Utilizing quantum genetic algorithm with TM to solve DEs (original) (raw)
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Quantum fuzzy genetic algorithm with Turing to solve DE
Periodicals of Engineering and Natural Sciences (PEN), 2023
In this study, we create the quantum fuzzy Turing machine (QFTM) approach for solving fuzzy differential equations under Seikkala differentiability by combining it with a differential equation and a genetic algorithm. A theoretical model of computation called a quantum fuzzy Turing machine (QFTM) incorporates aspects of fuzzy logic and quantum physics.
Optimization with Quantum Genetic Algorithm
Recent development in quantum technology have shown that quantum computer can provide a dramatic advantage over classical computers for some algorithms. In particular, a polynomial-time algorithm for factoring, a problem which was previously thought to be hard for classical computers, has recently been developed [13]. Similarly, a quantum algorithm searching for unsorted database in square root of time it would take on a classical computer has also been described by Grover [4]-[3]. Both algorithms rely upon the inherent parallelism, superposition and entanglement property of quantum computing to achieve their improvements. Since most problems of real interest for genetic algorithms have a vast search space, it seems appropriate how quantum parallelism can be applied to Genetic Algorithms. In this paper we provide a brief background of quantum computers. We explain why and how quantum algorithms provides a fundamental improvements over classical ones for some problems. Further, we present here the Conventional Genetic Algorithm and the quantum approach of Genetical Algorithms(QGA) as well. The benefits and drawbacks of QGA are also analyzed. Moreover, this paper provides an improved version over the conventional QGA. This improvement originates from the best partial immigration technique applied to the quantum chromosomes. The main objective of the best partial immigration is to consider the string of qubits from the quantum chromosomes having best fitness and transfer the same randomly to the chromosomes of next generation for better mixing. The process is reiterated. To observe the performance the best partial immigration technique we have considered some popular optimization problems and performed the experiment on it. These problems are namely Travelling Salesman Problem(TSP), Binpacking Problem and Vertex Cover Problem. It has been observed that the obtained results outperforms the conventional QGA.
Convergence Analysis of Quantum Genetic Algorithm
2008
ABSTRACT It is an important and a complicated task to investigate the convergence of a new genetic algorithm based on quantum mechanics concepts including qubits and superposition of states, namely Quantum Genetic Algorithm, in the field of evolutionary computation. This paper analyzes convergence property of quantum genetic algorithm which uses its special quantum operator instead of canonical operators of classical genetic algorithms, such as crossover and mutation operators and even selection techniques.
A Quantum-Inspired Evolutionary Algorithm for Optimization Numerical Problems
Lecture Notes in Computer Science, 2012
This paper proposes a new quantum-inspired evolutionary algorithm for solving ordering problems. Quantum-inspired evolutionary algorithms based on binary and real representations have been previously developed to solve combinatorial and numerical optimization problems, providing better results than classical genetic algorithms with less computational effort. However, for ordering problems, order-based genetic algorithms are more suitable than those with binary and real representations. This is because specialized crossover and mutation processes are employed to always generate feasible solutions. Therefore, this work proposes a new quantum-inspired evolutionary algorithm especially devised for ordering problems (QIEA-O). Two versions of the algorithm have been proposed. The so-called pure version generates solutions by using the proposed procedure alone. The hybrid approach, on the other hand, combines the pure version with a traditional order-based genetic algorithm. The proposed quantum-inspired order-based evolutionary algorithms have been evaluated for two well-known benchmark applications-the traveling salesman problem (TSP) and the vehicle routing problem (VRP)as well as in a real problem of line scheduling. Numerical results were obtained for ten cases (7 VRP and 3 TSP) with sizes ranging from 33 to 101 stops and 1 to 10 vehicles, where the proposed quantum-inspired order-based genetic algorithm has outperformed a traditional order-based genetic algorithm in most experiments.
Convergence Analysis of Quantum Genetic Algorithms
International Journal Of Computer Science And Applications Vol. 1, No. 2, August 2008 ISSN 0974-1003 ... Mehrshad Khosraviani, Dept. of Computer Engineering & IT, Amirkabir University of Technology (Tehran Polytechnic) 424 Hafez Ave., Tehran 15785, Iran ...
Quantum-inspired Evolutionary Algorithm: A Survey
DEStech Transactions on Engineering and Technology Research
To provide a reference for the study of Quantum-Inspired Evolutionary Algorithm (QIEA), the combination of qualitative and quantitative methods is applied to analyze the literatures and references about QIEA. The status, the hot spots and the development trends of QIEA are explored based on the literatures. The results show that the research on QIEA has been increasing every year since it is proposed. The theoretical research, algorithm research and application research have been expanded and deepened. There have been many achievements about the application and research about QIEA, and QIEA will be one of the protagonists of optimization algorithms in future.
2000
Recent developments in quantum technology have shown that quantum computers can provide a dramatic advantage over classical computers for some algorithms. In particular, a polynomial-time algorithm for factoring, a problem which was previously thought to be hard for classical computers, has recently been developed . Similarly, a quantum algorithm for searching an unsorted database in square root of the time it would take on a classical computer has also been described . Both algorithms rely upon the inherent parallel qualities of quantum computers to achieve their improvement. Unfortunately, not all problems can benefit so dramatically from quantum application . Since most problems of real interest for genetic algorithms (GAs) have a vast search space , it seems appropriate to consider how quantum parallelism can be applied to GAs. In this paper we provide a brief background of quantum computers. We explain how quantum algorithms can provide a fundamental improvement over classical ones for some problems. We present a simple quantum approach to genetic algorithms and analyze its benefits and drawbacks. This is significant because to date there are only a handful of quantum algorithms that take advantage of quantum parallelism ]. Finally, we provide ideas for directions of future research.
Quantum crossover based quantum genetic algorithm for solving non-linear programming
… and Systems (INFOS …, 2012
Quantum computing proved good results and performance when applied to solving optimization problems. This paper proposes a quantum crossover-based quantum genetic algorithm (QXQGA) for solving non-linear programming. Due to the significant role of mutation function on the QXQGA's quality, a number of quantum crossover and quantum mutation operators are presented for improving the capabilities of searching, overcoming premature convergence, and keeping diversity of population. For calibrating the QXQGA, the quantum crossover and mutation operators are evaluated using relative percentage deviation for selecting the best combination. In addition, a set of non-linear problems is used as benchmark functions to illustrate the effectiveness of optimizing the complexities with different dimensions, and the performance of the proposed QXQGA algorithm is compared with the quantum inspired evolutionary algorithm to demonstrate its superiority.
Modifying the quantum-assisted genetic algorithm
Proceedings of the Genetic and Evolutionary Computation Conference Companion
Based on the quantum-assisted genetic algorithm (QAGA) [11] and related approaches we introduce several modifications of QAGA to search for more promising solvers on (at least) graph coloring problems, knapsack problems, Boolean satisfiability problems, and an equal combination of these three. We empirically test the efficiency of these algorithmic changes on a purely classical version of the algorithm (simulated-annealing-assisted genetic algorithm, SAGA) and verify the benefit of selected modifications when using quantum annealing hardware. Our results point towards an inherent benefit of a simpler and more flexible algorithm design.
A Hybrid Quantum Evolutionary Algorithm
2015
This paper proposes a Hybrid Quantum Evolutionary Algorithm. Quantum computing is capable of processing huge numbers of quantum states simultaneously, in parallel, (“quantum parallelism”), whereas evolutionary computing can only process one chromosome per processor. In theory, QC ought to be able to process upto all possible points in a 2 search space (of N bit chromosomes). An evolutionary algorithm is effectively a guided search algorithm that samples the search space and in general is a slow process. Since QC can examine all or some of 2 points simultaneously, this Quantum Parallelism can be cleverly used to speed the Evolutionary Algorithms. This paper presents a Hybrid Quantum Evolutionary Algorithm that uses the Quantum Parallelism and an other well-known Quantum Algorithm to speed up the Evolutionary Algorithms.