In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

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We present local search algorithms for timing-driven placement optimization. They find local slack optima for cells under arbitrary delay models and can be applied late in the design flow.The key ingredients are an implicit path straightening and a clustering of neighboring cells. Cell clusters are moved jointly to speed up the algorithm and escape suboptimal solutions, in which single cell algorithms are trapped, particularly in the presence of layer assignments. Given a cell cluster, we initially perform a line search for maximum slack on the straight line segment connecting the most critical upstream and downstream cells of the cluster. Thereby, the Euclidean path length is minimized. An iterative application will implicitly straighten the path. Later, slacks are improved further by applying ascent steps in estimated supergradient direction.The benefit of our algorithms is demonstrated experimentally within an industrial microprocessor design flow, and on recent ICCAD benchmarks circuits.

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