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针对多目标优化问题中目标间相互冲突的情况,运用相似性理论客观地挖掘目标值间的信息,基于离散Fréchet距离构建一种新的多目标优化方法,建立Z-score标准化—Max值归一化的二元映射组合,用此二元映射组合处理Pareto前沿及理想解对应的各项子目标函数值,将其映射为离散有序点串,并构建多个比较曲线和一个参考曲线。用离散Fréchet距离度量参考曲线与比较曲线的相似程度实现多目标优化,并以该值为适应度值引导遗传算法进化。与另外3种算法进行仿真比较的结果表明,新算法求得的优化解和各项性能指标多数优于其他算法,证明了新算法的可行性和有效性。
Aiming at the mutual conflicts between targets in multi-objective optimization problems, the similarity theory is used to objectively mine the information between targets and a new multi-objective optimization method based on discrete Fréchet distance is established to establish Z-score normalization The binary mapping combination is used to process the sub-objective function values corresponding to the Pareto front and ideal solutions. The sub-objective function values are mapped into discrete ordered point strings and multiple comparison curves and a reference curve are constructed. Multi-objective optimization is achieved by measuring the similarity between the reference curve and the comparison curve using the discrete Fréchet distance, and using this value as the fitness value to guide the evolution of the genetic algorithm. Compared with the other three algorithms, the simulation results show that the optimal solution and the performance indexes obtained by the new algorithm are better than other algorithms, which proves the feasibility and effectiveness of the new algorithm.