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.

Article in: English

Article published: 2015-07-13