Genetic programming for the minimum time swing up and balance control acrobot problem

This work describes how genetic programming is applied to evolving controllers for the minimum time swing up and inverted balance tasks of the continuous state and action: limited torque acrobot. The best swing-up controller is able to swing the acrobot up to a position very close to the inverted ‘handstand’ position in a very short time, shorter than that of Coulom (2004), who applied the same constraints on the applied torque values, and to take only slightly longer than the approach by Lai et al. (2009) where far larger torque values were allowed. The best balance controller is able to balance the acrobot in the inverted position when starting from the balance position for the length of time used in the fitness function in all runs; furthermore, 47 out of 50 of the runs evolve controllers able to maintain the balance position for an extended period, an improvement on the balance controllers generated by Dracopoulos and Nichols (2012), which this paper is extended from. The most successful balance controller is also able to balance the acrobot when starting from a small offset from the balance position for this extended period.

Preconditioning 2D Integer Data for Fast Convex Hull Computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.