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Numerical Algorithms for Constrained Optimization
Published in Ossama Abdelkhalik, Algorithms for Variable-Size Optimization, 2021
The Sequential Quadratic Programming (SQP) is an iterative method that solves the general optimization problem in a direct way by approximating the objective and constraint functions. A quadratic function is used to approximate the objective function at the current guess (iterate) for the solution, while a linear function is used to approximate each of the constraint functions at each iterate. Hence the SQP approximates the general nonlinear programming problem to quadratic programming problem at each iteration. The SQP is one of the most effective methods. SQP was first proposed in 1960s by R. Wilson in his PhD dissertation at Harvard University. Since then, the SQP has evolved significantly, based on a rigorous theory, to a class of methods suitable for a wide range of problems.
Memetic Algorithms with Extremal Optimization
Published in Yong-Zai Lu, Yu-Wang Chen, Min-Rong Chen, Peng Chen, Guo-Qiang Zeng, Extremal Optimization, 2018
Yong-Zai Lu, Yu-Wang Chen, Min-Rong Chen, Peng Chen, Guo-Qiang Chen
This section proposes a novel hybrid EO–SQP method with the combination of EO and the popular deterministic SQP under the conceptual umbrella of MAs. EO is a general-purpose heuristic algorithm, with the superior features of SOC, nonequilibrium dynamics, coevolutions in statistical mechanics, and ecosystems, respectively. Inspired by far-from-equilibrium dynamics, this approach provides a new philosophy to optimize based on nonequilibrium statistical physics and the capability to elucidate the properties of phase transitions in complex optimization problems. SQP has been one of the most popular methods for nonlinear optimization because of its efficiency in solving medium- and small-size nonlinear programming (NLP) problems. It guarantees local optima as it follows a GS direction from starting point toward optimum point and has special advantages in dealing with various constraints. This will be particularly helpful for the hybrid EO–SQP algorithm when solving constrained optimization problems: the SQP can also serve as a means of “repairing” infeasible solutions during EO evolution. The proposed method balances both aspects through the hybridization of heuristic EO as the global-search scheme and deterministic SQP as the LS scheme. The performance of the proposed EO–SQP algorithm is tested on 12 benchmark numerical optimization problems and compared with some other state-of-the-art approaches. The experimental results show the EO–SQP method is capable of finding the optimal or near-optimal solutions for NLP problems effectively and efficiently.
Wire Sizing
Published in Charles J. Alpert, Dinesh P. Mehta, Sachin S. Sapatnekar, Handbook of Algorithms for Physical Design Automation, 2008
Sanghamitra Roy, Charlie Chung-Ping Chen
The convex optimization problem of concurrent gate and wire sizing can also be solved using the sequential quadratic programming (SQP) method [Menezes 1997, Chu 1999b]. SQP reduces a nonlinear optimization to a sequence of quadratic programming (QP) subproblems. A general convex quadratic program can be represented as minimize12XTQX+XTCsubjecttoAiTX≤bi,i∈I
Neuro-evolutionary computing paradigm for two strain COVID-19 model
Published in Waves in Random and Complex Media, 2023
Muhammad Shoaib, Rafia Tabassum, Muhammad Asif Zahoor Raja, Kottakkaran Sooppy Nisar
The sequential quadratic programming (SQP) is a technique used to solve a nonlinear problem when the problem is smooth, not too large and gradients/functions can be analyzed with an acceptable level of high precision. The deterministic method would become stuck in the local optimums. However, GA converges very slowly towards the solution, particularly when the objective/fitness function is very near to the optimal results at the end of generations. If there is a strong starting point, deterministic strategies like SQP would, however, quickly lead to a final solution. To increase the effectiveness of their searches and to address optimization issues, some researchers have combined different optimization algorithms [3]. Many applications used GA as hybrid optimization tool, for instance, prediction of COVID-19 cases [4], constrained optimization [5], supply chain configuration model [6], production scheduling model [7], berth allocation problem [8], project scheduling problem [9], construction of balanced Boolean function [10], and multimodal functions [11].
Stage-independent multiple sampling plan by variables inspection for lot determination based on the process capability index Cpk
Published in International Journal of Production Research, 2023
Chien-Wei Wu, Armin Darmawan, Shih-Wen Liu
To solve optimisation model with the given constraints expressed in Equations (9)–(11), an iterative method, called the sequential quadratic programming (SQP) algorithm, is applied. The SQP algorithm is one of the most effective methods for nonlinearly constrained optimisation problems which generates steps by solving quadratic subproblems, and was introduced by Nocedal and Wright (1999). The main concept SQP algorithm combines the objective and constraint functions into a merit function and attempts to minimise the merit function subject to relaxed constraints (more details of the SQP algorithm can be seen in Nocedal and Wright (2006) and Chapra (2012)). In particular, the SQP algorithm has been implemented by some numerical programming languages, such as Matlab, Maple and Mathematica. Several studies have utilised the SQP algorithm to solve such minimisation problems, such as Balamurali et al. (2005), Liu and Wu (2014), Wu, Liu, and Lee (2015), and Nadi, Gildeh, and Afshari (2020). The plan parameters of the proposed plan are obtained using Matlab R2019b software with the routine function ‘fmincon’.
Stochastic Simulation of Vertical Components of Near-field Pulse-less Ground Motions
Published in Journal of Earthquake Engineering, 2022
Zakariya Waezi, M. Javad Hashemi
In Equation 14), , are the response spectrums of the target and simulated records, according to vector of model parameters . Even though complicated analytic formula (see (George Michaelov, Lutes, and Sarkani 2001)) can be developed to related the model parameters and mean values of , in this study, Monte Carlo simulation is used with 100 samples to decrease the computation time. The methods 5 and 6 denoted in Table 1 use this objective function to find the optimized parameters. The optimized model parameters for all of the methods investigated in this study are found by using the MATLAB function, ‘fmincon’, with sequential quadratic programming (SQP) algorithm because of high convergence rate compared to Heuristic methods. However, the SQP algorithm is sensitive to the initial guess and may get stuck in the local minima. The effects on the resulted parameters will be discussed further in Section 3–2. It will be shown that the proposed objective function is well-behaved enough that does not need costly Heuristic optimization algorithms.