Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

The multivariate L1-median and associated data depth

This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in ℝd.

Real time optimization in chemical process: evaluation of strategies, improvements and industrial application.

The increasing economic competition drives the industry to implement tools that improve their processes efficiencies. The process automation is one of these tools, and the Real Time Optimization (RTO) is an automation methodology that considers economic aspects to update the process control in accordance with market prices and disturbances. Basically, RTO uses a steady-state phenomenological model to predict the process behavior, and then, optimizes an economic objective function subject to this model. Although largely implemented in industry, there is not a general agreement about the benefits of implementing RTO due to some limitations discussed in the present work: structural plant/model mismatch, identifiability issues and low frequency of set points update. Some alternative RTO approaches have been proposed in literature to handle the problem of structural plant/model mismatch. However, there is not a sensible comparison evaluating the scope and limitations of these RTO approaches under different aspects. For this reason, the classical two-step method is compared to more recently derivative-based methods (Modifier Adaptation, Integrated System Optimization and Parameter estimation, and Sufficient Conditions of Feasibility and Optimality) using a Monte Carlo methodology. The results of this comparison show that the classical RTO method is consistent, providing a model flexible enough to represent the process topology, a parameter estimation method appropriate to handle measurement noise characteristics and a method to improve the sample information quality. At each iteration, the RTO methodology updates some key parameter of the model, where it is possible to observe identifiability issues caused by lack of measurements and measurement noise, resulting in bad prediction ability. Therefore, four different parameter estimation approaches (Rotational Discrimination, Automatic Selection and Parameter estimation, Reparametrization via Differential Geometry and classical nonlinear Least Square) are evaluated with respect to their prediction accuracy, robustness and speed. The results show that the Rotational Discrimination method is the most suitable to be implemented in a RTO framework, since it requires less a priori information, it is simple to be implemented and avoid the overfitting caused by the Least Square method. The third RTO drawback discussed in the present thesis is the low frequency of set points update, this problem increases the period in which the process operates at suboptimum conditions. An alternative to handle this problem is proposed in this thesis, by integrating the classic RTO and Self-Optimizing control (SOC) using a new Model Predictive Control strategy. The new approach demonstrates that it is possible to reduce the problem of low frequency of set points updates, improving the economic performance. Finally, the practical aspects of the RTO implementation are carried out in an industrial case study, a Vapor Recompression Distillation (VRD) process located in Paulínea refinery from Petrobras. The conclusions of this study suggest that the model parameters are successfully estimated by the Rotational Discrimination method; the RTO is able to improve the process profit in about 3%, equivalent to 2 million dollars per year; and the integration of SOC and RTO may be an interesting control alternative for the VRD process.

Particle Swarm Optimization Based Reactive Power Dispatch for Power Networks with Distributed Generation

Reactive power is critical to the operation of the power networks on both safety aspects and economic aspects. Unreasonable distribution of the reactive power would severely affect the power quality of the power networks and increases the transmission loss. Currently, the most economical and practical approach to minimizing the real power loss remains using reactive power dispatch method. Reactive power dispatch problem is nonlinear and has both equality constraints and inequality constraints. In this thesis, PSO algorithm and MATPOWER 5.1 toolbox are applied to solve the reactive power dispatch problem. PSO is a global optimization technique that is equipped with excellent searching capability. The biggest advantage of PSO is that the efficiency of PSO is less sensitive to the complexity of the objective function. MATPOWER 5.1 is an open source MATLAB toolbox focusing on solving the power flow problems. The benefit of MATPOWER is that its code can be easily used and modified. The proposed method in this thesis minimizes the real power loss in a practical power system and determines the optimal placement of a new installed DG. IEEE 14 bus system is used to evaluate the performance. Test results show the effectiveness of the proposed method.

On stable uniqueness in linear semi-infinite optimization

This paper is intended to provide conditions for the stability of the strong uniqueness of the optimal solution of a given linear semi-infinite optimization (LSIO) problem, in the sense of maintaining the strong uniqueness property under sufficiently small perturbations of all the data. We consider LSIO problems such that the family of gradients of all the constraints is unbounded, extending earlier results of Nürnberger for continuous LSIO problems, and of Helbig and Todorov for LSIO problems with bounded set of gradients. To do this we characterize the absolutely (affinely) stable problems, i.e., those LSIO problems whose feasible set (its affine hull, respectively) remains constant under sufficiently small perturbations.

Logic hybrid simulation-optimization algorithm for distillation design

In this paper, we propose a novel algorithm for the rigorous design of distillation columns that integrates a process simulator in a generalized disjunctive programming formulation. The optimal distillation column, or column sequence, is obtained by selecting, for each column section, among a set of column sections with different number of theoretical trays. The selection of thermodynamic models, properties estimation etc., are all in the simulation environment. All the numerical issues related to the convergence of distillation columns (or column sections) are also maintained in the simulation environment. The model is formulated as a Generalized Disjunctive Programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation. Some examples involving from a single column to thermally coupled sequence or extractive distillation shows the performance of the new algorithm.

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

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.

Isobutane Alkylation Process Synthesis by means of Hybrid Simulation-Multiobjective Optimization

Multiobjective Generalized Disjunctive Programming (MO-GDP) optimization has been used for the synthesis of an important industrial process, isobutane alkylation. The two objective functions to be simultaneously optimized are the environmental impact, determined by means of LCA (Life Cycle Assessment), and the economic potential of the process. The main reason for including the minimization of the environmental impact in the optimization process is the widespread environmental concern by the general public. For the resolution of the problem we employed a hybrid simulation- optimization methodology, i.e., the superstructure of the process was developed directly in a chemical process simulator connected to a state of the art optimizer. The model was formulated as a GDP and solved using a logic algorithm that avoids the reformulation as MINLP -Mixed Integer Non Linear Programming-. Our research gave us Pareto curves compounded by three different configurations where the LCA has been assessed by two different parameters: global warming potential and ecoindicator-99.

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.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Optimization of the Modular Educational Program Structure

Optimized structure of the educational program consisting of a set of the interconnected educational objects is offered by means of problem solution of optimum partition of the acyclic weighed graph. The condition of acyclicity preservation for subgraphs is formulated and the quantitative assessment of decision options is executed. The original algorithm of search of quasioptimum partition using the genetic algorithm scheme with coding chromosomes by permutation is offered. Object-oriented realization of algorithm in language C++ is described and results of numerical experiments are presented.