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Frontiers in artificial intelligence and applications

An Improved Quantum Evolutionary Algorithm for High Dimension Knapsack Problem

Hao Li, Lei Ma, Na Qin

Published Jan 1, 2017• 0 citations
Publisher

Abstract

Knapsack problem is a typical combinatorial optimization problem, which has attracted wide attention because of its simple description, difficult solution and wide application background. For the knapsack problem, we proposed an improved quantum evolutionary algorithm. In this algorithm, the qubits are initialized according to the value densities of their corresponding items, the angle of Q-gate is determinated through direct comparison between the quantum chromosome and the optimal solution, random crossover method is taken to share information among chromosomes, and Hϵ gate is used to prevent from premature convergence. Finally, experiment demonstrates the effectiveness of the algorithm.

DOI
10.3233/978-1-61499-785-6-203

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Knapsack problem is a typical combinatorial optimization problem, which has attracted wide attention because of its simple description, difficult solution and wide application background. For the knapsack problem, we proposed an improved quantum evolutionary algorithm. In this algorithm, the qubits are initialized according to the value densities of their corresponding items, the angle of Q-gate is determinated through direct comparison between the quantum chromosome and the optimal solution, random crossover method is taken to share information among chromosomes, and Hϵ gate is used to prevent from premature convergence. Finally, experiment demonstrates the effectiveness of the algorithm.
Abstract The quadratic knapsack problem(QKP) is a typical combinatorial optimization problem. It is arisen in many optimization fields, but there exist no pseudo-polynomial time algorithm to solve it. In this paper, we propose an angle-expressed quantum evolutionary algorithm to solve QKP. In this algorithm, the qubits are expressed in the angle and initialized according to the value densities of their corresponding items, the rotation angle of Q-gate is determined through an analytical formula, and Hε gate is used to prevent from premature convergence. For infeasible solution, a dynamic value density is introduced to choose item to be selected or dropped. Finally, experiment demonstrates the effectiveness of the algorithm.
According to the characteristics of combinatorial optimization problems,a novel improved quantum evolutionary algorithm for combinatorial optimization problems(NIQEA) is proposed.The NIQEA initializes population based on the idea of niche cooperative evolutionary,increasing the diversity of individuals,and adopts the dynamic adjustment strategy to adjust the quantum rotation corner,speeding up convergence rate,and uses the cross strategy of excellent individuals to get crossover operation,enhancing local search ability.To validate its performance,the NIQEA is applied to solve the typical combinatorial optimization problems: two examples of multidimensional 0/1 knapsack problem,and the results show that the NIQEA is feasible and effective.
The method of calculating rotation angle of quantum rotation gate plays an important role to the performance of quantum evolutionary algorithm (QEA). This paper proposes an improved quantum evolutionary algorithm (IQEA), whose core is that a new approach of adaptive calculating rotation angle of quantum rotation gate is designed on the basis of the probability amplitude ratio of the corresponding states. Rapid convergence and good global search capability characterize the performance of IQEA. Based on a typical combinatorial optimization problem - 0/1 knapsack problems, the influence of the relative parameter to the performance of IQEA is demonstrated, and then comparing experiments have been done. The results show that IQEA is superior to the previous quantum evolutionary algorithm.
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.
Quantum Genetic Algorithm (QGA) has a number of advantages in comparison with its classical version: operating speed, small population size and auto-balance between the global search and the local search. It is based on the ideas of traditional evolutionary algorithms, applied to the quantum computations technology, which operate with quantum bits, superposition of states and quantum measurements. This paper proposes a QGA with a new adaptive quantum gate operator and a restoring technology for the quantum chromosome during the process of solving combinatorial problems with constraints. Meta-optimization of the primary algorithm parameters is used for providing the algorithm efficiency. The productiveness of the suggested approach is proven by the model studies, carried out using a wide range of test 0–1 knapsack problems.
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.