19 research outputs found
A New Approach to Solving Stochastic Optimal Control Problems
A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle
Mixed Integer Nonlinear Programming Model for Sustainable Water Management in Macroscopic Systems: Integrating Optimal Resource Management to the Synthesis of Distributed Treatment Systems
Recognizing
the growing pressure on water resources, the literature reports several
efforts in the area of mathematical programming to deal with the management
of industrial and macroscopic water systems. This paper presents a
mathematical programming model which integrates two strategies for
sustainable water management. On the one hand, the model allows finding
an optimal schedule for the distribution and storage of natural and
alternative water sources to satisfy the demands of different users
in a macroscopic system, while maintaining sustainable levels of water
in the natural water resources. On the other hand, optimal decisions
also involve the number, capacity, type, and location of treatment
units in a macroscopic system. Our approach results in a mixed integer
linear programming (MINLP) multiperiod model which has been solved
through the GAMS modeling environment. A case study with different
scenarios shows the scope of the proposed approach and the significance
of the results
Two-Stage Stochastic Approach to the Optimal Location of Booster Disinfection Stations †
An Approach to the Representation of Gradual Uncertainty Resolution in Stochastic Multiperiod Planning
This work focuses on the modeling of multistage stochastic problems with endogenous (decision dependent) uncertainties. We assume that the probability distributions of the uncertain parameters are discrete, so that a scenario tree representation can be used. As the main contribution, the paper describes an approach to represent the gradual resolution of endogenous uncertainties after an investment in information is made; partial resolution of uncertainty through time is defined in terms of a percentage of variance reduction. The approach is based on the concepts of posterior and revelation distributions and on the practical propositions of the theory of conditional expectations. A mining production planning problem with endogenous uncertainty in ore quality is used as a case-study to show the scope of the proposed representation as well as to evaluate the effect of the gradual resolution of uncertainties on the optimal solution