A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems

2016 ◽  
Vol 28 (S1) ◽  
pp. 421-438 ◽  
Author(s):  
Wen Long ◽  
Ximing Liang ◽  
Shaohong Cai ◽  
Jianjun Jiao ◽  
Wenzhuan Zhang
Keyword(s):  
Constrained Optimization ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Grey Wolf ◽  
Grey Wolf Optimization ◽  
Constrained Optimization Problems

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 Chaotic grey wolf optimization algorithm for constrained optimization problems

2017 ◽  
Vol 5 (4) ◽  
pp. 458-472 ◽  
Author(s):  
Mehak Kohli ◽  
Sankalap Arora
Keyword(s):  
Constrained Optimization ◽  
Engineering Design ◽  
Optimization Algorithm ◽  
Chaotic Maps ◽  
Optimization Problems ◽  
Chaotic Map ◽  
Flower Pollination Algorithm ◽  
Grey Wolf ◽  
Constrained Optimization Problems ◽  
Engineering Design Problems

Abstract The Grey Wolf Optimizer (GWO) algorithm is a novel meta-heuristic, inspired from the social hunting behavior of grey wolves. This paper introduces the chaos theory into the GWO algorithm with the aim of accelerating its global convergence speed. Firstly, detailed studies are carried out on thirteen standard constrained benchmark problems with ten different chaotic maps to find out the most efficient one. Then, the chaotic GWO is compared with the traditional GWO and some other popular meta-heuristics viz. Firefly Algorithm, Flower Pollination Algorithm and Particle Swarm Optimization algorithm. The performance of the CGWO algorithm is also validated using five constrained engineering design problems. The results showed that with an appropriate chaotic map, CGWO can clearly outperform standard GWO, with very good performance in comparison with other algorithms and in application to constrained optimization problems. Highlights Chaos has been introduced to the GWO to develop Chaotic GWO for global optimization. Ten chaotic maps have been investigated to tune the key parameter ‘a’, of GWO. Effectiveness of the algorithm is tested on many constrained benchmark functions. Results show CGWO's better performance over other nature-inspired optimization methods. The proposed CGWO is also used for some engineering design applications.

scholarly journals A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Wilhelm P. Freire ◽  
Afonso C. C. Lemonge ◽  
Tales L. Fonseca ◽  
Hernando J. R. Franco
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Augmented Lagrangian ◽  
Dual Problem ◽  
Optimization Problems ◽  
Lagrangian Duality ◽  
Dual Function ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Nonsmooth And Nonconvex Optimization

The Interior Epigraph Directions (IED) method for solving constrained nonsmooth and nonconvex optimization problem via Generalized Augmented Lagrangian Duality considers the dual problem induced by a Generalized Augmented Lagrangian Duality scheme and obtains the primal solution by generating a sequence of iterates in the interior of the epigraph of the dual function. In this approach, the value of the dual function at some point in the dual space is given by minimizing the Lagrangian. The first version of the IED method uses the Matlab routine fminsearch for this minimization. The second version uses NFDNA, a tailored algorithm for unconstrained, nonsmooth and nonconvex problems. However, the results obtained with fminsearch and NFDNA were not satisfactory. The current version of the IED method, presented in this work, employs a Genetic Algorithm, which is free of any strategy to handle the constraints, a difficult task when a metaheuristic, such as GA, is applied alone to solve constrained optimization problems. Two sets of constrained optimization problems from mathematics and mechanical engineering were solved and compared with literature. It is shown that the proposed hybrid algorithm is able to solve problems where fminsearch and NFDNA fail.

An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems

2020 ◽  
Author(s):  
Xiaodi Bai ◽  
Jie Sun ◽  
Xiaojin Zheng
Keyword(s):  
Constrained Optimization ◽  
Decomposition Method ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Chance Constraint ◽  
Medium Size ◽  
Lagrangian Decomposition ◽  
Constrained Optimization Problems ◽  
Left Hand ◽  
Integer Programs

Joint chance-constrained optimization problems under discrete distributions arise frequently in financial management and business operations. These problems can be reformulated as mixed-integer programs. The size of reformulated integer programs is usually very large even though the original problem is of medium size. This paper studies an augmented Lagrangian decomposition method for finding high-quality feasible solutions of complex optimization problems, including nonconvex chance-constrained problems. Different from the current augmented Lagrangian approaches, the proposed method allows randomness to appear in both the left-hand-side matrix and the right-hand-side vector of the chance constraint. In addition, the proposed method only requires solving a convex subproblem and a 0-1 knapsack subproblem at each iteration. Based on the special structure of the chance constraint, the 0-1 knapsack problem can be computed in quasi-linear time, which keeps the computation for discrete optimization subproblems at a relatively low level. The convergence of the method to a first-order stationary point is established under certain mild conditions. Numerical results are presented in comparison with a set of existing methods in the literature for various real-world models. It is observed that the proposed method compares favorably in terms of the quality of the best feasible solution obtained within a certain time for large-size problems, particularly when the objective function of the problem is nonconvex or the left-hand-side matrix of the constraints is random.

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