Genetic search - An approach to the nonconvex optimization problem

AIAA Journal ◽  
1990 ◽  
Vol 28 (7) ◽  
pp. 1205-1210 ◽  
Author(s):  
P. Hajela
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Genetic Search

scholarly journals Power Allocation for Reducing PAPR of Artificial-Noise-Aided Secure Communication System

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Tao Hong ◽  
Geng-xin Zhang
Keyword(s):  
Power Allocation ◽  
Nonconvex Optimization ◽  
Communication System ◽  
Secure Communication ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Average Power ◽  
Finite Alphabet ◽  
Artificial Noise ◽  
Communication Signals

The research of improving the secrecy capacity (SC) of wireless communication system using artificial noise (AN) is one of the classic models in the field of physical layer security communication. In this paper, we consider the peak-to-average power ratio (PAPR) problem in this AN-aided model. A power allocation algorithm for AN subspaces is proposed to solve the nonconvex optimization problem of PAPR. This algorithm utilizes a series of convex optimization problems to relax the nonconvex optimization problem in a convex way based on fractional programming, difference of convex (DC) functions programming, and nonconvex quadratic equality constraint relaxation. Furthermore, we also derive the SC of the proposed signal under the condition of the AN-aided model with a finite alphabet and the nonlinear high-power amplifiers (HPAs). Simulation results show that the proposed algorithm reduces the PAPR value of transmit signal to improve the efficiency of HPA compared with benchmark AN-aided secure communication signals in the multiple-input single-output (MISO) model.

scholarly journals Genetiniai algoritmai komivojažieriaus uždaviniui: negatyvieji ir pozityvieji aspektai*

2009 ◽  
Vol 50 ◽  
pp. 173-180
Author(s):  
Alfonsas Misevičius ◽  
Andrius Blažinskas ◽  
Jonas Blonskis ◽  
Vytautas Bukšnaitis
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
High Quality ◽  
Genetic Search ◽  
Local Improvement ◽  
Effi Ciency ◽  
The Traveling Salesman Problem

Šiame straipsnyje nagrinėjami klausimai, susiję su genetinių algoritmų taikymu, sprendžiant gerai žinomą kombinatorinio optimizavimo uždavinį – komivojažieriaus uždavinį (KU) (angl. traveling salesman problem). Svarstoma, jog genetinio algoritmo efektyvumui didelę įtaką turi uždavinio specifi nės savybės, todėl labai svarbu kūrybiškai sudaryti genetinį algoritmą konkrečiam sprendžiamam uždaviniui. Pateikiami eksperimentų, atliktų su realizuotu genetiniu algoritmu, rezultatai, iliustruojantys skirtingų veiksnių įtaką rezultatų kokybei. Konstatuojama, kad tinkamas genetinių operatorių ir lokaliojo individų (sprendinių) gerinimo derinimas leidžia gerokai padidinti genetinės paieškos efektyvumą.On the Genetic Algorithms for the Traveling Salesman Problem: Negative and Positive AspectsAlfonsas Misevičius, Andrius Blažinskas, Jonas Blonskis, Vytautas Bukšnaitis SummaryIn this paper, we discuss some issues related to the application of genetic algorithms (GAs) to the well-known combinatorial optimization problem – the traveling salesman problem (TSP). The results obtained from the experiments with the different variants of the genetic algorithm are presented as well. Based on these results, it is concluded that the effi ciency of the genetic search is much infl uenced by both the specifi c nature of the problem and the features of the algorithm itself. In particular, it should be emphasized that the incorporation of the (postcrossover) procedures for the local improvement of offspring has one of the crucial roles in obtaining high-quality solutions.

scholarly journals Robust strong duality for nonconvex optimization problem under data uncertainty in constraint

2021 ◽  
Vol 6 (11) ◽  
pp. 12321-12338
Author(s):  
Yanfei Chai ◽  
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Conjugate Function ◽  
Strong Duality ◽  
Data Uncertainty ◽  
Abstract Convexity ◽  
Conjugate Duality ◽  
Dual Problems ◽  
Uncertain Optimization ◽  
Robust Strong Duality

<abstract><p>This paper deals with the robust strong duality for nonconvex optimization problem with the data uncertainty in constraint. A new weak conjugate function which is abstract convex, is introduced and three kinds of robust dual problems are constructed to the primal optimization problem by employing this weak conjugate function: the robust augmented Lagrange dual, the robust weak Fenchel dual and the robust weak Fenchel-Lagrange dual problem. Characterizations of inequality (1.1) according to robust abstract perturbation weak conjugate duality are established by using the abstract convexity. The results are used to obtain robust strong duality between noncovex uncertain optimization problem and its robust dual problems mentioned above, the optimality conditions for this noncovex uncertain optimization problem are also investigated.</p></abstract>

scholarly journals A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Mio Horai ◽  
Hideo Kobayashi ◽  
Takashi G. Nitta
Keyword(s):  
Global Optimization ◽  
Global Convergence ◽  
Nonlinear Optimization ◽  
Branch And Bound ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
New Method ◽  
Linear Relaxation ◽  
Global Optimization Problem ◽  
Nonconvex Global Optimization

We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

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