An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

Lian, Shujun; Meng, Sitong; Wang, Yiju

doi:10.1155/2018/7484256

Cited by 10 publications

(7 citation statements)

References 33 publications

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“…For illustration and validation of the previously proposed analytical model, this paper uses the IEEE39 node system for the algorithm demonstration; the wiring of the IEEE39 node system is shown in Figure 5. In the following example analysis, the results calculated in this paper are expressed as per-unit value, the reference capacity is considered as 100 MVA, and the reference voltage is consistent with the reference voltage of the IEEE36 bus data given in the literature [21].…”

Section: Example Analysismentioning

confidence: 74%

“…To cooperate with EPSO, all the equation constraints in Equation ( 12) are combined and written in the form eðxÞ = 0, and all the inequality constraints in Equation ( 12) are combined and written in the form kðxÞ ≥ 0. Then, the following objective function with the penalty factor may be further given [21]. The constrained problem is transformed into an unconstrained problem by adding a penalty function.…”

Section: Evaluation Idea For Power Grid Securitymentioning

confidence: 99%

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Research on Security Level Evaluation Method for Cascading Trips Based on WSN

Deng

Luo

Chang

et al. 2021

Wireless Communications and Mobile Computing

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In recent years, the application of wireless sensor networks (WSN) in power systems has received a great deal of attention. As we all know, the most important issue for the power system is security and stability, especially due to the massive outages caused by cascading trips. Therefore, in today’s era, from the perspective of cascading trips, how to effectively use WSN to analyze and evaluate the security level of the power grid is an important direction for future power development. In this paper, an algorithm based on the WSN collection of online data to calculate the corresponding security level of the system is proposed for the cascading trip phenomenon, to achieve the online evaluation of the cascading trips. First, this paper proposes a hybrid layered network structure based on WSN for monitoring system and details the acquisition of power grid parameters by its acquisition layer. Secondly, combined with the manifestation of cascading trips and the action equation of current-type line backup protection, the mathematical representation of the grid cascading trips is given, and the mathematical form corresponding to the critical situation is strictly proved, and an index for evaluating the security level of the power grid is proposed and then further combined with the actual physical constraints of the power grid and the establishment of a mathematical model for calculating the security level of the grid cascading trips. For this model, this paper relies on evolution particle swarm optimization (EPSO) to give specific ideas for solving the model. Finally, a case analysis is performed by the IEEE39 node system and the results of the case show the effectiveness of the model and method.

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Section: Example Analysismentioning

confidence: 74%

Section: Evaluation Idea For Power Grid Securitymentioning

confidence: 99%

Research on Security Level Evaluation Method for Cascading Trips Based on WSN

Deng

Luo

Chang

et al. 2021

Wireless Communications and Mobile Computing

View full text Add to dashboard Cite

show abstract

“…Therefore, many concepts have been developed, including the Pareto optimal conditions, in order to reach solutions in the multiple objectives case. Multiobjective optimization modeling has been used to solve many life-related problems, such as physical, economic, and transport [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms

Tougma,

Some

2024

Journal of Applied Mathematics

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This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.

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“…In this case, the concept of Pareto optimality is used, demonstrating an optimal solution to a multiobjective problem. In recent years, multiobjective optimization concepts have proven valuable for solving a wide variety of problems in various domains, including physics, economics, transportation, social choice, and many others [27,38,39].…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic Augmented Lagrangian algorithm for multiobjective optimization problems

Tougma,

Kaboré,

Somé

2024

GJOM

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In this article, we propose an adaptation of the Hyperbolic Augmented Lagrangian algorithm to solve multiobjective optimization problems. After conducting a literature review, we provide a definition of the Hyperbolic Augmented Lagrange method. Under clearly defined assumptions, we demonstrate that any limit point of a sequence generated by the proposed approach is feasible and constitutes a Pareto-optimal solution. To assess the effectiveness of the proposed algorithm, we incorporate two variants of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, thereby offering two approaches for solving well-known tests problems from the literature. We employ metrics to evaluate the performance of these two approaches.

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An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

Cited by 10 publications

References 33 publications

Research on Security Level Evaluation Method for Cascading Trips Based on WSN

Research on Security Level Evaluation Method for Cascading Trips Based on WSN

Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms

Hyperbolic Augmented Lagrangian algorithm for multiobjective optimization problems

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