Development of some techniques for solving system of linear and nonlinear equations via hybrid algorithm

Kumar, Nirmal; Shaikh, Ali Akbar; Mahato, Sanat Kumar; Bhunia, Asoke Kumar

doi:10.1111/exsy.12669

Cited by 9 publications

(3 citation statements)

References 49 publications

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“…In recent years, many optimization algorithms combining quantum theory and swarm intelligence algorithms have been proposed, such as quantum genetic algorithm (QGA), 26 quantum PSO algorithm, 27 quantum cuckoo search algorithm, 28 and hybrid algorithms based on quantum PSO algorithm. [29][30][31][32] QGA uses quantum bits to encode individuals, quantum superposition states and quantum collapse to express more information, and quantum rotation gates to update individuals, which gives it a completely different search mechanism compared with the GA. Compared with GA, QGA has the advantages of good population diversity, strong global search capability, and fast convergence speed, which makes it has obvious advantages in solving combinatorial optimization problems.…”

Section: Multilevel Adaptive Quantum Genetic Algorithmmentioning

confidence: 99%

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Xiaoqian

Wang

et al. 2021

Int J Intell Syst

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Delay optimization has now emerged as an important optimization goal in logic synthesis. The delay optimization for ternary fixed polarity Reed-Muller (FPRM) circuits aims to find a ternary FPRM circuit with a minimum delay. Because the delay optimization for ternary FPRM circuits is a combinatorial optimization problem, in this paper, we first propose a multilevel adaptive quantum genetic algorithm (MAQGA), which divides individuals into three-level populations: high-level population, intermediate-level population, and low-level population and uses the proposed ternary quantum rotation gate, proposed ternary quantum correction gate, and proposed multi-operator adaptive mutation mechanism to make the three-level populations evolve. Moreover, based on the proposed delay decomposition strategy, we propose a delay optimization approach (DOA) for ternary FPRM circuits under the unit delay model, which searches for a ternary FPRM circuit with a minimum delay using the MAQGA. Experimental results demonstrated the effectiveness and superiority of the DOA in optimizing the delay of ternary FPRM circuits.

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Section: Multilevel Adaptive Quantum Genetic Algorithmmentioning

confidence: 99%

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Xiaoqian

Wang

et al. 2021

Int J Intell Syst

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“…For searching optimal regions in search space as widely as possible, Sun et al 17 and Kumar et al 18 introduce quantum theory into PSO and propose a Quantum‐behaved PSO (QPSO) algorithm. Kumar et al 19 develop some techniques for solving linear and nonlinear equations via hybrid algorithm. Cuckoo Search is another metaheuristic approach inspired by the cuckoo species laying their eggs in the nests of other host birds.…”

Section: Literature Reviewmentioning

confidence: 99%

Neutrino‐like particle for particle swarm optimization

Tseng

Yao

2021

Int J Intell Syst

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The real‐world optimal problems frequently encountered by various industries are the nonlinear constrained optimization problems (NCOPs), where the constraints represent the limitations of practical resources. Many researchers have attempted to improve particle swarm optimization (PSO) in the past decades; however, in solving the NCOPs, the PSO‐based approaches often cause premature convergences. The problem‐specific constraints frequently generate many infeasible regions that block the movements of particles. The particles' behavior causes the exploration abilities of particles that tend to weaken along with time. The decreasing of exploration ability often comes from the particle becoming stagnant or moving unusefully. This study proposes a neutrino‐like particle (NLP) with adaptive NLP hyperparameters that simulate the natural neutrino behavior. The proposed NLPs can be embedded in the PSO‐based approaches for overcoming premature convergence. The experiment results demonstrate that all referenced PSO‐based methods with the NLPs improved significantly compared with those without the NLPs to solve the NCOPs. All referenced PSO‐based methods that embedded the NLPs also significantly outperform four recent strong algorithms in most IEEE CEC 2020 benchmark problems. Therefore, the proposed NLPs with adaptive NLP hyperparameters can effectively solve the premature convergences, reinforce the exploration ability, and maintain the exploitation capability for solving the NCOPs over the whole evolution process.

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“…is the mean best position of the j-th component of all the particles i.e. Recently, some advanced versions of QPSO have been proposed (Kumar et al 2020(Kumar et al , 2021a(Kumar et al , 2021b. (1 ) This algorithm was developed after the development of Quantum behaved Particle Swarm Optimization (QPSO) with some additional features.…”

Section: Consideringmentioning

confidence: 99%

Development of a blended particle swarm optimization to optimize mission design life of a series–parallel reliable system with time dependent component reliabilities in imprecise environments

et al. 2021

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Maximization of system reliability is a topic of much concern in the field of engineering design, telecommunication, aircraft design, plant and factory establishing, producing of sensitive devices, and many production management. The main goal of reliability optimization is to construct highly reliable system or to design maximum reliable system so that the system can run smoothly without any hindrance under some restrictions in the form of constraints for a specified period of time maintaining the safety and efficiency. In this paper, we consider Redundancy Allocation Problem (RAP) involving time dependent component reliabilities for optimizing system reliability of the problem designed. Moreover, we have considered a new objective function as the Mission Design Life (MDL) of reliable system. The MDL is found by integrating the system reliability with respect to time from zero to mission time. This consideration makes the problem more realistic by taking the fact into account that reliability of the system varies with time. Here, we have maximized the Mission Design Life of reliable system with the time dependent component reliabilities by implementing the proposed Blended WQPSO (BWQPSO). The BWQPSO is developed by incorporating the Big-M penalty function in the Weighted Quantum behaved Particle Swarm Optimization and it is found to perform highly satisfactorily to solve the highly nonlinear combinatorial problem so designed as a time dependent redundancy allocation problem. Again, to tackle the uncertain behaviour of controlling parameters, we incorporated the fuzziness and intuitionistic fuzziness to develop the imprecise models. The three types of problems designed here are supplemented by numerical examples. The numerical experiments are carried out in each of the environments and comparative studies are presented. The statistical analysis along with computational time and convergence of the proposed algorithm are also produced.

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Development of some techniques for solving system of linear and nonlinear equations via hybrid algorithm

Cited by 9 publications

References 49 publications

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Neutrino‐like particle for particle swarm optimization

Development of a blended particle swarm optimization to optimize mission design life of a series–parallel reliable system with time dependent component reliabilities in imprecise environments

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