Interval multi-objective quantum-inspired cultural algorithms

It had been proved that the knowledge may promote more efficient evolution. Considering the knowledge defined in different form, we present interval multi-objective quantum-inspired cultural algorithms so as to effectively utilize the implicit information embodied in the evolution to promote more efficient search. It adopts the dual structure derived from cultural algorithm. In population space, the rectangle's height of each allele in real-encoding quantum individuals is calculated in terms of the possibility dominant rank, instead of the relative fitness values. Three kinds of crowding operators are defined, including the crowding distance of hypercube, the harmonic distance of hypercube and the coverage rate of hypercube to grids, to measure the crowding degree among evolutionary individuals. In belief space, the knowledge is used to guide selection and mutation operations of evolutionary individuals and the update operation of quantum individuals. The statistic simulation results for four benchmark functions indicate that the solutions obtained from the proposed algorithms more close to the true Pareto front uniformly and the uncertainty of non-dominant solutions is less. Furthermore, the knowledge extracted from the evolution plays a positive role in improving the convergence and distribution.