Gradient Surfing: A New Deterministic Approach for Low-Dimensional Global Optimization

2018 ◽  
Vol 180 (3) ◽  
pp. 855-878 ◽  
Author(s):  
Efrat Taig ◽  
Ohad Ben-Shahar
Keyword(s):  
Global Optimization ◽  
Deterministic Approach ◽  
Low Dimensional

scholarly journals Global Optimization Algorithm Based on Kriging Using Multi-Point Infill Sampling Criterion and Its Application in Transportation System

2021 ◽  
Vol 13 (19) ◽  
pp. 10645
Author(s):  
Xiaodong Song ◽  
Mingyang Li ◽  
Zhitao Li ◽  
Fang Liu
Keyword(s):  
Global Optimization ◽  
Single Point ◽  
Great Influence ◽  
Kriging Model ◽  
Expected Improvement ◽  
Particle Swarm Algorithm ◽  
Beijing City ◽  
Public Traffic ◽  
Low Dimensional ◽  
Infill Sampling

Public traffic has a great influence, especially with the background of COVID-19. Solving simulation-based optimization (SO) problem is efficient to study how to improve the performance of public traffic. Global optimization based on Kriging (KGO) is an efficient method for SO; to this end, this paper proposes a Kriging-based global optimization using multi-point infill sampling criterion. This method uses an infill sampling criterion which obtains multiple new design points to update the Kriging model through solving the constructed multi-objective optimization problem in each iteration. Then, the typical low-dimensional and high-dimensional nonlinear functions, and a SO based on 445 bus line in Beijing city, are employed to test the performance of our algorithm. Moreover, compared with the KGO based on the famous single-point expected improvement (EI) criterion and the particle swarm algorithm (PSO), our method can obtain better solutions in the same amount or less time. Therefore, the proposed algorithm expresses better optimization performance, and may be more suitable for solving the tricky and expensive simulation problems in real-world traffic problems.

scholarly journals On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic

2021 ◽  
Author(s):  
B. G.-Tóth ◽  
L. G. Casado ◽  
E. M. T. Hendrix ◽  
F. Messine
Keyword(s):  
Global Optimization ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Interval Arithmetic ◽  
Efficient Global Optimization ◽  
Test Problems ◽  
Simplicial Partition ◽  
Monotonicity Test ◽  
Low Dimensional ◽  
Linear Relaxations

AbstractBranch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is to use simplicial partition sets. Obtaining sharp and cheap bounds of the objective function over a simplex is very important in the construction of efficient Global Optimization B&B algorithms. Although enclosing a simplex in a box implies an overestimation, boxes are more natural when dealing with individual coordinate bounds, and bounding ranges with Interval Arithmetic (IA) is computationally cheap. This paper introduces several linear relaxations using gradient information and Affine Arithmetic and experimentally studies their efficiency compared to traditional lower bounds obtained by natural and centered IA forms and their adaption to simplices. A Global Optimization B&B algorithm with monotonicity test over a simplex is used to compare their efficiency over a set of low dimensional test problems with instances that either have a box constrained search region or where the feasible set is a simplex. Numerical results show that it is possible to obtain tight lower bounds over simplicial subsets.

scholarly journals On the choice of the low-dimensional domain for global optimization via random embeddings

2019 ◽  
Vol 76 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Mickaël Binois ◽  
David Ginsbourger ◽  
Olivier Roustant
Keyword(s):  
Global Optimization ◽  
Low Dimensional ◽  
Random Embeddings ◽  
Dimensional Domain

A Deterministic Lagrangian-Based Global Optimization Approach for Large Scale Decomposable Problems

2008 ◽  
Author(s):  
Aida Khajavirad ◽  
Jeremy J. Michalek
Keyword(s):  
Global Optimization ◽  
Lower Bounds ◽  
Large Scale ◽  
Product Family ◽  
Systems Design ◽  
Deterministic Approach ◽  
Solution Quality ◽  
Lower Bounding ◽  
Highly Nonlinear ◽  
Product Family Optimization

We propose a deterministic approach for global optimization of large-scale nonconvex quasiseparable problems encountered frequently in engineering systems design, such as multidisciplinary design optimization and product family optimization applications. Our branch and bound-based approach applies Lagrangian decomposition to 1) generate tight lower bounds by exploiting the structure of the problem and 2) enable parallel computing of subsystems and the use of efficient dual methods for computing lower bounds. We apply the approach to the product family optimization problem and in particular to a family of universal electric motors with a fixed platform configuration taken from the literature. Results show that the Lagrangian bounds are much tighter than convex underestimating bounds used in commercial software, and the proposed lower bounding scheme shows encouraging efficiency and scalability, enabling solution of large, highly nonlinear problems that cause difficulty for existing solvers. The deterministic approach also provides lower bounds on the global optimum, eliminating uncertainty of solution quality produced by popular applications of stochastic and local solvers. For instance, our results demonstrate that prior product family optimization results reported in the literature obtained via stochastic and local approaches are suboptimal, and application of our global approach improves solution quality by about 10%. The proposed method provides a promising scalable approach for global optimization of large-scale systems-design problems.

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