New results about multi-band uncertainty in Robust Optimization

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. The critical aim of our work is to close the knowledge gap about the adoption of a multi-band uncertainty set in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, which have been interested in getting a better modeling of arbitrary distributions, built on historical data of the uncertainty affecting the considered real-world problems. In this paper, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.Comment: 15 pages. The present paper is a revised version of the one appeared in the Proceedings of SEA 201

A fast ILP-based Heuristic for the robust design of Body Wireless Sensor Networks

We consider the problem of optimally designing a body wireless sensor network, while taking into account the uncertainty of data generation of biosensors. Since the related min-max robustness Integer Linear Programming (ILP) problem can be difficult to solve even for state-of-the-art commercial optimization solvers, we propose an original heuristic for its solution. The heuristic combines deterministic and probabilistic variable fixing strategies, guided by the information coming from strengthened linear relaxations of the ILP robust model, and includes a very large neighborhood search for reparation and improvement of generated solutions, formulated as an ILP problem solved exactly. Computational tests on realistic instances show that our heuristic finds solutions of much higher quality than a state-of-the-art solver and than an effective benchmark heuristic.Comment: This is the authors' final version of the paper published in G. Squillero and K. Sim (Eds.): EvoApplications 2017, Part I, LNCS 10199, pp. 1-17, 2017. DOI: 10.1007/978-3-319-55849-3\_16. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-55849-3_1

Towards the fast and robust optimal design of Wireless Body Area Networks

Wireless body area networks are wireless sensor networks whose adoption has recently emerged and spread in important healthcare applications, such as the remote monitoring of health conditions of patients. A major issue associated with the deployment of such networks is represented by energy consumption: in general, the batteries of the sensors cannot be easily replaced and recharged, so containing the usage of energy by a rational design of the network and of the routing is crucial. Another issue is represented by traffic uncertainty: body sensors may produce data at a variable rate that is not exactly known in advance, for example because the generation of data is event-driven. Neglecting traffic uncertainty may lead to wrong design and routing decisions, which may compromise the functionality of the network and have very bad effects on the health of the patients. In order to address these issues, in this work we propose the first robust optimization model for jointly optimizing the topology and the routing in body area networks under traffic uncertainty. Since the problem may result challenging even for a state-of-the-art optimization solver, we propose an original optimization algorithm that exploits suitable linear relaxations to guide a randomized fixing of the variables, supported by an exact large variable neighborhood search. Experiments on realistic instances indicate that our algorithm performs better than a state-of-the-art solver, fast producing solutions associated with improved optimality gaps.Comment: Authors' manuscript version of the paper that was published in Applied Soft Computin

Sensing Throughput Tradeoff for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel spectrum sensing algorithm, and examines the sensing throughput tradeoff for cognitive radio (CR) networks under noise variance uncertainty. It is assumed that there are one white sub-band, and one target sub-band which is either white or non-white. Under this assumption, first we propose a novel generalized energy detector (GED) for examining the target sub-band by exploiting the noise information of the white sub-band, then, we study the tradeoff between the sensing time and achievable throughput of the CR network. To study this tradeoff, we consider the sensing time optimization for maximizing the throughput of the CR network while appropriately protecting the primary network. The sensing time is optimized by utilizing the derived detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall (i.e., robust against noise variance uncertainty) and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal sensing times with perfect and imperfect noise variances are not the same. In particular, when the frame duration is 2s, and SNR is -20dB, and each of the bandwidths of the white and target sub-bands is 6MHz, the optimal sensing times are 28.5ms and 50.6ms with perfect and imperfect noise variances, respectively.Comment: Accepted in CROWNCOM, June 2014, Oulu, Finlan

Optimization of Trading Physics Models of Markets

We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models