Application of Semidefinite Programming to Truss Design Optimization
Application of Semidefinite Programming to Truss Design Optimization
复制标题
半定规划在桁架设计优化中的应用
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Rasa Giniūnaitė
中科院分区：
文献类型：
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作者：
Rasa Giniūnaitė
半定规划（SDP）是一个相当新的方法来解决优化问题，在我们快速发展的世界变得越来越重要。它是半正定矩阵锥与仿射空间的交上的线性函数的极小化，即非线性但凸的约束。所有的线性问题和许多工程及组合优化问题都可以用SDP表示，因此它具有很强的适用性。有许多软件包使用不同的算法来解决SDP问题。它们可以从互联网上下载，很容易学会如何使用，其中两个是SeDuMi和SDPT-3。本文以桁架结构质量最小为目标，对桁架结构进行优化设计。经过一些代数运算后，该问题可以用半定规划来表示。采用SeDuMi和SDPT-3软件包进行求解，初始解的选择对SeDuMi的求解结果有很大影响。使用SDPT-3获得的质量平均小于使用SeDuMi获得的质量。此外，SDPT-3的工作效率更高。然而，我的方法和两个版本的粒子群优化算法的比较表明，半定规划一般更适合解决此类问题。
Semidefinite Programming (SDP) is a fairly recent way of solving optimization problems which are becoming more and more important in our fast moving world. It is a minimization of linear function over the intersection of the cone of positive semidefinite matrices with an affine space, i.e. non-linear but convex constraints. All linear problems and many engineering and combinatorial optimization problems can be expressed as SDP, so it is highly applicable. There are many packages that use different algorithms to solve SDP problems. They can be downloaded from internet and easily learnt how to use, two of these are SeDuMi and SDPT-3. In this paper truss structure optimization problem with the goal of minimizing the mass of the truss structure was solved. After doing some algebraic manipulation the problem was formulated suitably for Semidefinite Programming. SeDuMi and SDPT-3 packages were used to solve it. The choice of the initial solution had a great impact on the result using SeDuMi. The mass obtained using SDPT-3 was on average smaller than the one obtained using SeDuMi. Moreover, SDPT-3 worked more efficiently. However, the comparison of my approach and two versions of particle swarm optimization algorithm implied that semidefinite programming is in general more appropriate for solving such problems.