A dynamic utopia point updating strategy for multi-objective optimization

Multi-objective optimization problems widely exist in engineering practice, which are usually solved by repeatedly searching Pareto fronts. However, the search process faces the challenges of heavy computational burden and local optimality. To overcome these difficulties, a novel utopia optimization method is developed in the paper, where the multi-objective problems are converted into single-objective ones without repeatedly searching, and then the computational burden is reduced. In particular, different from the classical utopia optimization, where the utopia point is always fixed during the whole optimization process, a dynamical updating strategy is proposed by comparing the current optimization solution and the original utopia point, and the local optimality problem is also solved. Moreover, an improved particle swarm optimization method with the Logistic map and adaptive weights is developed to further enhance the computing ability of the optimization solution. Finally, three examples are taken for simulations, and the results indicate that the relative errors between the global optimums and the optimal values are respectively reduced by 1.45, 1.06, and 0.14, compared with the existing approaches.