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Genetic and Evolutionary Computation Conference (GECCO)

A novel quantum-inspired evolutionary algorithm for solving combinatorial optimization problems

Parvaz Mahdabi, Mahdi Abadi, Saeed Jalili

Published Jul 8, 2009• 7 citations
Publisher

Abstract

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.

DOI
10.1145/1569901.1570172

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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.
Quantum-inspired evolutionary algorithms (QIEAs), as a subset of evolutionary computation, are based on the principles of quantum computing such as quantum bits and quantum superposition. In this paper, we propose a multi-start quantum-inspired evolutionary algorithm, called MSQIEA. To improve the performance of the algorithm, a multi-measurement operator and a new strategy for updating the rotation angle is proposed. When Q-bit individuals start to converge to their final states, the best solution is stored and all Q-bits in each Q-bit individual are reinitialized. We compare the effectiveness of MSQIEA with a popular quantum-inspired evolutionary algorithm, called QEA, for solving 0-1 knapsack problem. The experimental results show that MSQIEA outperforms QEA and finds a solution with higher profit.
From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.
In this paper, an advanced quantum-inspired evolutionary optimization algorithm (A-QEOA) is proposed. This algorithm is based on the principle of quantum computing such as quantum bit representation and superposition of states. Like other evolutionary algorithms, the quantum-inspired evolutionary algorithm has characteristics of exploration and exploitation. The quantum-inspired evolutionary algorithm achieves exploration using observation process and exploitation using quantum rotation gate. Exploration helps to find the search space for a parameter that needs to be optimized. However, the observation process needs a random number which may sometimes increase the number of iterations to converge the algorithm or may lead to premature convergence. In this paper, we propose an algorithm with an updated observation process that helps to converge the algorithm optimally and helps to get results faster in comparison to the existing quantum inspired evolutionary algorithm (QEA).
Quantum-Inspired Evolutionary Algorithm (QEA), a type of stochastic algorithm for solving combinatorial optimization problems, is evolutionary computation using quantum bits and superposition states in quantum computation. Although coarse-grained parallel, QEA has many parameters that must be adjusted manually. The simpler algorithm, Quantum-inspired Evolutionary Computation with Pair Swap operator (QEAPS), the authors propose involves just one population and a simple genetic operation exchanging best solution information between two individuals chosen randomly, instead of the migration operation used in QEA, and thereby fewer parameters to be adjusted. The authors found in experiments that QEAPS finds highly qualified solutions, is more robust against constraint handling, and has a higher search performance of thanks to diversified best solution information.
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).
This paper extends the analogies employed in the development of quantum-inspired evolutionary algorithms by proposing quantum-inspired Hadamard walks, called QHW. A novel quantum-inspired evolutionary algorithm, called HQEA, for solving combinatorial optimization problems, is also proposed. The novelty of HQEA lies in it's incorporation of QHW Remote Search and QHW Local Search - the quantum equivalents of classical mutation and local search, that this paper defines. The intuitive reasoning behind this approach, and the exploration-exploitation balance thus occurring is explained. From the results of the experiments carried out on the 0,1-knapsack problem, HQEA performs significantly better than a conventional genetic algorithm, CGA, and two quantum-inspired evolutionary algorithms - QEA and NQEA, in terms of convergence speed and accuracy.