This thesis focuses on providing robust optimization models for minimization of the network congestion ratio and design of power efficient network that can handle fluctuation in traffic demands between source-destination pairs in the networks. It has become essential to design networks that are robust to different traffic conditions. In the first part of the thesis, we propose robust optimization models to minimize congestion ratio for better performance of the network. The simplest and widely used model to minimize the congestion ratio, called the pipe model, is based on precisely specified traffic demands. However, in practice, network operators are often unable to estimate exact traffic demands as they can fluctuate due to unpredictable factors. To overcome this weakness, we apply robust optimization to the problem of minimizing the network congestion ratio. First, we review existing models as robust counterparts of certain uncertainty sets. Then we consider robust optimization assuming ellipsoidal uncertainty sets; the total amount of squared errors in traffic demands is bounded by a positive constant which represents the total admissible fluctuations over the network, and derive a tractable optimization problem in the form of second-order cone programming (SOCP). Furthermore, we take uncertainty sets to be the intersection of ellipsoid and polyhedral sets, and considering the mirror subproblems inherent in the models, obtain tractable optimization problems, again in SOCP form. Compared to the previous model that assumes an error interval on each coordinate, our models have the advantage of being able to cope with the total amount of errors by setting a parameter that determines the volume of the ellipsoid. In the second part of the thesis, a green and robust optimization model is proposed to minimize the network power consumption. There are several researches that assume fluctuation in the traffic-demand matrix, our model is based on the idea of the green hose model where the knowledge of an exact traffic-demand matrix is not required. In the green hose model, the traffic sboundedbyjusttotal outgoing and incoming amount at each node. To allow fluctuations in traffic demands, here we also consider the same uncertainty set and subproblems as we did in the first part and formulate the green hose ellipsoid (green HE) model in the form of mixed-integer second-order cone programming (MISOCP) problem whose objective is to reduce the total energy by allowing some links to be put into the sleep mode.Furthermore, we establish a relationship between our model and the green HLT model, formulated from an extended version of the hose model called the hose model with bound of link traffic (HLT). Numerical results demonstrate that our proposed robust optimization models for congestion ratio and power efficent network achieves the performances with traffic luctuationscomparabletothe previous studies in terms of congestion ratio, computation time and power efficiency.本研究は、通信ネットワークの問題に対してロバスト最適化の手法を適用することをテーマとしている。1つ目の題材は、基幹ネットワークが混雑しないようにルーティングを定める問題である。基本的かつ重要な問題である。既存研究では、通信需要が正確にわかっているモデルや末端ノードにおける入出力量が制限されているモデルなど、さまざまなモデルが提案されている。この問題において通信需要が正確にはわかっていない場合を想定し、真の通信需要が楕円体と多面体の交わりに含まれているという仮定のもとでロバスト最適化の手法を適用し、その問題を2次錐計画問題として定式化した。いくつかの例に対して数値実験を行い、提案したモデルは汎用ソルバーを用いて合理的な時間内で求解可能であることを示し、また、従来のモデルとの比較検討を行なった。2つ目の題材は、エネルギーの節約のために不要なネットワークのリンクの電源を落とす問題である。このとき、真の通信需要が正確にはわからない状況は容易に起こりうるし、ネットワーク全体が通信需要のゆらぎに対して頑健であることが求められる。真の通信需要が楕円体と多面体の交わりに含まれているという仮定のもとでロバスト最適化の手法を適用し、その問題を整数2次錐計画問題として定式化し、実際に汎用最適化ソルバーで求解できることを示した。電気通信大学201
