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Quantum Differential Evolution Algorithm for Quadratic Knapsack Problem

LU Wen-lin

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A quantum differential evolution is proposed for discrete optimization.The population diversity is increased by superposition characteristic. Based on the idea of catastrophe theory, the algorithm uses mutation operation to avoid falling into local optimum. The algorithm has stronger global optimization capability .The results of experiments on quadratic knapsack problem and comparison with other algorithms show that the algorithm is feasible and effective.

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Abstract Solving combinatorial optimization problems represents a challenge for researchers, especially hard NP-complete problems that are commonly handled through heuristic methods providing approximate solutions. The emergence of quantum computing, which enables performing parallel computation, raises hope for solving such problems within a reasonable time frame. This paper proposes a quantum global optimization algorithm to solve combinatorial optimization problems intended to provide an improved performance. The proposed algorithm aims to amplify the probability of selecting the global optimum of the objective function defining the addressed problem using a specific variant of Grover’s search based on simultaneously exploring all comparison cases of possible solutions to recognize the global optimum. The paper also includes the study of precision and runtime of the presented concept and introduces a version of the proposed algorithm addressing the knapsack problem, along with its execution results and a comparison with other competing algorithms

•Mar 23, 2026•0 citations
A quantum differential evolution is proposed for discrete optimization.The population diversity is increased by superposition characteristic. Based on the idea of catastrophe theory, the algorithm uses mutation operation to avoid falling into local optimum. The algorithm has stronger global optimization capability .The results of experiments on quadratic knapsack problem and comparison with other algorithms show that the algorithm is feasible and effective.
In this paper, we propose a quantum differential evolution (QDE) algorithm for function optimization, which can improve the performance of differential evolution (DE) algorithm. First, the algorithm does some basic operations, such as mutation, crossover and selection of vectors. And then a quantum computing method is utilized to search the global optimal solutions, which avoids falling into the local minimums. Our experimental results show the proposed algorithm is feasible. And compared with other algorithms, the proposed algorithm is more effective. Furthermore it can improve the speed of convergence.
This paper proposes a genetic quantum algorithm based on discrete time quantum walk (QWGA) to solve 0-1 quadratic knapsack problem. Genetic Quantum Algorithms makes use of the qubit representation and superposition phenomenon which are the counter-intuitive characteristics of quantum mechanics. Discrete Quantum Walk (DQW) on a hypercube is used in the place of genetic operators like mutation, crossover, etc. Achievement of rapid convergence and avoidance of local optima with the help of the quantum principles is explained in this paper. The possibilities of extending the proposed algorithm to various combinatorial optimization problems is discussed in detail. Superiority of the proposed algorithm over genetic quantum algorithm based on rotation operators is evident from the results.
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.
Quantum evolutionary algorithm is a novel and efficient algorithm which inspired by the ideas of quantum computing,and it has excellent results on the computational efficiency and avoid falling into local extremum problems.Therefore,the combination of quantum mechanics and intelligent optimization algorithms will further expand the application areas of intelligent optimization algorithms to improve the optimization algorithm problem-solving ability.For this,the introduction of quantum computation to the differential evolution algorithm,we proposed a new evolutionary algorithm-quantum differential evolution algorithm.This method is the probability of quantum bits used in the real-coded chromosomes,with the quantum mutation,quantum crossover and quantum choose operation to achieve the update of chromosomal location,and using the quantum NOT gate to swap two probability amplitude of quantum bits,it can prevent the premature algorithm,while the algorithm converges faster.The function extreme value and TSP problems as an example to verify the effectiveness of the proposed algorithm.
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.
Abstract Solving combinatorial optimization problems represents a challenge for researchers, especially hard NP-complete problems that are commonly handled through heuristic methods providing approximate solutions. The emergence of quantum computing, which enables performing parallel computation, raises hope for solving such problems within a reasonable time frame. This paper proposes a quantum global optimization algorithm to solve combinatorial optimization problems intended to provide an improved performance. The proposed algorithm aims to amplify the probability of selecting the global optimum of the objective function defining the addressed problem using a specific variant of Grover’s search based on simultaneously exploring all comparison cases of possible solutions to recognize the global optimum. The paper also includes the study of precision and runtime of the presented concept and introduces a version of the proposed algorithm addressing the knapsack problem, along with its execution results and a comparison with other competing algorithms