Convergence performance comparison of quantum-inspired multi-objective evolutionary algorithms

In recent research, we proposed a general framework of quantum-inspired multi-objective evolutionary algorithms (QMOEA) and gave one of its sufficient convergence conditions to the Pareto optimal set. In this paper, two Q-gate operators, H"@e gate and R&N"@e gate, are experimentally validated as two Q-gate paradigms meeting the convergence condition. The former is a modified rotation gate, and the latter is a combination of rotation gate and NOT gate with the specified probability. To investigate their effectiveness and applicability, several experiments on the multi-objective 0/1 knapsack problems are carried out. Compared to two typical evolutionary algorithms and the QMOEA only with rotation gate, the QMOEA with H"@e gate and R&N"@e gate have more powerful convergence ability in high complex instances. Moreover, the QMOEA with R&N"@e gate has the best convergence in almost all of the experimental problems. Furthermore, the appropriate @e value regions for two Q-gates are verified.

[1]  Jong-Hwan Kim,et al.  Quantum-inspired Multiobjective Evolutionary Algorithm for Multiobjective 0/1 Knapsack Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[2]  Mohamed Batouche,et al.  A Quantum Inspired Evolutionary Framework for Multi-objective Optimization , 2005, EPIA.

[3]  Günter Rudolph,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods a Framework of Quantum-inspired Multi-objective Evolutionary Algorithms and Its Convergence Properties a Framework of Quantum-inspired Multi-objective Evolutionary Algorithms and Its Conve , 2022 .

[4]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[5]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[6]  Jong-Hwan Kim,et al.  Genetic quantum algorithm and its application to combinatorial optimization problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[7]  C. A. Coello Coello,et al.  A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques , 1999, Knowledge and Information Systems.

[8]  Jong-Hwan Kim,et al.  Quantum-inspired evolutionary algorithms with a new termination criterion, H/sub /spl epsi// gate, and two-phase scheme , 2004, IEEE Transactions on Evolutionary Computation.

[9]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[10]  Jong-Hwan Kim,et al.  Quantum-inspired evolutionary algorithm for a class of combinatorial optimization , 2002, IEEE Trans. Evol. Comput..

[11]  Jong-Hwan Kim,et al.  Quantum-Inspired Evolutionary Algorithms With a New Termination Criterion , H Gate , and Two-Phase Scheme , 2009 .

[12]  Jong-Hwan Kim,et al.  Parallel quantum-inspired genetic algorithm for combinatorial optimization problem , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[13]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[14]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[15]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[16]  Günter Rudolph,et al.  A framework of quantum-inspired multi-objective evolutionary algorithms and its convergence condition , 2007, GECCO '07.

[17]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[18]  G. Rudolph.  Evolutionary Search under Partially Ordered Fitness Sets , 2001 .

[19]  Ajit Narayanan,et al.  Quantum-inspired genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[20]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[21]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .