A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization pro...A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the o...By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.展开更多
A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems a...A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.展开更多
The potential role of formal structural optimization was investigated for designing foldable and deployable structures in this work.Shape-sizing nested optimization is a challenging design problem.Shape,represented by...The potential role of formal structural optimization was investigated for designing foldable and deployable structures in this work.Shape-sizing nested optimization is a challenging design problem.Shape,represented by the lengths and relative angles of elements,is critical to achieving smooth deployment to a desired span,while the section profiles of each element must satisfy structural dynamic performances in each deploying state.Dynamic characteristics of deployable structures in the initial state,the final state and also the middle deploying states are all crucial to the structural dynamic performances.The shape was represented by the nodal coordinates and the profiles of cross sections were represented by the diameters and thicknesses.SQP(sequential quadratic programming) method was used to explore the design space and identify the minimum mass solutions that satisfy kinematic and structural dynamic constraints.The optimization model and methodology were tested on the case-study of a deployable pantograph.This strategy can be easily extended to design a wide range of deployable structures,including deployable antenna structures,foldable solar sails,expandable bridges and retractable gymnasium roofs.展开更多
In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD）...In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.展开更多
To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver co...To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver constraint system. The comparison of the driver mechanics index of the experimental data with the simulation data in the frontal crash shows that the accuracy of simulation model meets the requirements. The optimal Latin test design is adopted, and the global sensitivity analysis of the design parameters is carried out based on the Kriging model. The four most sensitive parameters are selected, and the parameters are solved by a multi-island genetic algorithm.And then the nonlinear programming quadratic line(NLPQL) algorithm is used to search for accurate optimization. The optimal parameters of the occupant restraint system are determined: the limiting force value of force limiter 2 985.603 N, belt extension 12.684%, airbag point explosion time 27.585 ms, and airbag vent diameter 27.338 mm, with the weighted injury criterion(WIC) decreased by 12.97%, the head injury decreased by 22.60%, and the chest compression decreased by 7.29%. The results show that the system integration of passive safety devices such as seat belts and airbags can effectively protect the driver.展开更多
This study presents a hybrid algorithm obtained by combining a genetic algorithm (GA) with successive quadratic sequential programming (SQP), namely GA-SQP. GA is the main optimizer, whereas SQP is used to refine the ...This study presents a hybrid algorithm obtained by combining a genetic algorithm (GA) with successive quadratic sequential programming (SQP), namely GA-SQP. GA is the main optimizer, whereas SQP is used to refine the results of GA, further improving the solution quality. The problem formulation is done in the framework named RUNE (fRamework for aUtomated aNalog dEsign), which targets solving nonlinear mono-objective and multi-objective optimization problems for analog circuits design. Two circuits are presented: a transimpedance amplifier (TIA) and an optical driver (Driver), which are both part of an Optical Network-on-Chip (ONoC). Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results obtained with SQP algorithm. The outcome is very encouraging and suggests that the hybrid proposed method is very efficient in solving analog design problems.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10571137,10771162)
文摘A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金Supported by the National Natural Science Foundation of China (70371032,60574071)
文摘By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.
文摘A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.
基金Project(030103) supported by the Weaponry Equipment Pre-Research Key Foundation of ChinaProject(69982009) supported by the National Natural Science Foundation of China
文摘The potential role of formal structural optimization was investigated for designing foldable and deployable structures in this work.Shape-sizing nested optimization is a challenging design problem.Shape,represented by the lengths and relative angles of elements,is critical to achieving smooth deployment to a desired span,while the section profiles of each element must satisfy structural dynamic performances in each deploying state.Dynamic characteristics of deployable structures in the initial state,the final state and also the middle deploying states are all crucial to the structural dynamic performances.The shape was represented by the nodal coordinates and the profiles of cross sections were represented by the diameters and thicknesses.SQP(sequential quadratic programming) method was used to explore the design space and identify the minimum mass solutions that satisfy kinematic and structural dynamic constraints.The optimization model and methodology were tested on the case-study of a deployable pantograph.This strategy can be easily extended to design a wide range of deployable structures,including deployable antenna structures,foldable solar sails,expandable bridges and retractable gymnasium roofs.
文摘In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
基金Supported by Natural Science and Technology Research Project of the Jiangxi Education Department(GJJ202002, GJJ2202620)。
文摘To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid Ⅲ 50th dummy driver constraint system. The comparison of the driver mechanics index of the experimental data with the simulation data in the frontal crash shows that the accuracy of simulation model meets the requirements. The optimal Latin test design is adopted, and the global sensitivity analysis of the design parameters is carried out based on the Kriging model. The four most sensitive parameters are selected, and the parameters are solved by a multi-island genetic algorithm.And then the nonlinear programming quadratic line(NLPQL) algorithm is used to search for accurate optimization. The optimal parameters of the occupant restraint system are determined: the limiting force value of force limiter 2 985.603 N, belt extension 12.684%, airbag point explosion time 27.585 ms, and airbag vent diameter 27.338 mm, with the weighted injury criterion(WIC) decreased by 12.97%, the head injury decreased by 22.60%, and the chest compression decreased by 7.29%. The results show that the system integration of passive safety devices such as seat belts and airbags can effectively protect the driver.
文摘This study presents a hybrid algorithm obtained by combining a genetic algorithm (GA) with successive quadratic sequential programming (SQP), namely GA-SQP. GA is the main optimizer, whereas SQP is used to refine the results of GA, further improving the solution quality. The problem formulation is done in the framework named RUNE (fRamework for aUtomated aNalog dEsign), which targets solving nonlinear mono-objective and multi-objective optimization problems for analog circuits design. Two circuits are presented: a transimpedance amplifier (TIA) and an optical driver (Driver), which are both part of an Optical Network-on-Chip (ONoC). Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results obtained with SQP algorithm. The outcome is very encouraging and suggests that the hybrid proposed method is very efficient in solving analog design problems.
