Numerical experiments with partially separable optimization problems

2014 ◽

Vol 8 (1) ◽

pp. 218-221 ◽

Cited By ~ 2

Author(s):

Ping Hu ◽

Zong-yao Wang

Keyword(s):

Global Convergence ◽

Unconstrained Optimization ◽

Numerical Experiments ◽

Line Search ◽

Optimization Problems ◽

Search Algorithm ◽

New Combination ◽

Combination Rule ◽

Combination Technique ◽

Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

Download Full-text

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

Algorithms ◽

10.3390/a14050146 ◽

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.

Download Full-text

An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

Journal of Optimization Theory and Applications ◽

10.1007/s10957-021-01854-7 ◽

2021 ◽

Author(s):

Christian Kanzow ◽

Andreas B. Raharja ◽

Alexandra Schwartz

Keyword(s):

Constrained Optimization ◽

Numerical Experiments ◽

Penalty Method ◽

Augmented Lagrangian ◽

Constraint Qualification ◽

Optimization Problems ◽

Augmented Lagrangian Method ◽

Constrained Optimization Problems ◽

Strongly Stationary ◽

Type Constraint

AbstractA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.

Download Full-text

A randomized adaptive trust region line search method

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2020.00900 ◽

2020 ◽

Vol 10 (2) ◽

pp. 259-263

Author(s):

Saman Babaie-Kafaki ◽

Saeed Rezaee

Keyword(s):

Simulated Annealing ◽

Numerical Experiments ◽

Line Search ◽

Optimization Problems ◽

Trust Region ◽

Search Method ◽

Test Problems ◽

Unconstrained Optimization Problems ◽

Line Search Method ◽

Region Line

Hybridizing the trust region, line search and simulated annealing methods, we develop a heuristic algorithm for solving unconstrained optimization problems. We make some numerical experiments on a set of CUTEr test problems to investigate efficiency of the suggested algorithm. The results show that the algorithm is practically promising.

Download Full-text

Second-Order Cone Programming Formulations for Robust Multiclass Classification

Neural Computation ◽

10.1162/neco.2007.19.1.258 ◽

2007 ◽

Vol 19 (1) ◽

pp. 258-282 ◽

Cited By ~ 22

Author(s):

Ping Zhong ◽

Masao Fukushima

Keyword(s):

Numerical Experiments ◽

Optimization Problems ◽

Multiclass Classification ◽

Training Data ◽

Support Vector ◽

Research Subject ◽

Ongoing Research ◽

Second Order Cone ◽

Linear And Nonlinear ◽

Nonlinear Robust

Multiclass classification is an important and ongoing research subject in machine learning. Current support vector methods for multiclass classification implicitly assume that the parameters in the optimization problems are known exactly. However, in practice, the parameters have perturbations since they are estimated from the training data, which are usually subject to measurement noise. In this article, we propose linear and nonlinear robust formulations for multiclass classification based on the M-SVM method. The preliminary numerical experiments confirm the robustness of the proposed method.

Download Full-text

The Application of Fuzzification for Solving Quadratic Functions

10.21203/rs.3.rs-1121957/v1 ◽

2021 ◽

Author(s):

Lunshan Gao

Keyword(s):

Approximate Solution ◽

Approximation Algorithm ◽

Critical Point ◽

Numerical Experiments ◽

Optimization Problems ◽

Local Minimizer ◽

Quadratic Functions ◽

Computational Time ◽

Computational Results ◽

Average Computational Time

Abstract This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

Download Full-text

New dual-type decomposition algorithm for nonconvex separable optimization problems

Automatica ◽

10.1016/0005-1098(89)90076-9 ◽

1989 ◽

Vol 25 (2) ◽

pp. 233-242 ◽

Cited By ~ 12

Author(s):

P. Tatjewski

Keyword(s):

Optimization Problems ◽

Decomposition Algorithm ◽

Separable Optimization ◽

Type Decomposition

Download Full-text

A Bayesian Approach to Simulated Annealing

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800001327 ◽

1989 ◽

Vol 3 (4) ◽

pp. 453-475 ◽

Cited By ~ 3

Author(s):

P.J.M. Van Laarhoven ◽

C.G.E. Boender ◽

E.H.L. Aarts ◽

A. H. G. Rinnooy Kan

Keyword(s):

Markov Chain ◽

Simulated Annealing ◽

Probability Distribution ◽

Posterior Distribution ◽

Prior Distribution ◽

Numerical Experiments ◽

Optimization Problems ◽

Probabilistic Algorithm ◽

Unknown Parameters ◽

Combinatorial Optimization Problems

Simulated annealing is a probabilistic algorithm for approximately solving large combinatorial optimization problems. The algorithm can mathematically be described as the generation of a series of Markov chains, in which each Markov chain can be viewed as the outcome of a random experiment with unknown parameters (the probability of sampling a cost function value). Assuming a probability distribution on the values of the unknown parameters (the prior distribution) and given the sequence of configurations resulting from the generation of a Markov chain, we use Bayes's theorem to derive the posterior distribution on the values of the parameters. Numerical experiments are described which show that the posterior distribution can be used to predict accurately the behavior of the algorithm corresponding to the next Markov chain. This information is also used to derive optimal rules for choosing some of the parameters governing the convergence of the algorithm.

Download Full-text