The Dutch Seminar on Optimization is an initiative to bring together researchers from the Netherlands and beyond, with topics that are centered around Optimization in a broad sense. We would like to invite all researchers, especially also PhD students, who are working on related topics to join the events. We hereby announce the following two talks, given by PhD-students:
Speaker: Jesse van Rijn (Twente)
Title: Towards a Lower Bound for the Average Case Runtime of Simulated Annealing on TSP
Date: Thursday 29 September, 4pm-4:30pm
We analyze simulated annealing (SA) for simple randomized instances of the Traveling Salesperson Problem. Our analysis shows that the theoretically optimal cooling schedule of Hajek explores members of the solution set which are in expectation far from the global optimum. We obtain a lower bound on the expected length of the final tour obtained by SA on these random instances. In addition, we also obtain an upper bound on the expected value of its variance. These bounds assume that the Markov chain that describes SA is stationary, a situation that does not truly hold in practice. Hence, we also formulate conditions under which the bounds extend to the nonstationary case. These bounds are obtained by comparing the tour length distribution to a related distribution. We furthermore provide numerical evidence for a stochastic dominance relation that appears to exist between these two distributions, and formulate a conjecture in this direction. If proved, this conjecture implies that SA stays far from the global optimum with high probability when executed for any sub-exponential number of iterations. This would show that SA requires at least exponentially many iterations to reach a global optimum with nonvanishing probability.
Speaker: Sander Borst (CWI)
Title: Selection in explorable heaps
Date: Thursday 29 September, 4:30pm-5pm
Explorable heap selection is the problem of selecting the nth smallest value in a binary heap, where the values can only be accessed by traversing the binary tree. In this setting we want to minimize the distance traveled in the tree. The problem is related to the node selection problem for the branch-and-bound algorithm.
The problem was originally proposed by Karp, Saks and Widgerson (FOCS '86), who also proposed algorithms for this problem. Recently we found a new algorithm, that improves on the running time. In this talk I will explain the problem, our new algorithm and the connection between the problem and branch-and-bound.