Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

The topic for this dissertation is the optimisation of computer programs, as they are being compiled, using discrete optimisation techniques. The techniques introduced aim to optimise the runtime performance of programs executing on certain types of processors. A very important component of this dissertation is the movement of complexity from the processor to the compiler. Therefore both computer architecture and compilers are important supporting topics. The data output of the compiler is processed using information about the processor to produce execution information which is the goal of this dissertation. Concepts related to instruction level parallelism are covered in two parts. The first part discusses implicit parallelism, where parallel instruction scheduling is performed by the processor. The second part discusses explicit parallelism, where the compiler schedules the instructions. Explicit parallelism is attractive because it allows processor design to be simplified resulting in multiple benefits. Scheduling the instructions to execute while adhering to resource limitations is the area of focus for the rest of the dissertation. In order to find optimal schedules the problem is modelled as a mathematical program. Expressing instructions, instruction dependencies and resource limitations as a mathematical program are discussed in detail with several algorithms being introduced. Several aspects prevent the mathematical programs from being solved in their initial state, therefore additional techniques are introduced. A heuristic algorithm is introduced for scheduling instructions in a resource limited environment. The primary use of this heuristic is to reduce the computational complexity of the problem. However, this heuristic algorithm can be used to generate good schedules on its own. Finally information regarding a practical implementation of a compiler that implements the introduced techniques is introduced as well as experimental results. The experimental results are generated from a series of test programs illustrating the complete process and the computational complexity of the algorithms employed. / Smith, T.H.C., Prof.

The Tour Construction Framework (TCF) integrates both global and local heuristics in a complementary framework in order to efficiently solve the Travelling Salesman Problem (TSP). Most tour construction heuristics are strictly local in nature. However, the experimental method presented in this research includes a global heuristic to efficiently solve the TSP. The Global Path (GP) component and Super Node (SN) component comprise the TCF. Each component heuristic is tuned with one or more parameters. Genetic Algorithms (GA) are used to train the collection of parameters for the TCF components on subsets of benchmark TSPs. The GA results are used to run the TCF on the full TSP instances. The performance of the TCF is evaluated for speed, accuracy, and computational complexity, and it is compared against six mainstream TSP solvers: Lin-Kernighan-Helsgaun (LKH-2), 2-Opt, Greedy, Boruvka, Quick-Boruvka, and Nearest Neighbor. The empirical study demonstrates the effectiveness of the TCF in achieving near-optimal solutions for the TSP with reasonable costs.

Orientador: Flavio Keidi Miyazawa / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-07T21:41:01Z (GMT). No. of bitstreams: 1 Xavier_EduardoCandido_D.pdf: 20666026 bytes, checksum: 5e051653d938a813e227b1e2eebcd415 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho estudamos diversos problemas de empacotamento considerados NP-difíceis. Assumindo a hipótese de que P ? NP, sabemos que não existem algoritmos eficientes (complexidade de tempo polinomial) exatos para resolver tais problemas. Uma das abordagens consideradas para tratar tais problemas é a de algoritmos de aproximação, que são algoritmos eficientes e que geram soluções com garantia de qualidade. Neste trabalho apresentamos alguns algoritmos aproximados para problemas de empacotamento com aplicações práticas. Outra maneira de se lidar com problemas NP-difíceis é o desenvolvimento de heurísticas. Neste trabalho também apresentamos heurísticas baseadas no método de geração de colunas para problemas de corte e empacotamento bidimensional. Resultados computacionais sugerem que tais heurísticas são eficientes e geram soluções de muito boa qualidade. / Abstract: In this work we study several packing problems that are NP-hard. If we consider that P ? NP, we know that there are no efficient (polynomial time complexity) exact algorithms to solve these problems. One way to deal with these kind of problems is to use approximation algorithms, that are efficient algorithms that produce solutions with quality guarantee. We present several approximation algorithms for some packing problems that have practical applications. Another way to deal with NP-hard problems is to develop heuristics. We also consider column generation based heuristics for packing problems. In this case, we present column generation algorithms for some two dimensional packing problems and also present computational tests with the proposed algorithms. The computational results shows that the heuristics are efficient and produce solutions of very good quality. / Doutorado / Doutor em Ciência da Computação

Um emparelhamento em um grafo é um conjunto de arestas duas a duas não adjacentes. Dado um grafo G com pesos em suas arestas, o problema do emparelhamento de peso é máximo é encontrar um emparelhamento cuja soma dos pesos de suas arestas é máxima. Neste trabalho estudamos diferentes soluções para esse problema. Estudamos algoritmos combinatórios que resolvem o problema no caso em que G é bipartido e no caso geral. O algoritmo de Edmonds é um algoritmo polinomial cuja complexidade de tempo é O(n^4), onde n é o número de vértices do grafo G. Discutimos nesse trabalho nossa implementação desse algoritmo. Num trabalho de 1985, Grötschel e Holland propuseram o uso de ferramentas de programação linear para resolver o mesmo problema. O método chamado de planos-de-corte baseia-se em um resultado de Padberg e Rao de que o problema da separação associado ao poliedro dos emparelhamentos pode ser resolvido em tempo polinomial. Neste trabalho fizemos implementações dos dois métodos e os utilizamos para resolver diversos tipos de instâncias do problema. Nossa conclusão é que o método poliédrico, apesar de utilizar ferramentas genéricas, é bastante eficiente na prática. / A matching in a graph G is a set of pairwise disjoint edges of G. Given a graph G with edge weights, we define the maximum weight matching problem as that of finding a matching which maximizes the sum of its weights. In this thesis we study different solutions to this problem. We studied combinatorial algorithms that solve this problem in the case where G is bipartite and also in the general case. Edmonds algorithm [Edm65a] is a polynomial time algorithm with complexity O(n4 ), where n is the number of vertices in the graph G. We discuss in this document our implementation of this algorithm. In a paper from 1985, Gr tschel & Holland [GH85] discussed the use of linear programming o tools for solving the maximum weight matching problem. This so called cut-plane method relies on a result by Padberg & Rao [PR82] that proves that the separation problem associated with matching polyhedron is solvable in polinomial time. In this work we implemented both methods and used then to solve different instances of the problem. Our conclusion is that the polyhedral method, although using generical tools is very efficient in practice.

Given the complexity and range of combinatorial optimization problems, solving them can be computationally easy or hard. There are many ways to solve them, but all available methods share a problem: they take a long time to run and have to be rerun when new cases are introduced. Machine learning could prove a viable solution to solving combinatorial optimization problems due to the possibility for models to learn and generalize, eliminating the need to run a complex algorithm every time a new instance is presented. Uniter is a management consulting firm that provides services within product modularization. Product modularization results in the possibility for many different product variations to be created based on customer needs. Finding the best combination given a specific customer's need will require solving a combinatorial optimization problem. Based on Uniter's need, this thesis sought to develop and evaluate a machine learning model consisting of a Pointer Network architecture and trained using Reinforcement Learning.  The task was to find the combination of parts yielding the lowest cost, given a use case. Each use case had different attributes that specified the need for the final product. For each use case, the model was tasked with selecting the most appropriate combination from a set of 4000 distinct combinations. Three experiments were conducted: examining if the model could suggest an optimal solution after being trained on one use case, if the model could suggest an optimal solution of a previously seen use case, and if the model could suggest an optimal solution of an unseen use case. For all experiments, a single data set was used. The suggested model was compared to three baselines: a weighted random selection, a naive model implementing a feed-forward network, and an exhaustive search. The results showed that the proposed model could not suggest an optimal solution in any of the experiments. In most tests conducted, the proposed model was significantly slower at suggesting a solution than any baseline. The proposed model had high accuracy in all experiments, meaning it suggested almost only feasible solutions in the allowed solution space. However, when the model converged, it suggested only one combination for every use case, with the feed-forward baseline showing the same behavior. This behavior could suggest that the model misinterpreted the task and identified a solution that would work in most cases instead of suggesting the optimal solution for each use case. The discussion concludes that an exhaustive search is preferable for the studied data set and that an alternate approach using supervised learning may be a better solution.

Contemporary research in building optimization models and designing algorithms has become more data-centric and application-specific. While addressing three problems in the fields of combinatorial optimization and machine learning (ML), this work highlights the value of making data an important driver for building frameworks and designing solutions. In Chapter 2, we look into building frameworks for data-intensive applications, such as ML algorithms. We introduce a family of matrices, Structured Spinners, and use these to perform input data projections. This operation is commonly needed for a plethora of ML algorithms such as dimension reduction, cross-polytope LSH techniques or kernel approximation, yet comprises a major bottleneck in terms of time and space complexity. We design a generic framework that speeds up ML algorithms which perform such projections, with no or minor loss in accuracy. Our method applies for projections in both randomized and learned settings. We confirm our results via theoretical guarantees and numerical experiments. Moreover, we are the first to provide theoretical results for that type of work under adaptive settings. In Chapter 3, we rely on empirical analysis to design algorithms for an online packet scheduling problem with weighted packets and agreeable deadlines. We adopt the model presented in Jez et al. and use their Modified Greedy MG algorithm, which was the best-performing one in the literature, as our benchmark. The technique used for proving the competitive ratio for this benchmark is worst case analysis. Via extensive simulations, we shed light on practical bottlenecks and observe that these are not captured by the competitive analysis. We design three new algorithms, two of which make deterministic online decisions, while the third learns an adaptive one. When contrasted against the MG benchmark, our algorithms have significantly worse competitive ratios, yet noticeably better empirical performance. Our methodology is particularly useful for online algorithms and underlines the significance of leveraging data or simulations to guide algorithm design and testing. In Chapter 4, we study two different applications in cybersecurity: an adaptive ML problem and a game-theoretic model called PLADD. The common objective between both problems is to protect cybersystems against attacks by intelligent, adaptable and well-resourced adversaries while maintaining a cost budget. We introduce a novel combinatorial scheduling formulation to design useful defense strategies that meet this goal. Our work separates the formulation from the data-driven analysis and solution. As such, the scheduling formulation, which does not resemble any previously studied formulations from the scheduling literature, may be used as a new model by other researchers for different motivations. We keep the model generic enough for others to use, but design the algorithms that work best for our context. The formulation is inspired by stochastic programming and cast as a mixed integer program (MIP). We provide theoretical analysis, e.g. explore integrality gaps, exploit the combinatorial structure, prove NP-hardness, develop dynamic programming solutions for two-machine cases, then work towards data-driven heuristics and approximation algorithms using distribution assumptions and real data.

MSc., Faculty of Science, University of the Witwatersrand, 2011 / A vast array of important practical problems, in many di erent elds, can be modelled and solved as quadratic assignment problems (QAP). This includes problems such as university campus layout, forest management, assignment of runners in a relay team, parallel and distributed computing, etc. The QAP is a di cult combinatorial optimization problem and solving QAP instances of size greater than 22 within a reasonable amount of time is still challenging. In this dissertation, we propose two new solution approaches to the QAP, namely, a Branch-and-Bound method and a discrete dynamic convexized method. These two methods use the standard quadratic integer programming formulation of the QAP. We also present a lower bounding technique for the QAP based on an equivalent separable convex quadratic formulation of the QAP. We nally develop two di erent new techniques for nding initial strictly feasible points for the interior point method used in the Branch-and-Bound method. Numerical results are presented showing the robustness of both methods.

Recently meta-heuristics have become a popular solution methodology, in terms of both research and application, for solving combinatorial optimization problems. Meta-heuristic methods guide simple heuristics or priority rules designed to solve a particular problem. Meta-heuristics enhance these simple heuristics by using a higher level strategy. The advantage of using meta-heuristics over conventional optimization methods is meta-heuristics are able to find good (near optimal) solutions within a reasonable computation time. Investigating this line of research is justified because in most practical cases with medium to large scale problems, the use of meta-heuristics is necessary to be able to find a solution in a reasonable time. The specific meta-heuristic studied in this research is, Meta-RaPS; Meta-heuristic for Randomized Priority Search which is developed by DePuy and Whitehouse in 2001. Meta-RaPS is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element (Moraga, 2002). To date, Meta-RaPS had been applied to different types of combinatorial optimization problems and achieved comparable solution performance to other meta-heuristic techniques. The specific problem studied in this dissertation is parameter setting of Meta-RaPS. The topic of parameter setting for meta-heuristics has not been extensively studied in the literature. Although the parameter setting method devised in this dissertation is used primarily on Meta-RaPS, it is applicable to any meta-heuristic's parameter setting problem. This dissertation not only enhances the power of Meta-RaPS by parameter tuning but also it introduces a robust parameter selection technique with wide-spread utility for many meta-heuristics. Because the distribution of solution values generated by meta-heuristics for combinatorial optimization problems is not normal, the current parameter setting techniques which employ a parametric approach based on the assumption of normality may not be appropriate. The proposed method is Non-parametric Based Genetic Algorithms. Based on statistical tests, the Non-parametric Based Genetic Algorithms (NPGA) is able to enhance the solution quality of Meta-RaPS more than any other parameter setting procedures benchmarked in this research. NPGA sets the best parameter settings, of all the methods studied, for 38 of the 41 Early/Tardy Single Machine Scheduling with Common Due Date and Sequence-Dependent Setup Time (ETP) problems and 50 of the 54 0-1 Multidimensional Knapsack Problems (0-1 MKP). In addition to the parameter setting procedure discussed, this dissertation provides two Meta-RaPS combinatorial optimization problem applications, the 0-1 MKP, and the ETP. For the ETP problem, the Meta-RaPS application in this dissertation currently gives the best meta-heuristic solution performance so far in the literature for common ETP test sets. For the large ETP test set, Meta-RaPS provided better solution performance than Simulated Annealing (SA) for 55 of the 60 problems. For the small test set, in all four different small problem sets, the Meta-RaPS solution performance outperformed exiting algorithms in terms of average percent deviation from the optimal solution value. For the 0-1 MKP, the present Meta-RaPS application performs better than the earlier Meta-RaPS applications by other researchers on this problem. The Meta-RaPS 0-1 MKP application presented here has better solution quality than the existing Meta-RaPS application (Moraga, 2005) found in the literature. Meta-RaPS gives 0.75% average percent deviation, from the best known solutions, for the 270 0-1 MKP test problems.

Composite panel structure optimization is commonly decomposed into panel optimization subproblems, with specified local loads, resulting in manufacturing incompatibilities between adjacent panel designs. Using genetic algorithms to optimize local panel stacking sequences allows panel populations of stacking sequences to evolve in parallel and send migrants to adjacent panels, so as to blend the local panel designs globally. The blending process is accomplished using the edit distance between individuals of a population and the set of migrants from adjacent panels. The objective function evaluating the fitness of designs is modified according to the severity of mismatches detected between neighboring populations. This lays the ground work for natural evolution to a blended global solution without leaving the paradigm of genetic algorithms. An additional method applied here for constructing globally blended panel designs uses a parallel decomposition antithetical to that of earlier work. Rather than performing concurrent panel genetic optimizations, a single genetic optimization is conducted for the entire structure with the parallelism solely within the fitness evaluations. A guide based genetic algorithm approach is introduced to exclusively generate and evaluate valid globally blended designs, utilizing a simple master-slave parallel implementation, implicitly reducing the size of the problem design space and increasing the quality of discovered local optima. / Ph. D.