China
Africa
Explore chapters and articles related to this topic
Hull form hydrodynamic design using a discrete adjoint optimization method
Published in Pentti Kujala, Liangliang Lu, Marine Design XIII, 2018
P. He, G. Filip, J.R.R.A. Martins, K.J. Maki
pyOptSparse: an open source, object-oriented Python module, extended from pyOpt (Perez et al. 2012), for formulating and solving constrained nonlinear optimization problems. pyOptSparse provides a high-level API for defining the design variables, and the objective and constraints functions. It also provides interfaces for several optimization packages, including some open source packages. In this study, we choose SNOPT (Gill et al. 2002) as the optimizer. SNOPT uses the sequential quadratic programming (SQP) algorithm for the optimization, which solves the nonlinear equations resulting from the Karush-Kuhn-Tucker (KKT) optimality conditions using the quasi-Newton method.
Routing Optimization in Computer Networks
Published in Yezid Donoso, Ramon Fabregat, Multi-Objective Optimization in Computer Networks Using Metaheuristics, 2016
If we remove the link capacity constraint (7.c.4), the problem is of the mixed integer programming (MIP) type and we can use the cplex as solver. Considering the link capacity constraint, because a max function is included, we have a DNLP (nonlinear programming with discontinuous derivatives) type problem, and in this case, one must use solvers such as Sparse Nonlinear Optimizer (SNOPT) or Constraint Nonlinear Optimizer (COMOPT).
Economics of Electricity Generation
Published in Antonio Gómez-Expósito, Antonio J. Conejo, Claudio Cañizares, Electric Energy Systems, 2017
Francisco D. Galiana, Antonio J. Conejo
Finally, we note that the ED (including losses) is most conveniently solved through nonlinear programming algorithms such as those implemented in solvers MINOS, CONOPT, or SNOPT [3]. Nonetheless, the analytic results derived in the sections above are important as they provide useful insight into the nature of the optimal solution.
Multi-objective optimal design of microchannel cooling heat sink using topology optimization method
Published in Numerical Heat Transfer, Part A: Applications, 2020
In this article, COMSOL Multiphysics [31] is used to carry out topology optimization. The laminar flow module and optimization module are selected to solve governing equations and implement the optimization of the design domain, respectively. This problem is solved using the algorithm based on the SNOPT code, which is developed by Philip E. Gill of the University of California San Diego, and Walter Murray and Michael A. Saunders of Stanford University. When using SNOPT, the objective function can have any form and any constraints can be applied. The algorithm uses a gradient-based optimization technique to find optimal designs and when the underlying PDE is stationary, frequency-dependent or time-dependent, analytic sensitivities of the objective function with respect to the control variables can be used.
On the interaction between personal comfort systems and centralized HVAC systems in office buildings
Published in Advances in Building Energy Research, 2020
Rachel Kalaimani, Milan Jain, Srinivasan Keshav, Catherine Rosenberg
It has been suggested in Biegler (1998) that Sequential Quadratic Programming (SQP) techniques can be used to handle non-linear MPCs. Solvers like SNOPT and NPSOL use an SQP algorithm to compute a solution though there is no guarantees that the solution is optimal. In the following, we use SNOPT to solve our optimization problem, though we do so with some care. Since the problem is non-convex the solution provided by SNOPT depends on the initial guess provided to the solver. To avoid the pitfall of a local solution, we investigated if different initial guesses yielded widely different solutions. We performed the analysis for 1000 randomly generated initial guesses, with a uniform distribution, within the specified ranges for the input variables, for several instances of the optimization problem. We concluded that for each instance of the optimization problem, if we compute the solution for 15 randomly generated initial guesses and take the minimum value among these as the solution, then we almost always find a solution that is within 5% of the best value obtained for the 1000 guesses. In short, we observed that by using 15 random initial guesses we could avoid the risk of a bad local optimum obtained by using just a single initial guess or the default initial guess of the solver.
Mathematical optimization in enhancing the sustainability of aircraft trajectory: A review
Published in International Journal of Sustainable Transportation, 2020
Ahmed W.A. Hammad, David Rey, Amani Bu-Qammaz, Hanna Grzybowska, Ali Akbarnezhad
SNOPT, which stands for Sparse Nonlinear Optimizer, is a software package that is commonly adopted in many trajectory optimization solvers. A sparse sequential quadratic programing (SQP) algorithm along with limited-memory quasi-Newton approximations to the Hessian of the Lagrangian, form the main components of SNOPT (Gill et al., 2005). SNOPT determines search directions using quadratic programing (QP) subproblems through minimizing a quadratic model composed of the Lagrangian function and linearized constraints. In order to ensure convergence, an augmented Lagrangian merit function is reduced along each search direction detected.