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IEEE Congress on Evolutionary Computation (CEC)

Parallel quantum-inspired genetic algorithm for combinatorial optimization problem

Kuk-Hyun Han, Kui-Hong Park, Ci-Ho Lee, Jong-Hwan Kim

Published Nov 13, 2002• 193 citations
Publisher

Abstract

This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.

DOI
10.1109/cec.2001.934358

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This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.
This paper proposes a novel evolutionary computing method called a genetic quantum algorithm (GQA). GQA is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting qubit chromosome as a representation GQA can represent a linear superposition of solutions due to its probabilistic representation. As genetic operators, quantum gates are employed for the search of the best solution. Rapid convergence and good global search capability characterize the performance of GQA. The effectiveness and the applicability of GQA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that GQA is superior to other genetic algorithms using penalty functions, repair methods and decoders.
The genetic algorithm is an efficient optimization tool for its independence of problems, intrinsic parallelism and inherent learning capacity; however, it has some disadvantages such as slow convergence and prematurity. In this paper, a novel algorithm, called the quantum genetic algorithm—QGA, is proposed based on the combination of the quantum theory with the evolutionary theory. By adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. The random observation simulating the quantum collapse can bring diverse individuals, and the evolution of quantum chromosome can also pilot the evolution. So it has better diversity than the classical genetic algorithm. Rapid convergence and good global search capacity characterize the performance of QGA. The paper not only proves the global convergence of the QGA, but also some simulation experiments are shown to prove its superiority over other algorithms.
In this paper, a novel Quantum Genetic Algorithm (QGA) called Parallel Probability-gate Quantum Genetic Algorithm (PPQGA) is proposed.The main points of PPQGA are that a new chromosome representation called qubit representation, a new updating gate called probability-gate and a novel evolutionary strategy being used in update procedure are introduced.Based on the concepts and principles of quantum computing introduced, PPQGA is characterized by rapid convergence, good global search capability and the ability of possessing exploitation simultaneously.The experimental results of several special functions show that PPQGA can speedup the migration of the top individuals of subpopulations and is superior to other several genetic algorithms greatly in quality and efficiency.
This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.
Qubit-inspired Genetic Algorithm (QGA) is an extension of genetic algorithm in which quantum mechanics and its representations are introduced. A chromosome in our QGA is concretized as a series of quantum-bit (qubit) described by its complex-valued representation, and phase-rotation gates are embedded into the selection process over generations. In our previous work, it has been shown that this scheme has better performances than the classical ones in several problems such as N-K landscape problem, Knapsack Problem, Maximum Search, and Construction of image filters. In this paper, we make clear the effectiveness of the QGA by comparing QGA with GA through minimum solution problem on De Jong's functions.
Based on quantum mutation, a quantum genetic algorithm (QGA) to solve combinatorial optimization problem is proposed.It has good features of genetic quantum algorithm (GQA) and traditional genetic algorithm,which can obtain the best solution with one chromosome in a short time.Comparing experiments have been conducted on a typical combinatorial optimization problem——0/1 knapsack problem.Experimental results have shown that the proposed quantum genetic algorithm is superior to genetic quantum algorithm and traditional genetic algorithm on performance.