best bounds [15]. In some cases combinations of bounds (3) may give better results.…”

Section: Branch and Bound With Simplicial Partitions And Improved Commentioning

confidence: 93%

Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds

Paulavičius¹,

Žilinskas²,

Grothey

2009

Optim Lett

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“…The Piyavskii type (4) Lipschitz bound with the first norm ϕ 1 was proposed in (Paulavičius, Žilinskas 2008): …”

Section: Combination Of Bounds With Various Normsmentioning

confidence: 99%

Influence of Lipschitz Bounds on the Speed of Global Optimization

Paulavičius

Žilinskas

2012

Technological and Economic Development of Economy

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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.

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“…An improved bound based on the first norm was proposed in (Paulavičius and Žilinskas 2008b), where a method from the first class is used:…”

Section: Lipschitz Optimizationmentioning

confidence: 99%

“…However, the bounds based on the first norm are not always best (Paulavičius and Žilinskas 2008b). In some cases, combinations of bounds (7) may give better results.…”

Section: Branch-and-bound With a Combination Of Various Bounds For LImentioning

confidence: 99%

“…In (Paulavičius and Žilinskas 2007), we have shown that, for n = 4, the number of function evaluations is smaller by 13% on the average and, for n = 5, 6, the number of function evaluations is smaller by 37% on the average, if combination (7) is used. In (Paulavičius and Žilinskas 2008b) it has been shown that the improved upper bound F (8) gives better results for Lipschitz optimization than that used as usual. Depending on the dimensionality of test problems, the number of function evaluations is from 4% to 30% smaller than with a simpler bound.…”

Section: Computational Comparison Of Various Boundsmentioning

confidence: 99%

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Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

Paulavičius¹,

Žilinskas²

2009

Technological and Economic Development of Economy

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Abstract. 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.

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

Cited by 13 publications

References 25 publications

Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds

Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds

Influence of Lipschitz Bounds on the Speed of Global Optimization

Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

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