scholarly journals A Bayesian approach for quantile optimization problems with high-dimensional uncertainty sources

2021 ◽  
Vol 376 ◽  
pp. 113632
Author(s):  
Christian Sabater ◽  
Olivier Le Maître ◽  
Pietro Marco Congedo ◽  
Stefan Görtz
Keyword(s):  
Bayesian Approach ◽  
Optimization Problems ◽  
High Dimensional ◽  
Uncertainty Sources

scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

2021 ◽  
Author(s):  
Xiting Gong ◽  
Tong Wang
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
High Dimensional ◽  
Value Functions

Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochastic Optimization Problems

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

scholarly journals A consensus-based global optimization method for high dimensional machine learning problems

2020 ◽  
Author(s):  
Jose Carrillo ◽  
Shi Jin ◽  
Lei Li ◽  
Yuhua Zhu
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Weighted Average ◽  
Planck Equation ◽  
Optimization Method ◽  
Learning Problems ◽  
High Dimensional ◽  
Nonconvex Functions ◽  
The Individual ◽  
Parameter Constraints

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183{204, 2017], which is a gradient-free optimization method for general nonconvex functions. We rst replace the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems. Secondly, we utilize the random mini-batch ideas to reduce the computational cost of calculating the weighted average which the individual particles tend to relax toward. For its mean- eld limit{a nonlinear Fokker-Planck equation{we prove, in both time continuous and semi-discrete settings, that the convergence of the method, which is exponential in time, is guaranteed with parameter constraints independent of the dimensionality. We also conduct numerical tests to high dimensional problems to check the success rate of the method.

scholarly journals Local search for parallel optimization algorithms for high diminsional optimization problems

2018 ◽  
Vol 210 ◽  
pp. 04052 ◽  
Author(s):  
Nadia Abd-Alsabour
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Search Algorithms ◽  
Parallel Optimization ◽  
High Dimensional ◽  
Search Process ◽  
Local Search Algorithms

Local search algorithms perform an important role when being employed with optimization algorithms tackling numerous optimization problems since they lead to getting better solutions. However, this is not practical in many applications as they do not contribute to the search process. This was not much studied previously for traditional optimization algorithms or for parallel optimization algorithms. This paper investigates this issue for parallel optimization algorithms when tackling high dimensional subset problems. The acquired results show impressive recommendations.

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

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