The Application of Fuzzification for Solving Quadratic Functions

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.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
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.

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.

scholarly journals An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

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.

scholarly journals Ions motion optimization algorithm for multiobjective optimization problems

2021 ◽  
pp. 93-110 ◽  
Author(s):  
Hitarth Buch ◽  
Indrajit Trivedi
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Computational Time ◽  
Selection Strategy ◽  
Pareto Optimum ◽  
Optimal Solutions ◽  
Good Convergence ◽  
Motion Optimization ◽  
Multiobjective Approach ◽  
Benchmark Test Functions

This paper offers a novel multiobjective approach – Multiobjective Ions Motion Optimization (MOIMO) algorithm stimulated by the movements of ions in nature. The main inspiration behind this approach is the force of attraction and repulsion between anions and cations. A storage and leader selection strategy is combined with the single objective Ions Motion Optimization (IMO) approach to estimate the Pareto optimum front for multiobjective optimization. The proposed method is applied to 18 different benchmark test functions to confirm its efficiency in finding optimal solutions. The outcomes are compared with three novel and well-accepted techniques in the literature using five performance parameters quantitatively and obtained Pareto fronts qualitatively. The comparison proves that MOIMO can approximate Pareto optimal solutions with good convergence and coverage with minimum computational time.

scholarly journals A randomized adaptive trust region line search method

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.

scholarly journals Second-Order Cone Programming Formulations for Robust Multiclass Classification

2007 ◽  
Vol 19 (1) ◽  
pp. 258-282 ◽  
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.

A Nelder and Mead Methodology for Solving Small Fixed-Charge Transportation Problems

2011 ◽  
pp. 345-356
Author(s):  
G. Kannan ◽  
P. Senthil ◽  
P. Sasikumar ◽  
V. P. Vinay
Keyword(s):  
Supply Chain ◽  
Transportation Problem ◽  
Optimization Problems ◽  
Fixed Charge ◽  
Computational Time ◽  
Variable Cost ◽  
Fixed Cost ◽  
Supply Chain Optimization ◽  
Business World ◽  
Fixed Charge Transportation Problem

The term ‘supply chain management’ has become common in the business world, which can be understood from the positive results of research in the area, particularly in supply chain optimization. Transportation is a frontier in achieving the objectives of the supply chain. Thrust is also given to optimization problems in transportation. The fixed-charge transportation problem is an extension of the transportation problem that includes a fixed cost, along with a variable cost that is proportional to the amount shipped. This article approaches the problem with another meta-heuristics known as the Nelder and Mead methodology to save the computational time with little iteration and obtain better results with the help of a program in C++.

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