Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xi, 87 p. : ill. Includes abstract. Includes bibliographical references (p. 84-87).

The study of Stochastic Local Search (SLS) algorithms is becoming more pivotal these days, due to their vast number of applications in decision making. Prior to the implementation of algorithmic knowledge for decision making, many decisions were made based on manual calculation, on the fly, or even based on guts feeling. Nowadays, such an approach is more rarely seen, especially when the decisions that need to be made are high-risk, cost intensive, or time-consuming. The increasingly often used SLS algorithms are one of the options available to assist the decision making process these days.The work discussed in this thesis concerns the study of SLS algorithms for solving the Quadratic Assignment Problem (QAP), a prominent combinatorial optimization problem, which until today is very hard to solve. Our interest is to study the behavior and performance of SLS algorithms for solving QAP instances of different characteristics, such as size, sparsity, and structure. In this study, we have also proposed new variants of SLS algorithms, inspired by existing, well-performing SLS algorithms for solving the QAP. The new variants of SLS algorithms are then further extended for solving the bi-objective QAP (bQAP).One main focus in this study is to see how the performance of algorithms scales with instance size. We have considered instances that are much larger than the ones usually used in the studies of algorithms for solving the QAP. By understanding how the algorithms perform when the instance size changes, we might be able to solve other problems effectively by considering the similarity in their characteristics to the ones of the QAP, or by seeing common trends in the relative performance of the various available SLS methods. For single objective QAP instances we found that the structure and size of instances do have a significant impact on the performance of SLS algorithms. For example, comparisons between Tabu Search (TS) and Simulated Annealing (SA) on instances with randomly generated matrices show that the overall performance of TS is better than SA, irrespective the size of instances considered. The results on a class of structured instances however show that TS performs well on small-sized instances, while on the larger ones, SA shows better results. In another experiment, Hierarchical Iterated Local Search (HILS) has shown very good results compared to several Iterated Local Search (ILS) variants. This experiment was done on a class of structured instances of size from 100 to 500. An extensive experiment on a class of structured instances of size 30 to 300 using tuned parameter settings shows that population based algorithms perform very well on most of the instance classes considered. SA however, shows very good performance especially on large-sized instances with low sparsity level. For the bQAP, the correlation between the flow matrices does have a strong effect that determines the performance of algorithms for solving them. Hybrid Simulated Annealing (HSA) clearly outperforms Hybrid Iterative Improvement (HII). When compared to Multi Objective Ant Colony Optimization (MOACO) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), HSA shows very good performance, where HSA outperforms MOACO and SPEA2, especially on instances of large size, thus, offering a better scaling behavior. Based the results obtained in this study, it is possible to come up with a general idea on the suitability of SLS algorithms for solving instances with a certain characteristic. Given an unknown QAP instance, one can guess the most suitable algorithm for solving it depending on the type, size, and sparsity of the instance, while for a bQAP instance the most suitable algorithm can be guessed based on its size and correlation between the flow matrices. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

The quadratic assignment problem (QAP) is known to be one of the most computationally difficult combinatorial problems. Optimally solvable instances of the QAP remain of size n ≤ 40 with heuristics used to solve instances in the range 40 ≤ n ≤ 256. In this thesis we develop a local optimization algorithm called GradSwaps (GS). GS uses the first-order Taylor approximation (FOA) to efficiently determine improving swaps in the solution. We use GS to locally optimize instances of the QAP of size 1000 ≤ n ≤ 70000 where the data matrices are given in factored form, enabling efficient computations. We give theoretical background and justification for using the FOA and bound the error inherent in the approximation. A strategy for extending GS to larger scale QAPs using blocks of indices is described in detail. Three novel large-scale applications of the QAP are developed. First, a strategy for data visualization using an extreme learning machine (ELM) where the quality of the visualization is measured in the original data space instead of the projected space. Second, a version of the traveling salesperson problem (TSP) with the squared Euclidean distance metric; this distance metric allows the factorization of the data matrix, a key component for using GS. Third, a method for generating random data with designated distribution and correlation to an accuracy surpassing traditional techniques.

Thesis (Ph. D.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains xi, 86 p. : ill. Includes abstract. Includes bibliographical references (p. 82-86).

Thesis (M.S.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains ix, 55 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 53-55).

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.

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.

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.

This thesis is focused on the topic of assignment problems. The theoretical part presents a summary of the most important previously published findings on linear and quadratic assignment problem. The basic formulations of both problems are introduced, as well as the outline of some methods developed for their solution. Finally both problems are illustrated by practical applications that have appeared in the literature. The practical part gives insight into the issue of assignment of transport orders to drivers in a company and proposes a suitable model that speeds up the process of distributing the orders. The transfers conducted by the company start at the airport and terminate in a hotel in the city centre of Prague or vice versa. When proposing order schedules for the drivers, it is necessary to take into account not only the time of the transfers, but additionally the capacity and the category of the vehicle.