Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems

In this paper, a novel genetic algorithm is developed by generating artificial chromosomes with probability control to solve the machine scheduling problems. Generating artificial chromosomes for Genetic Algorithm (ACGA) is closely related to Evolutionary Algorithms Based on Probabilistic Models (EAPM). The artificial chromosomes are generated by a probability model that extracts the gene information from current population. ACGA is considered as a hybrid algorithm because both the conventional genetic operators and a probability model are integrated. The ACGA proposed in this paper, further employs the ``evaporation concept'' applied in Ant Colony Optimization (ACO) to solve the permutation flowshop problem. The ``evaporation concept'' is used to reduce the effect of past experience and to explore new alternative solutions. In this paper, we propose three different methods for the probability of evaporation. This probability of evaporation is applied as soon as a job is assigned to a position in the permutation flowshop problem. Experimental results show that our ACGA with the evaporation concept gives better performance than some algorithms in the literature.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

A real coded genetic algorithm for data partitioning and scheduling in networks with arbitrary processor release time

The problem of scheduling divisible loads in distributed computing systems, in presence of processor release time is considered. The objective is to find the optimal sequence of load distribution and the optimal load fractions assigned to each processor in the system such that the processing time of the entire processing load is a minimum. This is a difficult combinatorial optimization problem and hence genetic algorithms approach is presented for its solution.

On the ignition and extinction problems in forced convection systems

In this paper the problem of ignition and extinction has been formulated for the flow of a compressible fluid with Prandtl and Schmidt numbers taken as unity. In particular, the problems of (i) a jet impinging on a wall of combustible material and (ii) the opposed jet diffusion flame have been studied. In the wall jet case, three approximations in the momentum equation namely, (i) potential flow, (ii) viscous flow, (ii) viscous incompressible with k = 1 and (iii) Lees' approximation (taking pressure gradient terms zero) are studied. It is shown that the predictions of the mass flow rates at extinction are not very sensitive to the approximations made in the momentum equation. The effects of varying the wall temperature in the case (i) and the jet temperature in the case (ii) on the extinction speeds have been studied. The effects of varying the activation energy and the free stream oxidant concentration in case (ii), have also been investigated.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

Efficient Algorithms for Computing All Low s-t Edge Connectivities and Related Problems

Given an undirected unweighted graph G = (V, E) and an integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk3) for this problem, where |V| = n and |E| = m. Our output is a weighted tree T whose nodes are the sets V1, V2,..., V l of a partition of V, with the property that the edge connectivity in G between any two vertices s ε Vi and t ε Vj, for i ≠ j, is equal to the weight of the lightest edge on the path between Vi and Vj in T. Also, two vertices s and t belong to the same Vi for any i if and only if they have an edge connectivity greater than k. Currently, the best algorithm for this problem needs to compute all-pairs min-cuts in an O(nk) edge graph; this takes Õ(m + n5/2kmin{k1/2, n1/6}) time. Our algorithm is much faster for small values of k; in fact, it is faster whenever k is o(n5/6). Our algorithm yields the useful corollary that in Õ(m + nc3) time, where c is the size of the global min-cut, we can compute the edge connectivities of all those pairs of vertices whose edge connectivity is at most αc for some constant α. We also present an Õ(m + n) Monte Carlo algorithm for the approximate version of this problem. This algorithm is applicable to weighted graphs as well. Our algorithm, with some modifications, also solves another problem called the minimum T-cut problem. Given T ⊆ V of even cardinality, we present an Õ(m + nk3) algorithm to compute a minimum cut that splits T into two odd cardinality components, where k is the size of this cut.

An Accurate Model for EESM and its Application to Analysis of CQI Feedback Schemes and Scheduling in LTE

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Joint evaluation of channel feedback schemes, rate adaptation, and scheduling in OFDMA downlinks with feedback delays

Orthogonal frequency-division multiple access (OFDMA) systems divide the available bandwidth into orthogonal subchannels and exploit multiuser diversity and frequency selectivity to achieve high spectral efficiencies. However, they require a significant amount of channel state feedback for scheduling and rate adaptation and are sensitive to feedback delays. We develop a comprehensive analysis for OFDMA system throughput in the presence of feedback delays as a function of the feedback scheme, frequency-domain scheduler, and rate adaptation rule. Also derived are expressions for the outage probability, which captures the inability of a subchannel to successfully carry data due to the feedback scheme or feedback delays. Our model encompasses the popular best-n and threshold-based feedback schemes and the greedy, proportional fair, and round-robin schedulers that cover a wide range of throughput versus fairness tradeoff. It helps quantify the different robustness of the schedulers to feedback overhead and delays. Even at low vehicular speeds, it shows that small feedback delays markedly degrade the throughput and increase the outage probability. Further, given the feedback delay, the throughput degradation depends primarily on the feedback overhead and not on the feedback scheme itself. We also show how to optimize the rate adaptation thresholds as a function of feedback delay.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

Low Complexity Power and Scheduling Policies for Wireless Networks to Provide Quality of Service

We consider optimal power allocation policies for a single server, multiuser system. The power is consumed in transmission of data only. The transmission channel may experience multipath fading. We obtain very efficient, low computational complexity algorithms which minimize power and ensure stability of the data queues. We also obtain policies when the users may have mean delay constraints. If the power required is a linear function of rate then we exploit linearity and obtain linear programs with low complexity.

DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

Scheduling parallel batch processors with incompatible job families using ant colony optimization

The present work concerns with the static scheduling of jobs to parallel identical batch processors with incompatible job families for minimizing the total weighted tardiness. This scheduling problem is applicable in burn-in operations and wafer fabrication in semiconductor manufacturing. We decompose the problem into two stages: batch formation and batch scheduling, as in the literature. The Ant Colony Optimization (ACO) based algorithm called ATC-BACO algorithm is developed in which ACO is used to solve the batch scheduling problems. Our computational experimentation shows that the proposed ATC-BACO algorithm performs better than the available best traditional dispatching rule called ATC-BATC rule.

Joint Power Control, Scheduling and Routing for Multihop Energy Harvesting Sensor Networks

We study wireless multihop energy harvesting sensor networks employed for random field estimation. The sensors sense the random field and generate data that is to be sent to a fusion node for estimation. Each sensor has an energy harvesting source and can operate in two modes: Wake and Sleep. We consider the problem of obtaining jointly optimal power control, routing and scheduling policies that ensure a fair utilization of network resources. This problem has a high computational complexity. Therefore, we develop a computationally efficient suboptimal approach to obtain good solutions to this problem. We study the optimal solution and performance of the suboptimal approach through some numerical examples.