scholarly journals A modification of the imperialist competitive algorithm with hybrid methods for constrained optimization problems

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jianfu Luo ◽  
Jinsheng Zhou ◽  
Xi Jiang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Hybrid Methods ◽  
Imperialist Competitive Algorithm ◽  
Constrained Optimization Problems ◽  
Competitive Algorithm

Development of seven hybrid methods based on collective intelligence for solving nonlinear constrained optimization problems

2016 ◽  
Vol 49 (2) ◽  
pp. 245-279 ◽  
Author(s):  
Sergio Gerardo de-los-Cobos-Silva ◽  
Roman Anselmo Mora-Gutiérrez ◽  
Miguel Angel Gutiérrez-Andrade ◽  
Eric Alfredo Rincón-García ◽  
Antonin Ponsich ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Hybrid Methods ◽  
Collective Intelligence ◽  
Constrained Optimization Problems ◽  
Nonlinear Constrained Optimization

scholarly journals A Modification of the Imperialist Competitive Algorithm with Hybrid Methods for Multi-Objective Optimization Problems

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 173
Author(s):  
Jianfu Luo ◽  
Jinsheng Zhou ◽  
Xi Jiang ◽  
Haodong Lv
Keyword(s):  
Evaluation Method ◽  
Optimization Problems ◽  
Hybrid Methods ◽  
Comprehensive Evaluation ◽  
Imperialist Competitive Algorithm ◽  
Multi Objective Optimization ◽  
Allocation Mechanism ◽  
Multi Objective ◽  
Competitive Algorithm ◽  
Radar Map

This paper proposes a modification of the imperialist competitive algorithm to solve multi-objective optimization problems with hybrid methods (MOHMICA) based on a modification of the imperialist competitive algorithm with hybrid methods (HMICA). The rationale for this is that there is an obvious disadvantage of HMICA in that it can only solve single-objective optimization problems but cannot solve multi-objective optimization problems. In order to adapt to the characteristics of multi-objective optimization problems, this paper improves the establishment of the initial empires and colony allocation mechanism and empire competition in HMICA, and introduces an external archiving strategy. A total of 12 benchmark functions are calculated, including 10 bi-objective and 2 tri-objective benchmarks. Four metrics are used to verify the quality of MOHMICA. Then, a new comprehensive evaluation method is proposed, called “radar map method”, which could comprehensively evaluate the convergence and distribution performance of multi-objective optimization algorithm. It can be seen from the four coordinate axes of the radar maps that this is a symmetrical evaluation method. For this evaluation method, the larger the radar map area is, the better the calculation result of the algorithm. Using this new evaluation method, the algorithm proposed in this paper is compared with seven other high-quality algorithms. The radar map area of MOHMICA is at least 14.06% larger than that of other algorithms. Therefore, it is proven that MOHMICA has advantages as a whole.

scholarly journals Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

2019 ◽  
Vol 7 (6) ◽  
pp. 532-549
Author(s):  
Chun-an Liu ◽  
Huamin Jia
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Imperialist Competitive Algorithm ◽  
Search Space ◽  
Feasible Region ◽  
Constrained Optimization Problem ◽  
Diverse Range ◽  
Nonlinear Constrained Optimization ◽  
Competitive Algorithm

Abstract Nonlinear constrained optimization problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

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.

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