Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

A new approach for semi-automatic rock mass joints recognition from 3D point clouds

Rock mass characterization requires a deep geometric understanding of the discontinuity sets affecting rock exposures. Recent advances in Light Detection and Ranging (LiDAR) instrumentation currently allow quick and accurate 3D data acquisition, yielding on the development of new methodologies for the automatic characterization of rock mass discontinuities. This paper presents a methodology for the identification and analysis of flat surfaces outcropping in a rocky slope using the 3D data obtained with LiDAR. This method identifies and defines the algebraic equations of the different planes of the rock slope surface by applying an analysis based on a neighbouring points coplanarity test, finding principal orientations by Kernel Density Estimation and identifying clusters by the Density-Based Scan Algorithm with Noise. Different sources of information —synthetic and 3D scanned data— were employed, performing a complete sensitivity analysis of the parameters in order to identify the optimal value of the variables of the proposed method. In addition, raw source files and obtained results are freely provided in order to allow to a more straightforward method comparison aiming to a more reproducible research.

Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty

In this work, we analyze the effect of demand uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear program (MILP) with the unique feature of incorporating explicitly the demand uncertainty using scenarios with given probability of occurrence. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.