Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Modeling a teacher in a tutorial-like system using Learning Automata

The goal of this paper is to present a novel approach to model the behavior of a Teacher in a Tutorial- like system. In this model, the Teacher is capable of presenting teaching material from a Socratic-type Domain model via multiple-choice questions. Since this knowledge is stored in the Domain model in chapters with different levels of complexity, the Teacher is able to present learning material of varying degrees of difficulty to the Students. In our model, we propose that the Teacher will be able to assist the Students to learn the more difficult material. In order to achieve this, he provides them with hints that are relative to the difficulty of the learning material presented. This enables the Students to cope with the process of handling more complex knowledge, and to be able to learn it appropriately. To our knowledge, the findings of this study are novel to the field of intelligent adaptation using Learning Automata (LA). The novelty lies in the fact that the learning system has a strategy by which it can deal with increasingly more complex/difficult Environments (or domains from which the learning as to be achieved). In our approach, the convergence of the Student models (represented by LA) is driven not only by the response of the Environment (Teacher), but also by the hints that are provided by the latter. Our proposed Teacher model has been tested against different benchmark Environments, and the results of these simulations have demonstrated the salient aspects of our model. The main conclusion is that Normal and Below-Normal learners benefited significantly from the hints provided by the Teacher, while the benefits to (brilliant) Fast learners were marginal. This seems to be in-line with our subjective understanding of the behavior of real-life Students

Probabilistic coloring of bipartite and split graphs

We revisit in this paper the probabilistic coloring problem (probabilistic coloring) and focus ourselves on bipartite and split graphs. We first give some general properties dealing with the optimal solution. We then show that the unique 2-coloring achieves approximation ratio 2 in bipartite graphs under any system of vertex-probabilities and propose a polynomial algorithm achieving tight approximation ratio 8/7 under identical vertex-probabilities. Then we deal with restricted cases of bipartite graphs. Main results for these cases are the following. Under non-identical vertex-probabilities probabilistic coloring is polynomial for stars, for trees with bounded degree and a fixed number of distinct vertex-probabilities, and, consequently, also for paths with a fixed number of distinct vertex-probabilities. Under identical vertex-probabilities, probabilistic coloring is polynomial for paths, for even and odd cycles and for trees whose leaves are either at even or at odd levels. Next, we deal with split graphs and show that probabilistic coloring is NP-hard, even under identical vertex-probabilities. Finally, we study approximation in split graphs and provide a 2-approximation algorithm for the case of distinct probabilities and a polynomial time approximation schema under identical vertex-probabilities

Characterization of the probabilistic traveling salesman problem

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E((L) over bar (pruned))=rootnp(0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np-->infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L-a priori)=rootn/pbeta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05less than or equal topless than or equal to0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required

A semidefinite optimization approach to the steady-state analysis of queueing systems

10.1007/s11134-007-9028-7Queueing Systems56127-3

A novel information theory method for filter feature selection

In this paper, we propose a novel filter for feature selection. Such filter relies on the estimation of the mutual information between features and classes. We bypass the estimation of the probability density function with the aid of the entropic-graphs approximation of Rényi entropy, and the subsequent approximation of the Shannon one. The complexity of such bypassing process does not depend on the number of dimensions but on the number of patterns/samples, and thus the curse of dimensionality is circumvented. We show that it is then possible to outperform a greedy algorithm based on the maximal relevance and minimal redundancy criterion. We successfully test our method both in the contexts of image classification and microarray data classification.This research is funded by the project DPI2005-01280 from the Spanish Government