应用于工程设计的多目标优化方法比较

Comparison of multi-objective optimization methods on engineering design

归纳并分析了几种常用的多目标优化方法,在悬臂梁的双目标极小化问题和火箭发动机系统的双目标极大化问题中,用线性加权法、逐步宽容约束法、NCGA(Neighbor-hood Cultivation Genetic A lgorithm)法求解优化问题的非劣解集;用p模理想点法、最短距离法、极大模理想点法、目标规划法求解优化问题的非劣解.并且在悬臂梁的优化问题中,对不同的定值点用目标点法求解优化问题的非劣解,结果说明不同的定值点对应不同的优化结果.最后分别采用二元相对比较法和模糊关联度法求出以上问题的最佳非劣解.通过2个实例说明了这些方法的特点,证明了这些方法的实用性,适用于一般的多目标优化问题.

Several multi-objective optimization methods in common use were concluded. In two examples of bi-objective optimization for cantilever beam and rocket engine, linear weighted method and gradual easy constraint method and neighborhood cultivation genetic algorithm （NCGA） method were used to obtain Pareto Front. Ideal point method with p-module, the least distance method, ideal point method with max-module and goal programming method were used to obtain non-inferior solutions. The goal point was performed with diverse specific point that corresponded to diverse result in cantilever beam optimization. The optimal solution was respectively found from all non-inferior solutions by dualistic relative comparison and fuzzy related degree method. Examples indicate that multi-objective optimization methods and identification methods of the optimal solution are efficient and reliable applying to the general multi-objective optimization problems.