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The mine production schedule defines the sequence of extraction of selected mine units over the life of the mine, and consequentially establishes the ore supply and total material movement. This sequence should be optimized so as to maximize the overall discounted value of the project. Conventional schedule approaches are unable to incorporate grade uncertainty into the scheduling problem formulation and may lead to serious deviations from forecasted production targets. Stochastic mine production schedulers are considered to obtain more robust mine production schedule solutions. / The application of stochastic approaches to the mine production schedule problem is recent and additional testing is required to better understand these tools and to define the value of a stochastic solution as compared to the conventional result. Two stochastic schedulers are tested in a low-grade variability copper deposit, optimization parameters are discussed and their results compared with a conventional schedule. / The first method uses a stochastic combinatorial optimization approach based on simulated annealing to address the mine production schedule problem. The method aims for maximization of the net present value (NPV) of the project and minimization of deviations from the production targets. These objectives are attained by incorporating grade uncertainty into the mine production schedule problem formulation. The second method formulates the problem as a stochastic integer programming problem, in which the objective is the maximization of the projects' NPV and the minimization of production targets deviations. The model can also manage how the risk of deviating from the targets is distributed between production periods. / Both stochastic approaches were tested in a low-grade variability copper deposit. In both case studies, the value of a stochastic solution is demonstrated to be higher than the conventional one. This fact demonstrated the misleading results that a conventional schedule may produce and shows the importance of not ignoring the presence of uncertainty when defining the mine production schedule for a project.

Adaptive modulation has been actively researched as a means to increase spectral efficiency of wireless communications systems. In general, analytic closed form models have been derived for the performance of the communications system as a function of the control parameters. However, in systems where general error correction coding is employed, it may be difficult to derive closed form performance functions of the communications systems. In addition, in closed form optimization, real time adaptation is not possible. Systems designed with deterministic state optimization are developed offline for a certain set of parameters and hardwired into mobile devices. In this thesis we present stochastic learning algorithms for adaptive modulation design. The algorithms presented allow for adaptive modulation system design in-dependent of error correction coding and modulation constellation requirements. In real time, the performance of the system is measured and stochastic approximation techniques are used to learn the optimal transmission parameters of the system. The technique is applied to Software Defined Radio (SDR) platforms, an emerging wireless technology which is currently being researched as a means of designing intelligent communications devices. The fundamental property that sets SDR apart from traditional radios is that the communications parameters are controlled in software, allowing for real-time control of physical layer communications. Our treatment begins by modeling the time evolution of the adaptive modulation process as a general state space Markov chain. We show the existence and uniqueness of the invariant measure and model performance functions as expectations with respect to the invariant measure. We consider constrained and unconstrained throughput optimization. We show that the cost functions considered are convex. Next we present stochastic approximation algorithms that are used to estimate the gradient of the cost function given only noisy estimates. We conclude by presenting simulation results obtained by the presented method. The learning based method is able to achieve the maximum throughput as dictated by exhaustive Monte Carlo simulation of the communications system, which provide an upper bound on performance. In addition, the learning algorithm is able to optimize communications under various error correction schemes. The tracking abilities of the algorithm are also demonstrated. We see that the proposed method is able to track optimal throughput settings as constraints are changed in time.

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