Seminar: Jesse van Rhijn (Universiteit Twente) and Sander Borst (CWI), 2 PhD talks

Speaker: Jesse van Rhijn (Universiteit Twente) and Sander Borst (Centrum Wiskunde & Informatica)

Title:

Jesse van Rhijn: Towards a Lower Bound for the Average Case Runtime of Simulated Annealing on TSP

Sander Borst: Selection in explorable heaps

Zoom link: 

https://cwi-nl.zoom.us/j/84909645595?pwd=b1M4QnNKVzNMdmNSVFNaZUJmR1kvUT09
(Meeting ID: 849 0964 5595, Passcode: 772448)

Abstract of "Towards a Lower Bound for the Average Case Runtime of Simulated Annealing on TSP" (Jesse van Rhijn):
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.

Video of the talk of Jesse van Rhijn:

Slides of the talk of Jesse van Rhijn:  
Slides

Abstract of "Selection in explorable heaps" (Sander Borst):
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.

Video of the talk of Sander Borst: 

Slides of the talk of Sander Borst:
Slides