Carlos Humes

Distributed scheduling of flexible manufacturing systems: stability and performance

We consider a manufacturing system producing several part-types on several machines. Raw parts are input to the system. Each unit of a given part-type requires a predetermined processing time at each of several machines, in a given order. A setup time is required whenever a machine switches from processing one part-type to another. For a single machine system with constant demand rates, we present a class of generalized round-robin scheduling policies for which the buffer level trajectory of each part-type converges to a steady state level. Furthermore, for all small initial conditions, we show that these policies can be Pareto-efficient with respect to the buffer sizes required. Allowing the input streams to have some burstiness, we derive upper bounds on the buffer levels for small initial conditions. For non-acyclic systems, we consider a class of policies which are stable for all inputs with bounded burstiness. We show how to employ system elements, called regulators, to stabilize systems. Using the bounds for the single machine case, we analyze the performance of regulated systems implementing generalized round-robin scheduling policies. >

The symmetric eigenvalue complementarity problem

In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.

Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances

This paper presents a convergence proof technique for a broad class of proximal algorithms in which the perturbation term is separable and may contain barriers enforcing interval constraints. There are two key ingredients in the analysis: a mild regularity condition on the differential behavior of the barrier as one approaches an interval boundary and a lower stepsize limit that takes into account the curvature of the proximal term. We give two applications of our approach. First, we prove subsequential convergence of a very broad class of proximal minimization algorithms for convex optimization, where different stepsizes can be used for each coordinate. Applying these methods to the dual of a convex program, we obtain a wide class of multiplier methods with subsequential convergence of both primal and dual iterates and independent adjustment of the penalty parameter for each constraint. The adjustment rules for the penalty parameters generalize a well-established scheme for the exponential method of multipliers. The results may also be viewed as a generalization of recent work by Ben-Tal and Zibulevsky [SIAM J. Optim, 7 (1997), pp. 347--366] and Auslender, Teboulle, and Ben-Tiba [ Comput. Optim. Appl., 12 (1999), pp. 31--40; Math. Oper. Res., 24 (1999), pp. 645--668] on methods derived from

The delay of open Markovian queueing networks: uniform functional bounds, heavy traffic pole multiplicities, and stability

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An Exact Algorithm for Optimal MAE Stack Filter Design

-divergences. The second application established full convergence, under a novel stepsize condition, of Bregman-function-based proximal methods for general monotone operator problems over a box. Prior results in this area required strong restrictive assumptions on the monotone operator.

A feature selection approach for identification of signature genes from SAGE data

For open Markovian queueing networks, we study the functional dependence of the mean number in the system and thus also the mean delay since it is proportional to it by Littles Theorem on the arrival rate or load factor. We obtain linear programs LPs which provide bounds on the pole multiplicity M of the mean number in the system, and automatically obtain lower and upper bounds on the coefficients {Ci} of the expansion ρCM/1-ρM + ρCM-1/1-ρM-1 +... + ρC1/1-ρ + ρC0, where ρ is the load factor, which are valid for all ρ ∈ [0, 1. Our LPs can thus establish the stability of open networks for all arrival rates within capacity, while providing uniformly bounding functional expansions for the mean delay, valid for all arrival rates in the capacity region. The coefficients {Ci} can be optimized to provide the best bound at any desired value of the load factor, while still maintaining its validity for all ρ ∈ [0, 1. While the above LPs feature LL + 1M + 1/2 variables where L is the number of buffers in the network, for balanced systems we further provide a lower dimensional LP featuring just SS + 1/2 variables, where S is the number of stations in the network. This bound asymptotically dominates in heavy traffic a bound obtainable from the Pollaczek-Khintchine formula, and can capture interactions between multiple bottleneck stations in heavy traffic. We also provide an explicit upper bound for all scheduling policies in acyclic networks, and for the FBFS policy in open re-entrant lines.

A heuristic for the continuous capacity and flow assignment

We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems. Finally, we propose a specialization of the network Simplex algorithm based on column generation to solve these smaller subproblems. Using our method, we were able to efficiently solve instances of the filter problem with window size up to 25 pixels. To the best of our knowledge, this is the largest dimension for which this problem was ever solved exactly

A mixed dynamics approach for linear corridor policies: A revisitation of dynamic setup scheduling and flow control in manufacturing systems

BackgroundOne goal of gene expression profiling is to identify signature genes that robustly distinguish different types or grades of tumors. Several tumor classifiers based on expression profiling have been proposed using microarray technique. Due to important differences in the probabilistic models of microarray and SAGE technologies, it is important to develop suitable techniques to select specific genes from SAGE measurements.ResultsA new framework to select specific genes that distinguish different biological states based on the analysis of SAGE data is proposed. The new framework applies the bolstered error for the identification of strong genes that separate the biological states in a feature space defined by the gene expression of a training set. Credibility intervals defined from a probabilistic model of SAGE measurements are used to identify the genes that distinguish the different states with more reliability among all gene groups selected by the strong genes method. A score taking into account the credibility and the bolstered error values in order to rank the groups of considered genes is proposed. Results obtained using SAGE data from gliomas are presented, thus corroborating the introduced methodology.ConclusionThe model representing counting data, such as SAGE, provides additional statistical information that allows a more robust analysis. The additional statistical information provided by the probabilistic model is incorporated in the methodology described in the paper. The introduced method is suitable to identify signature genes that lead to a good separation of the biological states using SAGE and may be adapted for other counting methods such as Massive Parallel Signature Sequencing (MPSS) or the recent Sequencing-By-Synthesis (SBS) technique. Some of such genes identified by the proposed method may be useful to generate classifiers.

On finding global optima for the hinge fitting problem

Abstract This work deals with the Continuous Capacity and Flow Assignment (CFA) problem for the design of computer networks. This is a nonconvex optimization problem which has been usually solved by applying local optimization techniques. By rephrasing the problem in the context of concave programming and bringing an alternative formulation of the projected pairwise multicommodity flow polyhedron, a heuristic method for the search of a global minimum of the CFA is proposed. Its implementation is discussed, and computational tests with real backbone networks show that the proposed method compares favorably to previous approaches.

The projected pairwise multicommodity flow polyhedron

Sharifnia, Caramanis, and Gershwin [1991] introduced a class of policies for manufacturing systems, called by themlinear corridor policies. They proved that their stability can be discussed by the study of a simpler subset of such policies (cone policies). This paper revisits their work presenting a different description of the dynamics of the systems under study and explores it to device a necessary and sufficient condition for stability, obtained by the strengthening of the assumptions in Sharifnia et al. (1991). This condition is shown to be simply tested (M−1≥0) and valid for various realizations.