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, HϵHϵ gate and R&NϵR&Nϵ 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 HϵHϵ gate and R&NϵR&Nϵ gate have more powerful convergence ability in high complex instances. Moreover, the QMOEA with R&NϵR&Nϵ gate has the best convergence in almost all of the experimental problems. Furthermore, the appropriate εε value regions for two Q-gates are verified.