Tai-yong Lee

Robust economic optimization of process design under uncertainty

In this study, ranges of model parameters are analyzed for robustness measures. In particular, the properties of partial mean and worst-case cost in robust optimization are investigated. The robust optimization models are considered as multiobjective problems having two objectives, the expected performance (i.e. expected cost) and a robustness measure (Suh, M. and Lee, T. (2001) Robust optimization method for the economic term in chemical process design and planning. Industrial & Engineering Chemical Research, 40, 5950–5959). The robust partial mean model is defined with objectives of expected value and partial mean. The robust worst-case model is defined with the objective of expected value and worst-case. They are proved to guarantee Pareto optimality, which should be satisfied for multiobjective optimization problems. A graphical representation of the meaningful parameter ranges is clearly defined with mathematical proofs. The robustness of the solutions is discussed, based on the analysis of the ranges of the parameters. Three meaningful ranges of the parameters are investigated to choose a proper target value for the robust partial mean model. The worst-case value obtained from the worst-case analysis is recommended as the most effective target value, in order to obtain the optimal solution in a tradeoff between robustness and optimality. The proposed analysis in this study is validated with examples in chemical process design problems.

Robust optimization for engineering design

This study proposes a robust optimization model to handle uncertainty during the process design stage, together with a decision-making procedure. Different robustness concepts are presented to describe the characteristic, either economic or technical, of a given variable in the model. Among economic robustness measures, partial mean of costs is analysed to address its intrinsic problem of excessive variability of performance with respect to the change of values in its parameters. To resolve it, a novel formulation of robust economic optimization is derived, providing a conceptual framework for suggesting a proper range of parameter values. Then, the model is further extended to consider technical robustness as well. Lastly, the decision-making procedure is presented using the proposed nadir vector which is computationally inexpensive and also useful in selecting a final solution. The applicability of the model was successfully demonstrated by applying it to process design examples.

A new deterministic global optimization method for general twice-differentiable constrained nonlinear programming problems

A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.

A new global optimization method for univariate constrained twice-differentiable NLP problems

In this paper, a new global optimization method is proposed for an optimization problem with twice-differentiable objective and constraint functions of a single variable. The method employs a difference of convex underestimator and a convex cut function, where the former is a continuous piecewise concave quadratic function, and the latter is a convex quadratic function. The main objectives of this research are to determine a quadratic concave underestimator that does not need an iterative local optimizer to determine the lower bounding value of the objective function and to determine a convex cut function that effectively detects infeasible regions for nonconvex constraints. The proposed method is proven to have a finite ε-convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering method, the index branch-and-bound algorithm, which uses the Lipschitz constant.

Sharing benefits of Eco-Industrial Park by multiobjective material flow optimization

Abstract The goal of an Eco-Industrial Park (EIP) is to improve the economic performances of the participating companies while minimizing their environmental impacts. But various socio-economic problems are obstacles for realization. From the economic point of view, EIP has the benefit sharing problem in which the interest of each company may conflict depending on the configuration of material flow network of an ecosystem so that it is not recommended to insist on one-sided concession. That is, to make a compromise is the key of success of an EIP. In this study, the concept of robust optimal design is applied for construction of EIP so that reasonable alternatives are proposed to distribute the benefit of each company without conflicts in an EIP at the point of Pareto optimality. The industrial example constructed by EIP is addressed to show the performance of the proposed approach.

Iterative dynamic programming of optimal control problem using a new global optimization technique

Abstract This work presents an efficient global optimization algorithm suitable for the basic numerical engine of iterative dynamic programming (IDP). Random search method which is utilized with IDP, generally does not guarantee the optimality and hence a deterministic algorithm with finite s-convergence is recommended. In this work difference of convex envelope method is used as the global optimization technique, which generate the difference of convex underestimator of objective function iteratively. Using the proposed modified IDP, two optimal control problems are solved successfully. Keywords iterative dynamic programming, optimal control problem, global optimization, deterministic optimization, difference of convex underestimator

Retrofit design of chemical processing networks under uncertainties: Application to petrochemical industry

Publisher Summary Retrofit design means addition of new units and expansion of existing units to satisfy the economic needs and product demand requirements. In retrofit design of a chemical processing network, decisions on structural variables, such as process network configuration and capacity expansions, have to be made under forecasted uncertain parameters, for example, product demand and material cost data. Because these parameters highly affect the profitability of the system, uncertainties should be taken into account in the design. The most common way of representing the uncertainties is to specify scenarios of the expected values of the parameters. Based on the scenario-based approach, multiscenario mathematical model can be driven by the stochastic programming framework. In comparison with the deterministic model that does not consider the parameter uncertainty, the stochastic model forms a large-size problem because of the scenario-dependent variables and constraints. Need for an efficient solution algorithm is emphasized in design models considering uncertainties. Together with process network synthesis for new process design, the retrofit design of chemical processing network has common binary decision variables of unit existence. P-graph theory and combinatorial algorithms are rebuilt to adapt to the multiscenario retrofit design problem.

Analysis of Adsorption Phenomena of Hydrogen on Carbon Nanotube usint Molecular Simulation

Molecular simulation was performed to evaluate the possibility of hydrogen storage of carbon nanotubes. The equilibrium state of hydrogen adsorbed on carbon nanotubes was simulated by grand canonical Monte Carlo method at constant temperature and pressure. The interaction energy between hydrogen molecule and carbon nanotube was calculated by Lennard-Jones potential model. According to the interaction energy calculated, more hydrogen molecules were adsorbed on the inside than the outside of nanotubes. Whereas the adsorption strength was higher outside than inside. Adsorption capacity was investigated for various temperature and pressure. The maximum capacity of carbon nanotube for hydrogen storage was 2.5wt% at 200 K and 200 bar.

Robust Optimization of Microgrids - An Application to Taichung Industrial Park

Abstract Despite a number of studies of a microgrid, robust optimization of a microgrid has not been studied yet. This is critical to a microgrid because it has lots of uncertainties concerning main grid failure, power quality issues, estimates of demand, energy price, regulation change, etc. It is therefore of importance to study and develop robust optimization strategies that take the uncertainty into account at planning a microgrid. The current study aims at developing a robust optimization model for a microgrid which provides set of robust solutions and decision-making procedure for a best solution. The model enables us to consider various uncertainties including energy price, regulation change, and estimates of demand using scenario based approach. The proposed model is validated with Taichung Industrial Park in Taiwan.

A novel global optimization algorithm using D.C. envelope and convex cut function

Abstract This work presents a novel global optimization algorithm which is applicable to general NLPs consist of twice differentiable objective and constraint functions. The algorithm iteratively generates continuous piecewise concave underestimators, difference of convex (d.c.) envelope, of objective function and it generates convex cut functions of constraint functions when acquired lower bound is located at infeasible region.