Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

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.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.

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.

Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.

Retrofit of heat exchanger networks with pressure recovery of process streams at sub-ambient conditions

This paper presents a new mathematical programming model for the retrofit of heat exchanger networks (HENs), wherein the pressure recovery of process streams is conducted to enhance heat integration. Particularly applied to cryogenic processes, HENs retrofit with combined heat and work integration is mainly aimed at reducing the use of expensive cold services. The proposed multi-stage superstructure allows the increment of the existing heat transfer area, as well as the use of new equipment for both heat exchange and pressure manipulation. The pressure recovery of streams is carried out simultaneously with the HEN design, such that the process conditions (streams pressure and temperature) are variables of optimization. The mathematical model is formulated using generalized disjunctive programming (GDP) and is optimized via mixed-integer nonlinear programming (MINLP), through the minimization of the retrofit total annualized cost, considering the turbine and compressor coupling with a helper motor. Three case studies are performed to assess the accuracy of the developed approach, including a real industrial example related to liquefied natural gas (LNG) production. The results show that the pressure recovery of streams is efficient for energy savings and, consequently, for decreasing the HEN retrofit total cost especially in sub-ambient processes.

Optimization and Machine Learning Frameworks for Complex Network Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Network lifetime maximization with cross-layer design in wireless sensor networks

This paper investigates a cross-layer design approach for minimizing energy consumption and maximizing network lifetime (NL) of a multiple-source and single-sink (MSSS) WSN with energy constraints. The optimization problem for MSSS WSN can be formulated as a mixed integer convex optimization problem with the adoption of time division multiple access (TDMA) in medium access control (MAC) layer, and it becomes a convex problem by relaxing the integer constraint on time slots. Impacts of data rate, link access and routing are jointly taken into account in the optimization problem formulation. Both linear and planar network topologies are considered for NL maximization (NLM). With linear MSSS and planar single-source and single-sink (SSSS) topologies, we successfully use Karush-Kuhn-Tucker (KKT) optimality conditions to derive analytical expressions of the optimal NL when all nodes are exhausted simultaneously. The problem for planar MSSS topology is more complicated, and a decomposition and combination (D&C) approach is proposed to compute suboptimal solutions. An analytical expression of the suboptimal NL is derived for a small scale planar network. To deal with larger scale planar network, an iterative algorithm is proposed for the D&C approach. Numerical results show that the upper-bounds of the network lifetime obtained by our proposed optimization models are tight. Important insights into the NL and benefits of cross-layer design for WSN NLM are obtained.

Online trendy topics detection in microblogs with selective user monitoring under cost constraints

As microblog services such as Twitter become a fast and convenient communication approach, identification of trendy topics in microblog services has great academic and business value. However detecting trendy topics is very challenging due to huge number of users and short-text posts in microblog diffusion networks. In this paper we introduce a trendy topics detection system under computation and communication resource constraints. In stark contrast to retrieving and processing the whole microblog contents, we develop an idea of selecting a small set of microblog users and processing their posts to achieve an overall acceptable trendy topic coverage, without exceeding resource budget for detection. We formulate the selection operation of these subset users as mixed-integer optimization problems, and develop heuristic algorithms to compute their approximate solutions. The proposed system is evaluated with real-time test data retrieved from Sina Weibo, the dominant microblog service provider in China. It's shown that by monitoring 500 out of 1.6 million microblog users and tracking their microposts (about 15,000 daily) with our system, nearly 65% trendy topics can be detected, while on average 5 hours earlier before they appear in Sina Weibo official trends.

Cost-effective node monitoring for online hot event detection in sina weibo microblogging

We propose a cost-effective hot event detection system over Sina Weibo platform, currently the dominant microblogging service provider in China. The problem of finding a proper subset of microbloggers under resource constraints is formulated as a mixed-integer problem for which heuristic algorithms are developed to compute approximate solution. Preliminary results show that by tracking about 500 out of 1.6 million candidate microbloggers and processing 15,000 microposts daily, 62% of the hot events can be detected five hours on average earlier than they are published by Weibo.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach:the need to assess evolving units

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.