Selecting the system most likely to be the best in the presence of an infinite number of alternatives

• Main Author: Hélcio Vieira Junior
• Publication Date: 2011
• Format: Doctoral thesis
• Language: eng
• Source: Biblioteca Digital de Teses e Dissertações do ITA
• Download full: http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=1973
• topic: Escolhas ótimas; Simulação; Otimização; Probabilidade; Modelos matemáticos; Defesa aérea; Matemática aplicada; Engenharia aeronáutica

Simulation Optimization (SO) belongs to a broader class of problems called Stochastic Optimization. Most of the proposed SO methodologies in the literature aim to optimize the expected value of the performance measure. This thesis focus is on another class of problems: Multinomial Selection Procedures (MSPs). These procedures select the best alternative, where best is defined more broadly as that which has the largest probability of yielding the desired response in only one trial. The MSPs found in the literature aim to compare a (small) finite set of alternatives. There are real-world multinomial selection problems in which at least one variable is continuous. The number of alternatives in this kind of problem is infinite. This fact suggests that a new approach be used. Our proposal to solve this new problem is composed by four steps: (1) Initial Sampling: this step aims to reduce the dimension of the problem by identifying the factors that have the greatest influence on the performance measure. In order to accomplish this step, we developed a novel Design of Experiments (DOE) algorithm that generates a design which is nearly orthogonal and also nearly balanced for any mix of factor types (categorical, numerical discrete and numerical continuous) and/or number of factor levels; (2) Subset Selection: the reduction of a great number of sampled points to a subset of small size which has great probability of containing the best system is the purpose of this step. A novel algorithm for the restricted multinomial subset selection problem is proposed as solution to this step; (3) Local Search: the improvement of the solutions generated by the previous step is made by a local search algorithm. We propose an improvement on the algorithm called COMPASS to allow it to deal with two stochastic objective functions as an answer for this step; and (4) Selection of the Best: once we improve the small number of solutions found in step 2, the classical MSP called is used to select the best among them. We also solved a real problem of the Brazilian Air Force: how to elaborate better air-to-air tactics for Beyond Visual Range (BVR) combat that maximize our aircraft';s survival probability, as well as the probability of downing enemy aircraft. In this study, we were able to increase an average success rate of 16.69\% and 16.23\% for and, respectively, to an average success rate of 76.85\% and 79.30\%. We can assure with low probability of being wrong that the selected tactic has greater probability of yielding greater success rates in both and than any simulated tactic.