Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of Lagrangian Relaxation and the semidefinite relaxation. Then we focus on two special classes of QCQP, whose objective and constraint functions take the form trace(X^TQX + 2C^T X) + β, and trace(X^TQX + XPX^T + 2C^T X)+ β respectively, where X is an n by r real matrix. For each class of problems, we proposed different semidefinite relaxation formulations and compared their strength. The theoretical results obtained in this thesis have found interesting applications, e.g., solving the Quadratic Assignment Problem.

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Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of Lagrangian Relaxation and the semidefinite relaxation. Then we focus on two special classes of QCQP, whose objective and constraint functions take the form trace(X^TQX + 2C^T X) + β, and trace(X^TQX + XPX^T + 2C^T X)+ β respectively, where X is an n by r real matrix. For each class of problems, we proposed different semidefinite relaxation formulations and compared their strength. The theoretical results obtained in this thesis have found interesting applications, e.g., solving the Quadratic Assignment Problem.

This Master’s Thesis deals with a special problem that may be of importance when planning a frequency hopping mobile communication network. In normal cases the Frequency Assignment Problem is solved, in order to plan the use of frequencies in a network. The special case discussed in this thesis occurs when the network operator requires that the frequencies must be arranged into groups. In this case the Frequency Assignment Problem must be solved with respect to the groups, i.e. a Group assignment Problem. The thesis constitutes the final part of the Master of Science in Communication and Transport Systems Engineering education, at Linköping University, Campus Norrköping. The Group Arrangement Problem was presented by ComOpt, a company that has specialized in solving the Frequency Assignment Problem for network operators. This thesis does not deal with solutions for the Frequency Assignment Problem, with respect to the groups. The main issue in the thesis is to construct a computer based algorithm that solves the Group Arrangement Problem, i.e. creating the groups. The goal is to construct an algorithm that creates groups which imply a better solution for the Frequency Assignment Problem than manually created groups. Two algorithms are presented and tested on two cases. Their respective results for both cases are compared with the results from a manual grouping. The two computer based algorithms creates better groups than the manual grouping strategy, according to an artificial quality measure. As of spring 2003 a variant of one of the presented algorithms was implemented in ComOpt’s product for solving the Frequency Assignment Problem.

Grid computing has emerged as a global platform to support organizations for coordinated sharing of distributed data, applications, and processes. Additionally, Grid computing has also leveraged web services to define standard interfaces for Grid services adopting the service-oriented view. Consequently, there have been significant efforts to enable applications capable of tackling computationally intensive problems as services on the Grid. In order to ensure that the available services are assigned to the high volume of incoming requests efficiently, it is important to have a robust service selection algorithm. The selection algorithm should not only increase access to the distributed services, promoting operational flexibility and collaboration, but should also allow service providers to scale efficiently to meet a variety of demands while adhering to certain current Quality of Service (QoS) standards. In this research, two service selection algorithms, namely the Particle Swarm Intelligence based Service Selection Algorithm (PSI Selection Algorithm) based on the Multiple Objective Particle Swarm Optimization algorithm using Crowding Distance technique, and the Constraint Satisfaction based Selection (CSS) algorithm, are proposed. The proposed selection algorithms are designed to achieve the following goals: handling large number of incoming requests simultaneously; achieving high match scores in the case of competitive matching of similar types of incoming requests; assigning each services efficiently to all the incoming requests; providing the service requesters the flexibility to provide multiple service selection criteria based on a QoS metric; selecting the appropriate services for the incoming requests within a reasonable time. Next, the two algorithms are verified by a standard assignment problem algorithm called the Munkres algorithm. The feasibility and the accuracy of the proposed algorithms are then tested using various evaluation methods. These evaluations are based on various real world scenarios to check the accuracy of the algorithm, which is primarily based on how closely the requests are being matched to the available services based on the QoS parameters provided by the requesters.

The growing extent and variety of present military operations forces to use the resources in hand at its best. Especially, the optimum usage and assignment of limited number of the air force resources to missions will provide a considerable advantage in the battle field. The problem of finding the feasible and optimum assignment has been known to be studied / yet performing the process faster is still a topic that captures researchers&rsquo / attention because of the computational complexity that the assignment problem involves within. In this thesis, exploring the optimal assignment of fleets/aircrafts to targets/groups of targets is going to be performed via algorithms and heuristics. As the best choice for finding the exact solution, Branch-and-Bound algorithm, which is an intelligent way of searching for the solution on a solution tree where the nodes with potential of not leading to the solution are fathomed, has been investigated and applied according to the specific problem needs. The number of nodes on the search tree increases exponentially as the problem size increases. Moreover / as the size of the assignment problem increases, attaining the solution solely by Branch-and-Bound algorithm is definitely computationally expensive due to memory and time requirements. Therefore, Genetic algorithm which can provide good solutions in a relatively short time without having computational difficulties is considered as the second algorithm. Branch-and-Bound algorithm and Genetic algorithm are separately used for obtaining the solution. Hybrid algorithms which are combinations of Branch-and-Bound and Genetic algorithms are used with heuristics for improving the results.

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The research reported in this thesis considers the classical combinatorial optimization problem known as the Generalized Assignment Problem (GAP). Since the mid 1970's researchers have been developing solution approaches for this particular type of problem due to its importance both in practical and theoretical terms. Early attempts at solving GAP tended to use exact integer programming techniques such as Branch and Bound. Although these tended to be reasonably successful on small problem instances they struggle to cope with the increase in computational effort required to solve larger instances. The increase in available computing power during the 1980's and 1990's coincided with the development of some highly efficient heuristic approaches such as Tabu Search (TS), Genetic Algorithms (GA) and Simulated Annealing (SA). Heuristic approaches were subsequently developed that were able to obtain high quality solutions to larger and more complex instances of GAP. Most of these heuristic approaches were able to outperform highly sophisticated commercial mathematical programming software since the heuristics tend to be tailored to the problem and therefore exploit its structure. A new approach for solving GAP has been developed during this research that combines the exact Branch and Bound approach and the heuristic strategy of Tabu Search to produce a hybrid algorithm for solving GAP. This approach utilizes the mathematical programming software Xpress-MP as a Branch and Bound solver in order to solve sub-problems that are generated by the Tabu Search guiding heuristic. Tabu Search makes use of memory structures that record information about attributes of solutions visited during the search. This information is used to guide the search and in the case of the hybrid algorithm to generate sub problems to pass to the Branch and Bound solver. The new algorithm has been developed, imp lemented and tested on benchmark test problems that are extremely challenging and a comprehensive report and analysis of the experimentation is reported in this thesis.

Tabu search based algorithms are among the widely used heuristic algorithms for combinatorial optimization problems. In this project, we propose an improved enhanced tabu search algorithm for the well-known combinatorial optimization problem, the quadratic assignment problem (QAP). The new algorithm was tested on a number of instances from the library of the QAP instances  QAPLIB. The results obtained from the experiments show that the proposed algorithm appears to be superior to the earlier "pure" tabu search algorithms on many instances of the QAP.

Many computer vision problems, such as object classification, motion estimation or shape registration rely on solving the correspondence problem. Existing algorithms to solve spatial or temporal correspondence problems are usually NP-hard, difficult to approximate, lack flexible models and mechanism for feature weighting. This proposal addresses the correspondence problem in computer vision, and proposes two new spatio-temporal correspondence problems and three algorithms to solve spatial, temporal and spatio-temporal matching between video and other sources. The main contributions of the thesis are: (1) Factorial graph matching (FGM). FGM extends existing work on graph matching (GM) by finding an exact factorization of the affinity matrix. Four are the benefits that follow from this factorization: (a) There is no need to compute the costly (in space and time) pairwise affinity matrix; (b) It provides a unified framework that reveals commonalities and differences between GM methods. Moreover, the factorization provides a clean connection with other matching algorithms such as iterative closest point; (c) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (d) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (2) Canonical time warping (CTW). CTW is a technique to temporally align multiple multi-dimensional and multi-modal time series. CTW extends DTW by incorporating a feature weighting layer to adapt different modalities, allowing a more flexible warping as combination of monotonic functions, and has linear complexity (unlike DTW that has quadratic). We applied CTW to align human motion captured with different sensors (e.g., audio, video, accelerometers). (3) Spatio-temporal matching (STM). Given a video and a 3D motion capture model, STM finds the correspondence between subsets of video trajectories and the motion capture model. STM is efficiently and robustly solved using linear programming. We illustrate the performance of STM on the problem of human detection in video, and show how STM achieves state-of-the-art performance.