Algoritmo Q-learning como estratégia de exploração e/ou explotação para metaheurísticas GRASP e algoritmo genético

Techniques of optimization known as metaheuristics have achieved success in the resolution of many problems classified as NP-Hard. These methods use non deterministic approaches that reach very good solutions which, however, don t guarantee the determination of the global optimum. Beyond the inherent difficulties related to the complexity that characterizes the optimization problems, the metaheuristics still face the dilemma of xploration/exploitation, which consists of choosing between a greedy search and a wider exploration of the solution space. A way to guide such algorithms during the searching of better solutions is supplying them with more knowledge of the problem through the use of a intelligent agent, able to recognize promising regions and also identify when they should diversify the direction of the search. This way, this work proposes the use of Reinforcement Learning technique - Q-learning Algorithm - as exploration/exploitation strategy for the metaheuristics GRASP (Greedy Randomized Adaptive Search Procedure) and Genetic Algorithm. The GRASP metaheuristic uses Q-learning instead of the traditional greedy-random algorithm in the construction phase. This replacement has the purpose of improving the quality of the initial solutions that are used in the local search phase of the GRASP, and also provides for the metaheuristic an adaptive memory mechanism that allows the reuse of good previous decisions and also avoids the repetition of bad decisions. In the Genetic Algorithm, the Q-learning algorithm was used to generate an initial population of high fitness, and after a determined number of generations, where the rate of diversity of the population is less than a certain limit L, it also was applied to supply one of the parents to be used in the genetic crossover operator. Another significant change in the hybrid genetic algorithm is the proposal of a mutually interactive cooperation process between the genetic operators and the Q-learning algorithm. In this interactive/cooperative process, the Q-learning algorithm receives an additional update in the matrix of Q-values based on the current best solution of the Genetic Algorithm. The computational experiments presented in this thesis compares the results obtained with the implementation of traditional versions of GRASP metaheuristic and Genetic Algorithm, with those obtained using the proposed hybrid methods. Both algorithms had been applied successfully to the symmetrical Traveling Salesman Problem, which was modeled as a Markov decision process

Algoritmos experimentais para o problema biobjetivo da árvore geradora quadrática em adjacência de arestas

The Quadratic Minimum Spanning Tree (QMST) problem is a generalization of the Minimum Spanning Tree problem in which, beyond linear costs associated to each edge, quadratic costs associated to each pair of edges must be considered. The quadratic costs are due to interaction costs between the edges. When interactions occur between adjacent edges only, the problem is named Adjacent Only Quadratic Minimum Spanning Tree (AQMST). Both QMST and AQMST are NP-hard and model a number of real world applications involving infrastructure networks design. Linear and quadratic costs are summed in the mono-objective versions of the problems. However, real world applications often deal with conflicting objectives. In those cases, considering linear and quadratic costs separately is more appropriate and multi-objective optimization provides a more realistic modelling. Exact and heuristic algorithms are investigated in this work for the Bi-objective Adjacent Only Quadratic Spanning Tree Problem. The following techniques are proposed: backtracking, branch-and-bound, Pareto Local Search, Greedy Randomized Adaptive Search Procedure, Simulated Annealing, NSGA-II, Transgenetic Algorithm, Particle Swarm Optimization and a hybridization of the Transgenetic Algorithm with the MOEA-D technique. Pareto compliant quality indicators are used to compare the algorithms on a set of benchmark instances proposed in literature.

Algoritmos experimentais para o problema biobjetivo da árvore geradora quadrática em adjacência de arestas

The Quadratic Minimum Spanning Tree (QMST) problem is a generalization of the Minimum Spanning Tree problem in which, beyond linear costs associated to each edge, quadratic costs associated to each pair of edges must be considered. The quadratic costs are due to interaction costs between the edges. When interactions occur between adjacent edges only, the problem is named Adjacent Only Quadratic Minimum Spanning Tree (AQMST). Both QMST and AQMST are NP-hard and model a number of real world applications involving infrastructure networks design. Linear and quadratic costs are summed in the mono-objective versions of the problems. However, real world applications often deal with conflicting objectives. In those cases, considering linear and quadratic costs separately is more appropriate and multi-objective optimization provides a more realistic modelling. Exact and heuristic algorithms are investigated in this work for the Bi-objective Adjacent Only Quadratic Spanning Tree Problem. The following techniques are proposed: backtracking, branch-and-bound, Pareto Local Search, Greedy Randomized Adaptive Search Procedure, Simulated Annealing, NSGA-II, Transgenetic Algorithm, Particle Swarm Optimization and a hybridization of the Transgenetic Algorithm with the MOEA-D technique. Pareto compliant quality indicators are used to compare the algorithms on a set of benchmark instances proposed in literature.