Research On The Knowledge-inducing Interval Multi-objective Evolutionary Optimization Method

Interval multi-objective optimization problem is one of the most importantuncertain multi-objective optimization problem.This kind of problems widely exist inpractical engineering optimization problems and scientific researches. Traditionalmulti-objective optimization method hardly applied to solve this kind of problemssince they have multiple conflicting objectives and their objectives’ values are interval.Aiming at solving this kind of problems, three kinds of knowledge-inducing intervalmulti-objective optimization methods were put forward in this thesis.Firstly, a kind of multi-objective cultural particle swarm optimization methodwas proposed to solve uncertain optimizaiton problem with interval parameters. Itadopted the framework of cultural algorithm. A novel dominant relationship basedon possibility degree for individuals with interval objective values was defined.Particle swarm optimization was used in population space. Three types of knowledgeincluding situational knowledge,normative knowledge and topographical knowledgewere defined in belief space. The key flight parameters were adaptively adjusted andthe local best or the global best were selected in terms of above three kinds ofknowledge. The simulation results to benchmark functions indicated that thealgorithm can obtain a pareto front with good convergence、distribution anduncertainty.Secondly, considering the parallelism of existing quantum algorithm, a novelinterval multi-objective quantum cultural algorithm was proposed by combing culturalalgorithm. The dominance relationship comparing two interval individuals is definedbased on the possibility. A novel method caculating quantum individuals rectangleheight was defined in terms of this dominance relationship. In belief space, normativeknowledge,situational knowledge and topographical knowledge were adopted toupdate the quantum individuals and guided the mutation or selection operation of theevolutionary individuals. Three kinds of crowded operator were present to reflect thedistribution situation of the hypervolumes. The simulation results to benchmarkfunctions indicated that the algorithm can coverage to better Pareto front uniformlyand have small uncertainty.Finally, considering the weakness of interval dominance relationship andcrowded operator a novel knowledge-inducing interval multi-objective evolutionaryalgorithm based on decomposition was proposed.It adopted the decomposition strategy to decompose the interval multi-objective optimization problem into singleobjective optimization problems. A new chebyshev aggregate function was defined totest the performance of different solution by corresponding single objective. A newmethod to select the reference point was present. Situational knowledge,neighborhood knowledge and correlation knowledge were described in belief space.The worse individuals were evolutioned by knowledge-guided differential evolutionstrategy so as to improve the population’s diversity and the convergence. Thesimulation results for benchmark functions indicates that the algorithm can coverageto better Pareto front uniformly.Three proposed knowledge-inducing evolutionary optimization algorithms showthe rationality and validity of the guided role of knowledge in solving intervalmulti-objective optimization problems. They not only provide the efficient solutionsto solve this kind of problems, but also provide useful guidance forknowledge-inducing evolutionary optimization method in the application ofuncertainty optimization problems.