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International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA)

Quantum-Inspired Evolutionary Algorithm Based on Estimation Of Distribution

Ming Chen, Huiyun Quan

Published Sep 1, 2007• 6 citations
Publisher

Abstract

This paper proposed a novel quantum inspired evolutionary algorithm (called EQEA) based on estimation of distribution. In EQEA, the solution made from distribution model of candidate solutions collapsing from quantum probabilistic model is called estimated solution. Combining with group strategy and adaptive rotation gate, quantum probability amplitude is updated referring to the corresponding estimated solution and the best solution in its group. Rapid convergence and good global search capability characterize the performance of EQEA even if the population size is 1. Experiments on solving a class of combinatorial optimization problems show that EQEA performs better than QEA and EDA.

DOI
10.1109/bicta.2007.4806409

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This paper proposed a novel quantum inspired evolutionary algorithm (called EQEA) based on estimation of distribution. In EQEA, the solution made from distribution model of candidate solutions collapsing from quantum probabilistic model is called estimated solution. Combining with group strategy and adaptive rotation gate, quantum probability amplitude is updated referring to the corresponding estimated solution and the best solution in its group. Rapid convergence and good global search capability characterize the performance of EQEA even if the population size is 1. Experiments on solving a class of combinatorial optimization problems show that EQEA performs better than QEA and EDA.
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.
In this paper, we propose a novel quantum-inspired evolutionary algorithm, called NQEA, for solving combinatorial optimization problems. NQEA uses a new Q-bit update operator to increase the balance between the exploration and exploitation of the search space. In the operator, first, the Q-bits of each individual in the population are updated based on the personal best measurement of that individual and the best measurement of current generation. Then, a restriction is applied to each Q-bit to prevent the premature convergence of its values. The results of experiments on the 0-1 knapsack and NK-landscapes problems show that NQEA performs better than a classical genetic algorithm, CGA, and two quantum-inspired evolutionary algorithms, QEA and vQEA, in terms of convergence speed and accuracy.
Based on the probability amplitude ratio of the corresponding states of quantum bits, the rotation angle of quantum rotation gate is calculated adaptively and a new quantum rotation gate is constructed. A novel quantum evolutionary algorithms (NQEA), whose core is that the designed quantum rotation gate is used as evolutionary strategy is introduced, rapid convergence and good global search capability characterize the performance of NQEA, and NQEA is able to possess the two characteristics of exploration and exploitation, simultaneously. NQEA is applied on the physical distribution vehicle routing problem - a typical combinatorial optimization problem, the results show that NQEA is superior to the previous quantum evolutionary algorithm as well as other conventional genetic algorithms
A novel evolutionary algorithm called Probability Evolutionary Algorithm (PEA) is proposed, which is inspired by the Quantum computation and Quantum-inspired Evolutionary Algorithm (QEA). The individual in PEA is encoded by a probabilistic superposed bit which can represent a linear superposition of the states 0 to k (k ≥ 1). The observing step is used in PEA to obtain the observed individual, and the update method is used to evolve the population. The function optimization and 0-k knapsack problem experiments show that PEA has apparent superior in application area, searching capability and computation time compared with QEA and canonical genetic algorithm (CGA).
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.
The method of calculating the rotational angle of a quantum rotary gate palys an important role in the performance of quantum evolutionary algorithm(QEA). An improved quantum evolutionary algorithm(IQEA) is proposed, which adaptively calculates the rotational angle of quantum rotary gate based on the probability amplitude ratio of the corresponding states. Rapid convergence and good global search capability characterize the performance of IQEA. The influence of the relative parameter to the performance of IQEA is demonstrated on 0/1 knapsack problem, and then IQEA is applied to a real distribution routing problem, the results show that IQEA is superior to the previous quantum evolutionary algorithm and other conventional evolutionary algorithms.