Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times

We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

Hybrid algorithms for power system unit commitment

Four hybrid algorithms has been developed for the solution of the unit commitment problem. They use simulated annealing as one of the constituent techniques, and produce lower cost schedules; two of them have less overhead than other soft computing techniques. They are also more robust to the choice of parameters. A special technique avoids the generating of infeasible schedules, and thus reduces computation time.

New algorithms of the Q-learning type

We propose two algorithms for Q-learning that use the two-timescale stochastic approximation methodology. The first of these updates Q-values of all feasible state–action pairs at each instant while the second updates Q-values of states with actions chosen according to the ‘current’ randomized policy updates. A proof of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms on an application of routing in communication networks are presented on a few different settings.

OFDM-MAC algorithms and their impact on TCP performance in next generation mobile networks

Next generation wireless systems employ Orthogonal frequency division multiplexing (OFDM) physical layer owing to the high data rate transmissions that are possible without increase in bandwidth. While TCP performance has been extensively studied for interaction with link layer ARQ, little attention has been given to the interaction of TCP with MAC layer. In this work, we explore cross-layer interactions in an OFDM based wireless system, specifically focusing on channel-aware resource allocation strategies at the MAC layer and its impact on TCP congestion control. Both efficiency and fairness oriented MAC resource allocation strategies were designed for evaluating the performance of TCP. The former schemes try to exploit the channel diversity to maximize the system throughput, while the latter schemes try to provide a fair resource allocation over sufficiently long time duration. From a TCP goodput standpoint, we show that the class of MAC algorithms that incorporate a fairness metric and consider the backlog outperform the channel diversity exploiting schemes.

New approximation algorithms for minimum cycle bases of graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time 0(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time 0(n(3+2/k)), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega)) bound. We also present a 2-approximation algorithm with O(m(omega) root n log n) expected running time, a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Parametrized actor-critic algorithms for finite-horizon MDPs

Due to their non-stationarity, finite-horizon Markov decision processes (FH-MDPs) have one probability transition matrix per stage. Thus the curse of dimensionality affects FH-MDPs more severely than infinite-horizon MDPs. We propose two parametrized 'actor-critic' algorithms to compute optimal policies for FH-MDPs. Both algorithms use the two-timescale stochastic approximation technique, thus simultaneously performing gradient search in the parametrized policy space (the 'actor') on a slower timescale and learning the policy gradient (the 'critic') via a faster recursion. This is in contrast to methods where critic recursions learn the cost-to-go proper. We show w.p 1 convergence to a set with the necessary condition for constrained optima. The proposed parameterization is for FHMDPs with compact action sets, although certain exceptions can be handled. Further, a third algorithm for stochastic control of stopping time processes is presented. We explain why current policy evaluation methods do not work as critic to the proposed actor recursion. Simulation results from flow-control in communication networks attest to the performance advantages of all three algorithms.

Parallel implementation of AutoDock

Computational docking of ligands to protein structures is a key step in structure-based drug design. Currently, the time required for each docking run is high and thus limits the use of docking in a high-throughput manner, warranting parallelization of docking algorithms. AutoDock, a widely used tool, has been chosen for parallelization. Near-linear increases in speed were observed with 96 processors, reducing the time required for docking ligands to HIV-protease from 81 min, as an example, on a single IBM Power-5 processor ( 1.65 GHz), to about 1 min on an IBM cluster, with 96 such processors. This implementation would make it feasible to perform virtual ligand screening using AutoDock.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Splitting Algorithms for Fast Relay Selection: Generalizations, Analysis, and a Unified View

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new contention load' parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q >= 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

A Dynamic Migration Model for Self-adaptive Genetic Algorithms

In this paper, we propose a self Adaptive Migration Model for Genetic Algorithms, where parameters of population size, the number of points of crossover and mutation rate for each population are fixed adaptively. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions, when compared with Island model GA(IGA) and Simple GA(SGA).

Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

Two algorithms are outlined, each of which has interesting features for modeling of spatial variability of rock depth. In this paper, reduced level of rock at Bangalore, India, is arrived from the 652 boreholes data in the area covering 220 sqa <.km. Support vector machine (SVM) and relevance vector machine (RVM) have been utilized to predict the reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth. The support vector machine (SVM) that is firmly based on the theory of statistical learning theory uses regression technique by introducing epsilon-insensitive loss function has been adopted. RVM is a probabilistic model similar to the widespread SVM, but where the training takes place in a Bayesian framework. Prediction results show the ability of learning machine to build accurate models for spatial variability of rock depth with strong predictive capabilities. The paper also highlights the capability ofRVM over the SVM model.

A Dynamic Migration Model for self-adaptive Genetic Algorithms

In this paper, we propose a self Adaptive Migration Model for Genetic Algorithms, where parameters of population size, the number of points of crossover and mutation rate for each population are fixed adaptively. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions, when compared with Island model GA(IGA) and Simple GA(SGA).

Preparation, characterization and thermal decomposition of praseodymium, terbium and neodymium carbonates

The preparation of three different types of carbonates of praseodymium, neodymium and terbium has been described. The carbonates have been characterized by potentiometry, chemical analysis, X-ray crystallography, infra-red spectroscopy and by their thermal behaviour. The thermal decomposition of several carbonates has been studied exhaustively under a variety of conditions and the stoicheiometry, thermodynamics and energetics of the reactions at various stages of decomposition have been examined. The stoicheiometry of the oxides obtained as final products of decomposition has been examined.

Generic Routing Rules and a Scalable Access Enhancement for the Network-on-Chip RECONNECT

RECONNECT is a Network-on-Chip using a honeycomb topology. In this paper we focus on properties of general rules applicable to a variety of routing algorithms for the NoC which take into account the missing links of the honeycomb topology when compared to a mesh. We also extend the original proposal [5] and show a method to insert and extract data to and from the network. Access Routers at the boundary of the execution fabric establish connections to multiple periphery modules and create a torus to decrease the node distances. Our approach is scalable and ensures homogeneity among the compute elements in the NoC. We synthesized and evaluated the proposed enhancement in terms of power dissipation and area. Our results indicate that the impact of necessary alterations to the fabric is negligible and effects the data transfer between the fabric and the periphery only marginally.