Directed mating using inverted PBI function for constrained multi-objective optimization
Directed mating using inverted PBI function for constrained multi-objective optimization
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DOI：
10.1109/cec.2015.7257253
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发表时间：
2015-05
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影响因子：
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通讯作者：
Minami Miyakawa;K. Takadama;Hiroyuki Sato
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文献类型：
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作者：
Minami Miyakawa;K. Takadama;Hiroyuki Sato
在进化约束多目标优化中，利用目标函数值优于可行解的有用不可行解进行定向交配，显著提高了搜索性能。本文通过研究目标空间中的搜索方向，进一步提高了定向交配的有效性。由于传统的有向交配选择有用的不可行的解决方案的基础上Pareto优势，所有的解决方案被赋予相同的搜索方向，而不管它们在目标空间中的位置。为了提高进化约束多目标优化中所得解的多样性，我们提出了一种使用反向PBI（IPBI）标度化函数的定向交配变体。建议IPBI为基础的定向交配提供了唯一的搜索方向，所有的解决方案，这取决于他们在目标空间中的位置。此外，所提出的基于IPBI的定向交配可以通过参数θ来控制每个解的搜索方向的方向性强度。我们使用离散的m-目标k-背包问题和连续的mCDTLZ问题与2-4个目标，并比较TNSDM算法的搜索性能，使用传统的定向交配和建议TNSDM-IPBI使用IPBI为基础的定向交配。实验结果表明，在所有测试问题中，采用适当的θ*，TNSDM-IPBI算法通过提高目标空间解的多样性，获得了比传统TNSDM算法更高的搜索性能.
In evolutionary constrained multi-objective optimization, the directed mating utilizing useful infeasible solutions having better objective function values than feasible solutions significantly contributes to improving the search performance. This work tries to further improve the effectiveness of the directed mating by focusing on the search directions in the objective space. Since the conventional directed mating picks useful infeasible solutions based on Pareto dominance, all solutions are given the same search direction regardless of their locations in the objective space. To improve the diversity of the obtained solutions in evolutionary constrained multi-objective optimization, we propose a variant of the directed mating using the inverted PBI (IPBI) scalarizing function. The proposed IPBI-based directed mating gives unique search directions to all solutions depending on their locations in the objective space. Also, the proposed IPBI-based directed mating can control the strength of directionality for each solution's search direction by the parameter θ. We use discrete m-objective k-knapsack problems and continuous mCDTLZ problems with 2-4 objectives and compare the search performances of TNSDM algorithm using the conventional directed mating and the proposed TNSDM-IPBI using IPBI-based directed mating. The experimental results shows that the proposed TNSDM-IPBI using the appropriate θ* achieves higher search performance than the conventional TNSDM in all test problems used in this work by improving the diversity of solutions in the objective space.