Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems.
Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems.
复制标题
使用代理模型求解双层多目标规划问题的进化算法
DOI：
10.1371/journal.pone.0243926
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发表时间：
2020
期刊：
影响因子：
3.7
通讯作者：
Li H
中科院分区：
文献类型：
--
作者：
Liu Y;Li H;Li H
在领导者和/或追随者的层次上具有多个目标的双层规划问题，称为双层多目标规划问题（BMPP），是非常困难的，因为这个问题积累了层次结构和多目标优化的计算复杂性。作为一个强NP-hard问题，BMPP在两个层次上获得非支配解的计算成本很高，很少有研究解决这个问题。在这项研究中，一个进化算法开发使用代理优化模型来解决这些问题。首先，采用动态加权和方法来解决跟随者的多目标情况下，其中跟随者的问题被归类为几个单目标的。其次，对于每一个领导者的变量值，转换后的追随者的程序的最优解可以近似的自适应改进代理模型，而不是解决追随者的问题。最后，将这些技术嵌入到MOEA/D中，得到了领导者的非支配解。此外，在进化过程中利用梯度信息设计了启发式交叉算子。通过线性和非线性的算例验证了算法的有效性。
A bilevel programming problem with multiple objectives at the leader’s and/or follower’s levels, known as a bilevel multiobjective programming problem (BMPP), is extraordinarily hard as this problem accumulates the computational complexity of both hierarchical structures and multiobjective optimisation. As a strongly NP-hard problem, the BMPP incurs a significant computational cost in obtaining non-dominated solutions at both levels, and few studies have addressed this issue. In this study, an evolutionary algorithm is developed using surrogate optimisation models to solve such problems. First, a dynamic weighted sum method is adopted to address the follower’s multiple objective cases, in which the follower’s problem is categorised into several single-objective ones. Next, for each the leader’s variable values, the optimal solutions to the transformed follower’s programs can be approximated by adaptively improved surrogate models instead of solving the follower’s problems. Finally, these techniques are embedded in MOEA/D, by which the leader’s non-dominated solutions can be obtained. In addition, a heuristic crossover operator is designed using gradient information in the evolutionary procedure. The proposed algorithm is executed on some computational examples including linear and nonlinear cases, and the simulation results demonstrate the efficiency of the approach.
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