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Mixed optimization models

We start with continuous variable optimization and consider in the next section the solution of NLP problems with differentiable objective and constraint functions. If only local solutions are required for the NLP problem, then very efficient large-scale methods can be considered. This is followed by methods that are not based on local optimality criteria we consider direct search optimization methods that do not require derivatives as well as deterministic global optimization methods. Following this, we consider the solution of mixed integer problems and outline the main characteristics of algorithms for their solution. Finally, we conclude with a discussion of optimization modeling software and its implementation on engineering models. [Pg.60]

The realization of the need and importance of petrochemical planning has inspired a great deal of research in order to devise different models to account for the overall system optimization. Optimization models include continuous and mixed-integer programming under deterministic or parameter uncertainty considerations. Related literature is reviewed at a later stage in this book, based on the chapter topic. [Pg.14]

Oil refining is perhaps the best-developed example of a process operated in this continuous optimization mode. A refinery receives a different mixture of petroleum every day, and the prices of its various products fluctuate continuously. Exquisite knowledge of the process is used to determine the precise conditions (temperatures, pressures, recycle rates, etc.) that would product the optimum product mix for the available raw materials and market conditions. As the factory is operated, model predictions are compared to actual performance, and deviations are used to optimize model performance. [Pg.64]

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. [Pg.3]

Structure of Nonlinear and Mixed-Integer Optimization Models... [Pg.4]

In this book we will focus our studies on nonlinear and mixed integer optimization models and present the fundamental theoretical aspects, the algorithmic issues, and their applications in the area of Process Synthesis in chemical engineering. Furthermore, we will restrict our attention to algebraic models with a single objective. The structure of such nonlinear and mixed integer optimization models takes the following form ... [Pg.4]

A large number of optimization models have continuous and integer variables which appear linearly, and hence separably, in the objective function and constraints. These mathematical models are denoted as Mixed-Integer Linear Programming MILP problems. In many applications of MILP models the integer variables are 0 - 1 variables (i.e., binary variables), and in this chapter we will focus on this sub-class of MILP problems. [Pg.95]

Dealing with mixed-integer nonlinear optimization models of the form (6.1) or (6.2) present two major challenges/difficulties. These difficulties are associated with the nature of the problem, namely, the combinatorial domain (y-domain) and the continuous domain ( -domain). [Pg.112]

The general mathematical model of the superstructure presented in step 2 of the outline, and indicated as (7.1), has a mixed set of 0 - 1 and continuous variables and as a result is a mixed-integer optimization model. If any of the objective function and constraints is nonlinear, then (7.1) is classified as mixed- integer nonlinear programming MINLP problem. [Pg.235]

The objective function is nonlinear and nonconvex and hence despite the linear set of constraints the solution of the resulting optimization model is a local optimum. Note that the resulting model is of the MINLP type and can be solved with the algorithms described in the chapter of mixed-integer nonlinear optimization. Yee and Grossmann (1990) used the OA/ER/AP method to solve first the model and then they applied the NLP suboptimization problem for the fixed structure so as to determine the optimal flowrates of the split streams if these take place. [Pg.371]

Section 9.2 presents key issues that arise in the synthesis of heat-integrated sharp distillation columns and presents a mixed-integer nonlinear optimization model which allows for treating the pressure of each column explicitly as a variable while at the same time heat integration alternatives are incorporated. For further reading in this subject the reader is referred to Floudas and Paules (1988) and the other suggested references. [Pg.406]

H. H. Hoang. Topological optimization of networks A nonlinear mixed integer model employing generalized Benders decomposition. IEEE Trans. Automatic Control, AC-27 164, 1982. [Pg.443]

Nonlinear and Mixed-Integer Optimization addresses the problem of optimizing an objective function subject to equality and inequality constraints in the presence of continuous and integer variables. These optimization models have many applications in engineering and applied science problems and this is the primary motivation for the plethora of theoretical and algorithmic developments that we have been experiencing during the last two decades. [Pg.466]

Since scope economies are especially hard to quantify, a separate class of optimization models solely dealing with plant loading decisions can be found. For example, Mazzola and Schantz (1997) propose a non-linear mixed integer program that combines a fixed cost charge for each plant-product allocation, a fixed capacity consumption to reflect plant setup and a non-linear capacity-consumption function of the total product portfolio allocated to the plant. To develop the capacity consumption function the authors build product families with similar processing requirements and consider effects from intra- and inter-product family interactions. Based on a linear relaxation the authors explore both tabu-search heuristics and branch-and-bound algorithms to obtain solutions. [Pg.78]

The impact of shape was reduced, whereas the impact of the Water, Dry and Mix was reinforced. Then the data were correlated to the activity by means of PLS analysis. The PLS method condensed the overall information into two smaller matrices, which can be visualized by means of the score plot (which shows the pattern of the compounds) and the loading plot (which shows the pattern of the descriptors). The optimal model was obtained with three components, exhibiting a significant statistical quality, as evinced by good R = 0.94 and = 0.71 values. [Pg.111]

S. Retout, F. Mentre, and R. Bruno, Fisher information matrix for non-linear mixed-effects models evaluation and application for optimal design of enoxaparin population pharmacokinetics. StatMed 21 2623-2639 (2002). [Pg.301]

The objective of this analysis was to integrate all of the above information for making a hnal recommendation on optimal therapeutic dose of Botani. Nonlinear mixed effects modeling analyses were conducted only on dose-response data from study 2 because of its completeness at multiple dose levels and larger number of subjects. A total of 374 subjects with 1816 observations were included in the data analyses. An inhibitory effect model describes the response-time relationship (at a given... [Pg.944]

A new type of covariate screening method is to use partially linear mixed effects models (Bonate, 2005). Briefly, the time component in a structural model is modeled using a penalized spline basis function with knots at usually equally spaced time intervals. Under this approach, the knots are treated as random effects and linear mixed effects models can be used to find the optimal smoothing parameter. Further, covariates can be introduced into the model to improve the goodness of fit. The LRT between a full and reduced model with and without the covariate of interest can be used to test for the inclusion of a covariate in a model. The advantage of this method is that the exact structural model (i.e., a 1-compartment or 2-compartment model with absorption) does not have to be determined and it is fast and efficient at covariate identification. [Pg.236]


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