Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jianhua Zhou ◽  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Quadratic Programming ◽  
Robust Optimization ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Critical Role ◽  
Interval Uncertainty ◽  
Design Solution ◽  
Novel Approach ◽  
Design Variables ◽  
Feasibility Robustness

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, sequential quadratic programming for robust optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

2012 ◽  
Author(s):  
Jianhua Zhou ◽  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Critical Role ◽  
Interval Uncertainty ◽  
Design Solution ◽  
Novel Approach ◽  
Design Variables ◽  
Feasibility Robustness ◽  
Objective Robustness ◽  
Different Levels

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, Sequential Quadratic Programing for Robust Optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

Active-set sequential quadratic programming with variable probabilistic constraint evaluations for optimization problems under non-Gaussian uncertainties

2010 ◽  
Vol 224 (6) ◽  
pp. 1273-1285 ◽  
Author(s):  
K-Y Chan ◽  
Y-C Huang
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Probabilistic Constraints ◽  
Minimal Distance ◽  
Active Set ◽  
Structural Problems ◽  
Design Iteration ◽  
Design Variables ◽  
Non Gaussian

Design optimization under random uncertainties are formulated as problems with probabilistic constraints. Calculating these constraints presents a major challenge in the optimization. While most research concentrates on uncertainties that are Gaussian, a great number of uncertainties in the environment are non-Gaussian. In this work, various reliability analyses for non-Gaussian uncertainties within a sequential quadratic programming framework are integrated. An analytical reliability contour (RC) is first constructed in the design space to indicate the minimal distance from the feasible boundary of a design at a desired reliability level. A safe zone contour is then created so as to provide a quick estimate of the RC. At each design iteration reliability analyses of different accuracies are selected based on the level needed, depending on the activity of a constraint. For problems with a large number of constraints and relatively few design variables, such as structural problems, the active set strategies significantly improve efficiency, as demonstrated in the examples.

Multi-Objective Robust Optimization Using Differential Evolution and Sequential Quadratic Programming

2013 ◽  
Author(s):  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Quadratic Programming ◽  
Robust Optimization ◽  
Differential Evolution ◽  
Performance Improvement ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Multi Objective ◽  
Engineering Problems ◽  
And Performance

Multi-Objective Robust Optimization (MORO) can find Pareto solutions to multi-objective engineering problems while keeping the variation of the solutions being within an acceptable range when parameters vary. While the literature reports on many techniques in MORO, few papers focus on the implementation of Multi-Objective Differential Evolution (MODE) for robust optimization and the performance improvement of solutions. In this paper, MODE is first modified and implemented for robust optimization, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid MODE-SQP-RO algorithm is further proposed, where Sequential Quadratic Programming (SQP) is incorporated to enhance the local search. In the hybrid algorithm, two criteria, indicating the convergence speed of MODE-RO and the switch between MODE and SQP are proposed respectively. One numerical and one engineering examples are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving Multi-Objective Robust Optimization problems; while on the average, MODE-SQP-RO significantly improves the quality of robust solutions with comparable numbers of function evaluations.

A Mixed Interval Arithmetic/Affine Arithmetic Approach for Robust Design Optimization With Interval Uncertainty

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Shaobo Wang ◽  
Xiangyun Qing
Keyword(s):  
Interval Arithmetic ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Interval Uncertainty ◽  
Robust Design Optimization ◽  
Affine Arithmetic ◽  
Advantages And Disadvantages ◽  
Design Variables ◽  
Feasibility Robustness

Uncertainty is ubiquitous throughout engineering design processes. Robust optimization (RO) aims to find optimal solutions that are relatively insensitive to input uncertainty. In this paper, a new approach is presented for single-objective RO problems with an objective function and constraints that are continuous and differentiable. Both the design variables and parameters with interval uncertainties are represented as affine forms. A mixed interval arithmetic (IA)/affine arithmetic (AA) model is subsequently utilized in order to obtain affine approximations for the objective and feasibility robustness constraint functions. Consequently, the RO problem is converted to a deterministic problem, by bounding all constraints. Finally, nonlinear optimization solvers are applied to obtain a robust optimal solution for the deterministic optimization problem. Some numerical and engineering examples are presented in order to demonstrate the advantages and disadvantages of the proposed approach. The main advantage of the proposed approach lies in the simplicity of the conversion from a nonlinear RO problem with interval uncertainty to a deterministic single-looped optimization problem. Although this approach cannot be applied to problems with black-box models, it requires a minimal use of IA/AA computation and applies some widely used advanced solvers to single-looped optimization problems, making it more suitable for applications in engineering fields.

A Sequential-Quadratic-Programming-Filter Algorithm with a Modified Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear State Constraints

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 1938-1963 ◽  
Author(s):  
Zhe Liu ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Sequential Quadratic Programming ◽  
Optimization Problem ◽  
State Constraints ◽  
Optimization Problems ◽  
Filter Method ◽  
Reservoir Model ◽  
Nonlinear State

Summary Solving a large-scale optimization problem with nonlinear state constraints is challenging when adjoint gradients are not available for computing the derivatives needed in the basic optimization algorithm used. Here, we present a methodology for the solution of an optimization problem with nonlinear and linear constraints, where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic gradients using an improved stochastic simplex approximate gradient (StoSAG). Our discussion is focused on the application of our procedure to waterflooding optimization where the optimization variables are the well controls and the cost function is the life-cycle net present value (NPV) of production. The optimization algorithm used for solving the constrained-optimization problem is sequential quadratic programming (SQP) with constraints enforced using the filter method. We introduce modifications to StoSAG that improve its fidelity [i.e., the improvements give a more accurate approximation to the true gradient (assumed here to equal the gradient computed with the adjoint method) than the approximation obtained using the original StoSAG algorithm]. The modifications to StoSAG vastly improve the performance of the optimization algorithm; in fact, we show that if the basic StoSAG is applied without the improvements, then the SQP might yield a highly suboptimal result for optimization problems with nonlinear state constraints. For robust optimization, each constraint should be satisfied for every reservoir model, which is highly computationally intensive. However, the computationally viable alternative of letting the reservoir simulation enforce the nonlinear state constraints using its internal heuristics yields significantly inferior results. Thus, we develop an alternative procedure for handling nonlinear state constraints, which avoids explicit enforcement of nonlinear constraints for each reservoir model yet yields results where any constraint violation for any model is extremely small.

Optimization of DMC Transesterification Based Biodiesel Production

2015 ◽  
Vol 1113 ◽  
pp. 370-375 ◽  
Author(s):  
Nur Amirah Mohd Ali ◽  
Norashid Aziz
Keyword(s):  
Quadratic Programming ◽  
Palm Oil ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Batch Reactor ◽  
Biodiesel Production ◽  
Reactor Operation ◽  
Constraint Effect ◽  
Batch Time ◽  
Reactor Temperature

In this work, two types of optimization problems which are crucially related to batch reactor operation are considered. First problem is to maximize the conversion and second problem is to minimize the batch time. Both problems are solved using sequential quadratic programming (SQP) available in Aspen Plus. The manipulated variables i.e. reactor temperature and amount of palm oil are optimized simultaneously based on the specified objective function and equality constraint. Effect of intervals for both optimization problems are also evaluated in this paper. The results show that in maximizing conversion, the number of intervals did not significantly affect the amount of conversion. Meanwhile in minimizing batch time, the introduction of intervals was positively reduced the reactor temperature but negatively minimize the batch time.

Sequential Quadratic Programming

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 1-51 ◽  
Author(s):  
Paul T. Boggs ◽  
Jon W. Tolle
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Sequential Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Public Domain ◽  
Large Set ◽  
Constrained Optimization Problems ◽  
Nonlinearly Constrained Optimization

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

scholarly journals Customized Sequential Quadratic Programming for Solving Large-Scale AC Optimal Power Flow

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
mostafa Sahraei-Ardakani
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Optimization Problems ◽  
Test Cases ◽  
Time Limits ◽  
Optimal Power ◽  
Wide Range

After decades of research, efficient computation of AC Optimal Power Flow (ACOPF) still remains a challenge. ACOPF is a nonlinear nonconvex problem, and operators would need to solve ACOPF for large networks in almost real-time. Sequential Quadratic Programming (SQP) is one of the powerful second-order methods for solving large-scale nonlinear optimization problems and is a suitable approach for solving ACOPF with large-scale real-world transmission networks. However, SQP, in its general form, is still unable to solve large-scale problems within industry time limits. This paper presents a customized Sequential Quadratic Programming (CSQP) algorithm, taking advantage of physical properties of the ACOPF problem and the choice of the best performing ACOPF formulation. The numerical experiments suggest that CSQP outperforms commercial and noncommercial nonlinear solvers and solves test cases within the industry time limits. A wide range of test cases, ranging from 500-bus systems to 30,000-bus systems, are used to verify the test results.

scholarly journals Customized Sequential Quadratic Programming for Solving Large-Scale AC Optimal Power Flow

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
mostafa Sahraei-Ardakani
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Optimization Problems ◽  
Test Cases ◽  
Time Limits ◽  
Optimal Power ◽  
Wide Range

After decades of research, efficient computation of AC Optimal Power Flow (ACOPF) still remains a challenge. ACOPF is a nonlinear nonconvex problem, and operators would need to solve ACOPF for large networks in almost real-time. Sequential Quadratic Programming (SQP) is one of the powerful second-order methods for solving large-scale nonlinear optimization problems and is a suitable approach for solving ACOPF with large-scale real-world transmission networks. However, SQP, in its general form, is still unable to solve large-scale problems within industry time limits. This paper presents a customized Sequential Quadratic Programming (CSQP) algorithm, taking advantage of physical properties of the ACOPF problem and the choice of the best performing ACOPF formulation. The numerical experiments suggest that CSQP outperforms commercial and noncommercial nonlinear solvers and solves test cases within the industry time limits. A wide range of test cases, ranging from 500-bus systems to 30,000-bus systems, are used to verify the test results.

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