Branch and Bound Algorithm for Multiprocessor Scheduling

The multiprocessor task graph scheduling problem has been extensively studied asacademic optimization problem which occurs in optimizing the execution time of parallelalgorithm with parallel computer. The problem is already being known as one of the NPhardproblems. There are many good approaches made with many optimizing algorithmto find out the optimum solution for this problem with less computational time. One ofthem is branch and bound algorithm.In this paper, we propose a branch and bound algorithm for the multiprocessor schedulingproblem. We investigate the algorithm by comparing two different lower bounds withtheir computational costs and the size of the pruned tree.Several experiments are made with small set of problems and results are compared indifferent sections.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Optimization of cable cycles : a trade-off between reliability and cost

This paper elaborates the routing of cable cycle through available routes in a building in order to link a set of devices, in a most reasonable way. Despite of the similarities to other NP-hard routing problems, the only goal is not only to minimize the cost (length of the cycle) but also to increase the reliability of the path (in case of a cable cut) which is assessed by a risk factor. Since there is often a trade-off between the risk and length factors, a criterion for ranking candidates and deciding the most reasonable solution is defined. A set of techniques is proposed to perform an efficient and exact search among candidates. A novel graph is introduced to reduce the search-space, and navigate the search toward feasible and desirable solutions. Moreover, admissible heuristic length estimation helps to early detection of partial cycles which lead to unreasonable solutions. The results show that the method provides solutions which are both technically and financially reasonable. Furthermore, it is proved that the proposed techniques are very efficient in reducing the computational time of the search to a reasonable amount.

Computational study of the step size parameter of the subgradient optimization method

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.