scholarly journals Interval Tests and Contractors Based on Optimality Conditions for Bound-Constrained Global Optimization

2020 ◽  
Vol 29 (03n04) ◽  
pp. 2060001
Author(s):  
Laurent Granvilliers
Keyword(s):  
Experimental Study ◽  
Optimality Conditions ◽  
Branch And Bound ◽  
Global Optimum ◽  
Constrained Global Optimization ◽  
First Order ◽  
Branch And Bound Algorithms ◽  
Complete Search ◽  
Monotonicity Test ◽  
Interval Branch And Bound

We study the problem of finding the global optimum of a nonlinear real function over an interval box by means of complete search techniques, namely interval branch-and-bound algorithms. Such an algorithm typically generates a tree of boxes from the initial box by alternating branching steps and contraction steps in order to remove non optimal sub-boxes. In this paper, we introduce a new contraction method that is designed to handle the boundary of the initial box where a minimizer may not be a stationary point. This method exploits the first-order optimality conditions and we show that it subsumes the classical monotonicity test based on interval arithmetic. A new branch-and-bound algorithm has been implemented in the interval solver Realpaver. An extensive experimental study based on a set of standard benchmarks is presented.

scholarly journals An optimal solution for the budgets assignment problem

2021 ◽  
Author(s):  
Mahdi Jemmali
Keyword(s):  
Experimental Study ◽  
Community Development ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Optimal Solution ◽  
Service Organizations ◽  
Hard Problem ◽  
Branch And Bound Algorithms ◽  
Np Hard Problem ◽  
Developmental Role

Municipalities are service organizations that have a major role in strategic planning and community development that consider the future changes and society developments, by implementing set of projects with pre-allocated budgets. Projects have standards, budgets and constraints that differ from one community to another and from one city to another. Fair distributing of different projects to municipalities, while ensuring the provision of various capabilities to reach developmental role is NP-Hard problem. Assuming that all municipalities have the same strategic characteristics. The problem is as follows: given a set of projects with different budgets, how to distribute all projects to all municipalities with a minimum budget gap between municipalities. To derive equity distribution between municipalities, this paper developed lower bounds and eleven heuristics to be utilized in the branch-and-bound algorithms. The performance of the developed heuristics, lower bounds and the exact solutions are presented in the experimental study.

Analysis and design of thermo-mechanical interfaces

2012 ◽  
Vol 60 (2) ◽  
pp. 205-213
Author(s):  
K. Dems ◽  
Z. Mróz
Keyword(s):  
Optimality Conditions ◽  
Mechanical Loading ◽  
Material Properties ◽  
Structural Response ◽  
External Boundary ◽  
Mechanical Loads ◽  
Internal Interface ◽  
Analysis And Design ◽  
First Order ◽  
Mechanical Nature

Abstract. An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying internal interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived using the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.

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