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Optimization in Chemical and Biological Engineering using Julia
Published in Mariano Martín Martín, Introduction to Software for Chemical Engineers, 2019
Jordan Jalving, Victor M. Zavala
We highlight that, by default, all variables are treated as continuous. In our example, if we want to enforce that variable x1 is binary (i.e., can only take a value of zero or one) we use the syntax @variable(m,x1,Bin), and if we want it to be any positive integer (i.e., 0,1,2,…) we use @variable(m,x1>=0,Int). To handle such problems, the solver to be used needs to be able to handle integer variables (solvers such as Gurobi and SCIP can be used with JuMP). Table 18.1 provides an overview of some open-source and commercial solvers available in Julia to handle different problems. Linear programs (LP) contain all continuous variables and linear constraints, mixed-integer linear programs (MILP) introduce integer variables, nonlinear programs (NLP) introduce nonlinear constraints, and mixed-integer nonlinear programs (MINLP) contain both nonlinear constraints and integer variables. In this chapter we focus exclusively on nonlinear optimization problems (NLP) with continuous variables (which can be solved with Ipopt). The capabilities discussed are sufficient to help the reader handle problems with integer variables as well.
Dynamic Optimization in Drying
Published in Alex Martynenko, Andreas Bück, Intelligent Control in Drying, 2018
Barttfeld et al. (2006) considered a multi-zone air impingement dryer for coated film drying. Here the settings of the air conditions for succeeding zones were optimized. Different drying aims (scenarios) were considered, for example, minimizing the total heat consumption and maximizing the production rate. The control variables were the humidity and temperature of the air and the velocities of the impingement nozzles. The optimization concerned a partial differential equation model which was discretized over the thickness of the film and the residence time of the paper sheet in the dryer. The discretized model was implemented in AMPL (2017) and IPOPT (2017)was used as optimization tool to solve the nonlinear programming optimization problem. The optimization of the scenarios showed that 30% reduction of energy consumption can be achieved or the production capacity can be increased by 2.5 times.
Configuration-aware model predictive motion planning for Tractor–Trailer Mobile Robot
Published in Advanced Robotics, 2023
Nobuaki Ito, Hiroyuki Okuda, Tatsuya Suzuki
Table 2 shows values of parameters in each experiment. The number of prediction steps N is 20, the limitation of joint angles are , , a length of links are , a size of vehicles are , limitation of inputs are , , the reference are , 5, and the discretized period is . The optimization problem is solved by IPOPT [30] on CasADi [31] in this paper. IPOPT is an open-source nonlinear optimization solver and finds the solution by combination of filter line search and primal–dual interior point method (PDIPM). Note that the initial guess of the solution is given from the optimal solution in last control step in PDIPM after the second step for fast computation.
Minimum-time optimal control for vehicles with active rear-axle steering, transfer case and variable parameters
Published in Vehicle System Dynamics, 2021
Tadeas Sedlacek, Dirk Odenthal, Dirk Wollherr
The OCP is implemented using the domain-specific modelling language JuMP [34] for mathematical optimisation embedded in the programming language Julia [44]. Therein the derivative information is computed in advance and in machine precision using Forward Mode Automatic Differentiation [50] yielding accurate gradients and Hessians. IPOPT is selected as nonlinear programming solver which uses a gradient-based primal-dual interior-point strategy with a filter line-search and further features for performance enhancement [15]. Interior-point methods reach the optimum from within the attainable set by using slack variables to describe the distance to the set boundary. Opposite to the active-set strategy of sequential quadratic programming methods, there is no need figuring out the active inequality constraints which represents a problem of high combinatorial complexity. As a result, interior-points methods tend to have a faster convergence rate for large-scale sparse problems [51].
Computational design of metadevices for heat flux manipulation considering the transient regime
Published in Numerical Heat Transfer, Part A: Applications, 2019
Juan C. Álvarez Hostos, Víctor D. Fachinotti, Ignacio Peralta, Benjamín A. Tourn
Finally, the resulting nonlinear constrained large-scale optimization problem is solved using IPOPT, and the interior-point algorithm proposed by Wächter and Biegler [49]. IPOPT is a primal-dual barrier method that deals with the box constraints by introducing slack variables. It is particularly well suited for large-scale optimization problems, which was the main reason to be chosen for this work. Last but not least, IPOPT is released as an open source code that is freely available from the COIN-OR initiative (https://projects.coin-or.org/Ipopt).