An efficient basis update for asymptotic linear programming

AbstractFor a linear program in which the constraint coefficients vary linearly with the time parameter, we showed in a previous paper that a basic feasible solution can be evaluated using O((k + 1)m3) arithmetic operations, where m is the number of constraints and k is the index of the basis matrix pair. Here we show, in the special case when k = 1 for all basis matrix pairs, and when one of the matrices in each pair has nearly full rank, how the (possibly singular) matrix factorization can be updated with only O(m2) operations, using rank-one update techniques. This makes the arithmetic complexity of updating the basis in asymptotic linear programming comparable to that of updating the inverse in ordinary linear programming, in this case. Moreover, we show that the result holds, in particular, when computing a Blackwell optimal policy for Markov decision chains in the unichain case or when all policies have only a small number of recurrent subchains

Long non-coding RNAs: spatial amplifiers that control nuclear structure and gene expression

Over the past decade, it has become clear that mammalian genomes encode thousands of long non-coding RNAs (lncRNAs), many of which are now implicated in diverse biological processes. Recent work studying the molecular mechanisms of several key examples — including Xist, which orchestrates X chromosome inactivation — has provided new insights into how lncRNAs can control cellular functions by acting in the nucleus. Here we discuss emerging mechanistic insights into how lncRNAs can regulate gene expression by coordinating regulatory proteins, localizing to target loci and shaping three-dimensional (3D) nuclear organization. We explore these principles to highlight biological challenges in gene regulation, in which lncRNAs are well-suited to perform roles that cannot be carried out by DNA elements or protein regulators alone, such as acting as spatial amplifiers of regulatory signals in the nucleus

Minimizing the expected processing time on a flexible machine with random tool lives

We present a stochastic version of economic tool life models for machines with finite capacity tool magazines and a variable processing speed capability, where the tool life is a random variable. Using renewal theory to express the expected number of tool setups as a function of cutting speed and magazine capacity, we extend previously published deterministic mathematical programming models to the case of minimizing the expected total processing time. A numerical illustration with typical cutting tool data shows the deterministic model underestimates the optimal expected processing time by more than 8% when the coefficient of variation equals 0.3 (typical for carbide tools), and the difference exceeds 15% for single-injury tools having an exponentially distributed economic life (worst case). Copyright © IIE

Using tool life models to minimize processing time on a flexible machine

Economic tool life models are presented for machines with finite capacity tool magazines and variable processing speed capability. Single and multiple part models for minimizing the total throughput time are formulated as nonlinear, integer programs (NLIP). An algorithm is presented for the NLP relaxation and a marginal analysis approach for solving the NLIP is detailed, giving an optimal tool loading policy as well as the processing speeds for each of the part types so as to minimize the makespan. A numerical example illustrates the procedures. © 1997 Taylor & Francis Group, LLC

Tool planning for a lights-out machining system

The goal of most advanced manufacturing systems is to continuously improve uptime while reducing the amount of direct supervision required for operations. However, when there is randomness in system components, this improvement can be difficult to attain. For instance, when automating metal cutting operations, the randomness of tool life requires ensuring that there are sufficient cutting tools available on the machines to meet unsupervised production requirements, and variations in tool life can make planning challenging. This paper focuses on the problem of selecting the cutting speeds for processing a set of part types by an unsupervised metal cutting flexible machine in such a situation. The machine is set up to operate unsupervised for a specific known duration. The tool magazine of this machine is preloaded with tools commensurate with the processing requirements. The lifetime of each tool is random, with the coefficient of variation assumed to be constant, and a system for online monitoring of the tool condition is available. The objective in this situation is to ensure that disruption is minimized-in other words, that the machine operates while ensuring some minimum probability of completion. This is referred to as the required service level. This paper presents models for determining the optimal magazine loading and cutting speeds that will meet a required service level. Solutions obtained using commonly available nonlinear programming solvers are included for illustration, and differences when the tool life distributions are either normal or Erlang are contrasted. © 2008 The Society of Manufacturing Engineers

Novel self-adaptive particle swarm optimization methods

This paper proposes adaptive versions of the particle swarm optimization algorithm (PSO). These new algorithms present self-adaptive inertia weight and time-varying adaptive swarm topology techniques. The objective of these new approaches is to avoid premature convergence by executing the exploration and exploitation stages simultaneously. Although proposed PSOs are fundamentally based on commonly utilized swarm behaviors of swarming creatures, the novelty is that the whole swarm may divide into many sub-swarms in order to find a good source of food or to flee from predators. This behavior allows the particles to disperse through the search space (diversification) and the sub-swarm, where the worst performance dies out while that with the best performance grows by producing offspring. The tendency of an individual particle to avoid collision with other particles by means of simple neighborhood rules is retained in these algorithms. Numerical experiments show that the new approaches, survival sub-swarms adaptive PSO (SSS-APSO) and survival sub-swarms adaptive PSO with velocity-line bouncing (SSS-APSO-vb), outperform other competitive algorithms by providing the best solutions on a suite of standard test problem with a much higher consistency than the algorithms compared