Cultural particle swarm optimization algorithms for uncertain multi-objective problems with interval parameters

Traditional dominant comparison never fits for uncertain multi-objective optimization problems with interval parameters. Moreover, existing particle swarm optimization algorithm for solving these uncertain optimization problems could not adaptively adjust the key parameters and easily fell into premature. To alleviate above weakness, a novel multi-objective cultural particle optimization algorithm is proposed. The highlights of this algorithm are: (i) The possibility degree is introduced to construct a novel dominant comparison relationship so as to rationally measure the uncertainty of particles; (ii) The grid's coverage degree is defined based on topological knowledge and used to measure the uniformity of non-dominant solutions in objective space instead of the crowding distance. (iii) The key flight parameters are adaptively adjusted and the local or global best are selected in terms of the knowledge. The statistic simulation results for seven 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 rational impact on balancing exploration and exploitation.