A framework of quantum-inspired multi-objective evolutionary algorithms and its convergence properties

Abstract

In this paper, a general framework of quantum-inspired multiobjective evolutionary algorithms is proposed based on the basic principles of quantum computing and general schemes of multi-objective evolutionary algorithms. One of the sufficient convergence conditions to Pareto optimal set is presented and it is proved under partially order set theory. Moreover, two algorithms are given as examples meeting this convergence condition, in which two improved Q-gates are used. Their convergence properties are discussed. Additionally, one counterexample is also given.