The heuristic k-means algorithm, widely used for cluster analysis, does not guarantee optimality. We developed a dynamic programming algorithm for optimal one-dimensional clustering. The algorithm is implemented as an R package called Ckmeans.1d.dp. We demonstrate its advantage in optimality and runtime over the standard iterative k-means algorithm.

We study the problem of arranging circuit components on a straight line so as to minimize the total wire length needed to realize the inter component nets. Branch-and-bound and dynamic programming algorithms that find optimal solutions are presented. In addition, heuristic approaches including some that employ the Monte Carlo method are developed and an experimental evaluation provided.

We extend a relaxation technique due to Bertsimas and Niño-Mora for the restless bandit problem to the case where arbitrary costs penalize switching between the bandits. We also construct a one-step lookahead policy using the solution of the relaxation. Computational experiments and a bound for approximate dynamic programming provide some empirical support for the heuristic.

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most “informative” sensing action amon...

This paper contributes to solve effectively stochastic resource allocation problems known to be NP-Complete. To address this complex resource management problem the Labeled Real-Time Dynamic Programming (lrtdp) approaches is applied in an effective way. lrtdp concentrates the planning on significant states of the environment only, as the search is guided by an initial heuristic. As demonstrated...