An Adaptive Population-based Simplex Method for Continuous Optimization

2016 ◽  
Vol 7 (4) ◽  
pp. 23-51 ◽  
Author(s):  
Mahamed G.H. Omran ◽  
Maurice Clerc
Keyword(s):  
Simplex Method ◽  
Continuous Optimization ◽  
Optimization Method ◽  
Population Based ◽  
Function Optimization ◽  
Test Functions ◽  
Dimensional Simplex ◽  
Low Dimensional ◽  
Better Than ◽  
Real World Problems

This paper proposes a new population-based simplex method for continuous function optimization. The proposed method, called Adaptive Population-based Simplex (APS), is inspired by the Low-Dimensional Simplex Evolution (LDSE) method. LDSE is a recent optimization method, which uses the reflection and contraction steps of the Nelder-Mead Simplex method. Like LDSE, APS uses a population from which different simplexes are selected. In addition, a local search is performed using a hyper-sphere generated around the best individual in a simplex. APS is a tuning-free approach, it is easy to code and easy to understand. APS is compared with five state-of-the-art approaches on 23 functions where five of them are quasi-real-world problems. The experimental results show that APS generally performs better than the other methods on the test functions. In addition, a scalability study has been conducted and the results show that APS can work well with relatively high-dimensional problems.

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 Some modifications of low-dimensional simplex evolution and their convergence

2013 ◽  
Vol 28 (1) ◽  
pp. 54-81 ◽  
Author(s):  
Changtong Luo ◽  
Shao-Liang Zhang ◽  
Bo Yu
Keyword(s):  
Dimensional Simplex ◽  
Low Dimensional

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
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