China
Africa
Explore chapters and articles related to this topic
Problem Formulation and Solving Methods
Published in Arnold H. Lobbrecht, Dynamic Water-System Control, 2020
In the following subsections the optimization methods Network Programming, Linear Programming, Successive Linear Programming, Dynamic Programming and Nonlinear Programming will be discussed. The following order has been chosen: from high modeling restrictions and easy to understand to high modeling freedom and complex.
Optimisation of RO Process Superstructure for Wastewater Treatment
Published in Mudhar Al-Obaidi, Chakib Kara-Zaitri, I. M. Mujtaba, Wastewater Treatment by Reverse Osmosis Process, 2020
Mudhar Al-Obaidi, Chakib Kara-Zaitri, I. M. Mujtaba
Several case studies relating to the optimisation of RO process performance can be found in the open literature. These include the investigation of the transport phenomena of water and solute through the membrane using improved mathematical models and identifying the optimum set of operating variables. The main aim of an RO process optimisation is to identify the best design and operating parameters, which can yield the maximum process performance at minimum energy consumption and within the manufacturer’s specification. Water production costs as well as requirements of zero discharge pollutants (as in many countries) can readily be incorporated in the optimisation problem. Many optimisation methodologies and mathematical programming (constrained optimisation) are used in practice. These include Lagrange multipliers, linear and non-linear programming, dynamic programming, quadratic programming, fractional programming, and geometric programming (Loucks and Beek, 2017). The selection of a suitable solution method is basically dependent on the process structural model. Several attempts can be found in the literature where a non-linear programming methodology has been used to optimise the RO process. These include successive linear programming (SLP) and sequential quadratic programming (SQP) (Villafafila and Mujtaba, 2003), global optimisation algorithm (GOP) (Marcovecchio et al., 2005), genetic algorithm (GA) (Murthy and Vengal, 2006) and multi-objective optimisation and genetic algorithm (MOO+GA) (Guria et al., 2005). Also, Lu et al. (2006) used a complex NLP of mixed integer non-linear programming methodology. Sassi and Mujtaba (2013) used MINLP in a model for the removal of boron from seawater using an RO process. The remainder of this book demonstrates applications of the most commonly used NLP and GA methodologies in the optimisation of an RO process for wastewater treatment. To this extent, the superstructure optimisation using MINLP methodology is provided briefly. The next sections of this chapter discuss in detail the principles of the NLP solution methodology as applied to the superstructure optimisation problem at hand. The next chapter concentrates more on the GA optimisation methodology as applied to an RO process in wastewater treatment.
Optimization
Published in Slobodan P. Simonović, Managing Water Resources, 2012
The energy management by successive linear programming (EMSLP) algorithm uses this linearization procedure of the hydro production equation derived by Taylor expansion. Rewriting (9.98) in terms of the decision variables and sorting the unknown to the left and the constants to the right of the equality sign, the hydro production constraint in the tth time step has the form: () −2×∑s(HEs,t+[ERF(ST^t−1)+ERF(ST^t)×Rt+DERF(ST^t−1)×R^t×STt−1+DERF(ST^t)×R^t×STt=[DERF(ST^t−1)×ST^t−1+DERF(ST^t)×ST^t]×R^t])
An inexact first-order method for constrained nonlinear optimization
Published in Optimization Methods and Software, 2022
Hao Wang, Fan Zhang, Jiashan Wang, Yuyang Rong
On the contrary, little attention has been paid on first-order methods for solving general constrained optimization problems in the past decades. This is mainly due to the slow tail convergence of first-order methods, since it can cause heavy computational burden for obtaining accurate solutions. Most of the research efforts can date back to the successive linear programming (SLP) algorithms [3,30] designed in 1960s–1980s for solving pooling problems in oil refinery. Among various SLP algorithms, the most famous SLP algorithm is proposed by Fletcher and Maza in [20,21], which analyses the global convergence as well as the local convergence under strict complementarity, second-order sufficiency and regularity conditions. The other well-known work is the active-set algorithmic option implemented in the off-the-shelf solver Knitro [15], which sequentially solves a linear optimization subproblem and an equality constrained quadratic optimization subproblem.