Uniform sampling of local pareto-optimal solution curves by pareto path following and its applications in multi-objective GA
Uniform sampling of local pareto-optimal solution curves by pareto path following and its applications in multi-objective GA
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DOI：
10.1145/1276958.1277120
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
Ken Harada;J. Sakuma;S. Kobayashi;I. Ono
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文献类型：
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作者：
Ken Harada;J. Sakuma;S. Kobayashi;I. Ono
多目标遗传算法（莫加）是一种高效的多目标优化方法，但也存在一些需要解决的局限性，包括解的一致性不能保证，Pareto最优解的边界不能确定等。它已被证明，在双目标问题，这是本文的主题，局部帕累托最优解的形式曲线。在这种情况下，莫加的一些局限性可以通过在变量空间和目标空间中均匀采样曲线来解决。本文提出了Pareto路径跟踪算法（PPF），它通过扩展数值路径跟踪算法的框架来进行采样，验证了PPF具有期望的行为，并将PPF扩展到多个目标函数的问题，PPF的应用不局限于莫加得到的解的精化。PPF使得自然地具有局部Pareto最优解曲线作为搜索单元，这导致基于曲线的莫加。PPF还可以检查哪些Pareto最优解曲线是通过MOO方法找到的，并且可以定义基于它的性能度量。本文提出了这些应用的PPF在莫加和比较标准的莫加和曲线为基础的莫加使用的度量，以揭示他们的特点。
Although multi-objective GA (MOGA) is an efficient multi-objective optimization (MOO) method, it has some limitations that need to be tackled, which include unguaranteed uniformity of solutions and uncertain finding of periphery of Pareto-optimal solutions. It has been shown that, on bi-objective problems, which are the subject of this paper, local Pareto-optimal solutions form curves. In this case, some of the limitations of MOGA can be resolved by sampling the curves uniformly in the variable space and in the objective space. This paper proposes Pareto Path Following (PPF) which does the sampling by extending the framework of Numerical Path Following, verifies that PPF exhibits the desired behaviors, and addresses the extension of PPF for problems with more than two objective functions.Application of PPF is not limited to refinement of solutions obtained with MOGA. PPF makes it natural to have a local Pareto-optimal solution curve as the unit of search, which leads to curve-based MOGA. PPF also enables examination of which Pareto-optimal solution curves are found by MOO methods, and performance metrics based on it can be defined. This paper proposes these applications of PPF in MOGA and compares standard MOGA and curve-based MOGA using the metrics to reveal their characteristics.