Conference Paper

An adaptive quantum-inspired differential evolution algorithm for 0–1 knapsack problem

Dept. of Electr. Eng., Indian Inst. of Technol., Kharagpur, India
DOI: 10.1109/NABIC.2010.5716320 Conference: Nature and Biologically Inspired Computing (NaBIC), 2010 Second World Congress on
Source: arXiv


Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many real-life constrained combinatorial optimization problems which operate on binary space. On the other hand, the quantum inspired evolutionary algorithm (QEA) is very well suitable for handling such problems by applying several quantum computing techniques such as Q-bit representation and rotation gate operator, etc. This paper extends the concept of differential operators with adaptive parameter control to the quantum paradigm and proposes the adaptive quantum-inspired differential evolution algorithm (AQDE). The performance of AQDE is found to be significantly superior as compared to QEA and a discrete version of DE on the standard 0-1 knapsack problem for all the considered test cases.

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    • "In addition, the performances of BDE algorithms can also be improved by incorporating recombination operators of other EAs. Hota and Pat [12] proposed an adaptive quantum-inspired differential evolution algorithm (AQDE) applying quantum computing techniques , while He and Han [10] introduced the negative selection in artificial immune systems to obtain an artificial immune system based differential evolution (AIS-DE) algorithm. With respect to the fact that the logical operations introduced in AIS-DE tends to produce " 1 " bits with increasing probability, Wu and Tseng [29] proposed a modified binary differential evolution strategy to improve the performance of BDE algorithms on topology optimization of structures. "
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    ABSTRACT: Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), designing an efficient binary-coded DE algorithm is still a challenging task. Inspired by the learning mechanism in particle swarm optimization (PSO) algorithms, we propose a binary learning differential evolution (BLDE) algorithm that can efficiently locate the global optimal solutions by learning from the last population. Then, we theoretically prove the global convergence of BLDE, and compare it with some existing binary-coded evolutionary algorithms (EAs) via numerical experiments. Numerical results show that BLDE is competitive with the compared EAs. Further study is performed via the change curves of a renewal metric and a refinement metric to investigate why BLDE cannot outperform some compared EAs for several selected benchmark problems. Finally, we employ BLDE in solving the unit commitment problem (UCP) in power systems to show its applicability to practical problems.
    Neurocomputing 02/2015; 149:1038-1047. DOI:10.1016/j.neucom.2014.07.030 · 2.08 Impact Factor
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    • "Quantum-inspired variants have been proposed as well for differential evolution [10], used to solve both binary problems such as the knapsack [11] and continuous optimization ones [12]. "
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    ABSTRACT: In this paper, a new variant of a quantum-inspired evolutionary algorithm is proposed, which is characterised by a population-based elitism, a resetting mutation for the qubits, and an evolutionary hill-climbing phase at the end of the main search, meant to further improve the quality of the solution. The algorithm was applied for finding near-optimal outcomes for multi-issue multi-lateral negotiation in a multiagent system, and it was designed for situations where the agents involved are cooperative and are willing to reveal their private information regarding their utilities to an external, impartial mediator. The proposed algorithm is shown to outperform two other classical techniques and also two other variants of quantum-inspired evolutionary algorithms, especially for large optimization problems. An evolutionary optimization approach is particularly useful in negotiation settings where the utility functions of the agents are non-linear.
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    ABSTRACT: Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize efficient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.
    Soft Computing and Intelligent Systems (SCIS) and 13th International Symposium on Advanced Intelligent Systems (ISIS), 2012 Joint 6th International Conference on; 11/2012
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