A Framework for Algorithms in Globally Optimal Design

1989 ◽  
Vol 111 (3) ◽  
pp. 353-360 ◽  
Author(s):  
P. Hansen ◽  
B. Jaumard ◽  
S. H. Lu
Keyword(s):  
Combinatorial Optimization ◽  
Optimal Design ◽  
Branch And Bound ◽  
General Framework ◽  
Ad Hoc ◽  
Design Problems ◽  
Branch And Bound Algorithms ◽  
Monotonicity Analysis

Many problems of globally optimal design have been solved in the literature using monotonicity analysis and a variety of tests, often applied in an ad hoc way. These tests are developed here, expressed mathematically and classified according to the conclusions they yield. Moreover, many new tests, similar to those used in combinatorial optimization, are presented. Finally, a general framework is proposed in which branch-and-bound algorithms for globally optimal design problems can be expressed.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1988 ◽  
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Design Problems ◽  
Local Optima ◽  
Solution Strategies ◽  
Active Constraints ◽  
Active Sets ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Abstract Solution strategies for optimal design problems in nonlinear programming formulations may require verification of optimality for constraint-bound points. These points are candidate solutions where the number of active constraints is equal to the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs and it would be desirable to identify them early, or exclude them in a strategy using active sets. Potential constrained-bound solutions are usually identified based on the principles of monotonicity analysis. This article discusses some cases where these points are in fact global or local optima.

Activity Analysis: Simplifying Optimal Design Problems Through Qualitative Partitioning

1995 ◽  
Author(s):  
Brian C. Williams ◽  
Jonathan Cagan
Keyword(s):  
Numerical Analysis ◽  
Optimal Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Activity Analysis ◽  
Design Problems ◽  
Gradient Based ◽  
Monotonicity Analysis

Abstract Activity analysis is introduced as a means to strategically cut away subspaces of a design problem that can quickly be ruled out as suboptimal. This results in focused regions of the space in which additional symbolic or numerical analysis can take place. Activity analysis is derived from a qualitative abstraction of the Karush-Kuhn-Tucker conditions of optimality, used to partition an optimization problem into regions which are nonstationary and qualitatively stationary (qstationary). Activity analysis draws from the fields of gradient-based optimization, conflict-based approaches of combinatorial satisficing search, and monotonicity analysis.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1993 ◽  
Vol 115 (3) ◽  
pp. 374-379
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Active Set ◽  
Design Problems ◽  
Local Optima ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.

scholarly journals TEMPLATE REALIZATION OF GENERALIZED BRANCH AND BOUND ALGORITHM

2005 ◽  
Vol 10 (3) ◽  
pp. 217-236 ◽  
Author(s):  
M. Baravykaite ◽  
R. Čiegis ◽  
J. Žilinskas
Keyword(s):  
Global Optimization ◽  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Branch And Bound Algorithm ◽  
Computational Experiments ◽  
Branch And Bound Algorithms ◽  
Parallel Branch And Bound

In this work we consider a template for implementation of parallel branch and bound algorithms. The main aim of this package to ease implementation of covering and combinatorial optimization methods for global optimization. Standard parts of global optimization algorithms are implemented in the package and only method specific rules should be implemented by the user. The parallelization part of the tool is described in details. Results of computational experiments are presented and discussed. Straipsnyje pristatyta apibendrinto šaku ir režiu algoritmo šablono realizacija. Irankis skirtas palengvinti nuosekliuju ir lygiagrečiuju optimizacijos uždaviniu programu kūrima. Nuo uždavinio nepriklausančios algoritmo dalys yra idiegtos šablone ir vartotojui reikia sukurti tik nuo uždavinio priklausančiu daliu realizacija. Šablone idiegti keli lygiagretieji algoritmai, paremti tyrimo srities padalinimu tarp procesoriu. Pateikiami skaičiavimo eksperimentu rezultatai.

Language, procedures, and the non-perceptual origin of natural number concepts

2016 ◽  
Author(s):  
David Barner
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Number Words ◽  
Linguistic Markers ◽  
Logical Foundations ◽  
Large Numbers ◽  
Perceptual Representations ◽  
Positive Integers ◽  
Perceptual Systems

Perceptual representations – e.g., of objects or approximate magnitudes –are often invoked as building blocks that children combine with linguisticsymbols when they acquire the positive integers. Systems of numericalperception are either assumed to contain the logical foundations ofarithmetic innately, or to supply the basis for their induction. Here Ipropose an alternative to this general framework, and argue that theintegers are not learned from perceptual systems, but instead arise toexplain perception as part of language acquisition. Drawing oncross-linguistic data and developmental data, I show that small numbers(1-4) and large numbers (~5+) arise both historically and in individualchildren via entirely distinct mechanisms, constituting independentlearning problems, neither of which begins with perceptual building blocks.Specifically, I propose that children begin by learning small numbers(i.e., *one, two, three*) using the same logical resources that supportother linguistic markers of number (e.g., singular, plural). Several yearslater, children discover the logic of counting by inferring the logicalrelations between larger number words from their roles in blind countingprocedures, and only incidentally associate number words with perception ofapproximate magnitudes, in an *ad hoc* and highly malleable fashion.Counting provides a form of explanation for perception but is not causallyderived from perceptual systems.

scholarly journals Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning

2016 ◽  
Vol 19 ◽  
pp. 79-102 ◽  
Author(s):  
David R. Morrison ◽  
Sheldon H. Jacobson ◽  
Jason J. Sauppe ◽  
Edward C. Sewell
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithms ◽  
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