Likelihood estimate of treatment effects under selection bias

We consider methods for estimating causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, simple comparison of treated and control outcomes will not generally yield valid estimates of casual effects. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based onsome strong assumptions, which are not directly testable. In this paper, we present an alternative modeling approachto draw causal inference by using share random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but it is also less sensitive to model misspecifications, which we consider, than the existing methods.

Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

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.

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.

A computational comparison of different algorithms for very large p-median problems

In this paper, we propose a new method for solving large scale p-median problem instances based on real data. We compare different approaches in terms of runtime, memory footprint and quality of solutions obtained. In order to test the different methods on real data, we introduce a new benchmark for the p-median problem based on real Swedish data. Because of the size of the problem addressed, up to 1938 candidate nodes, a number of algorithms, both exact and heuristic, are considered. We also propose an improved hybrid version of a genetic algorithm called impGA. Experiments show that impGA behaves as well as other methods for the standard set of medium-size problems taken from Beasley’s benchmark, but produces comparatively good results in terms of quality, runtime and memory footprint on our specific benchmark based on real Swedish data.