Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A QUASI-SIMPLEX METHOD FOR STRICTLY CONVEX QUADRATIC PROGRAMMING

本文提出一个不用 Kuhn- Tucker条件而直接搜索严格凸二次规划最优目标点的鲁棒方法 .在搜索过程中 ,目标点沿约束多面体边界上的一条折线移动 .这种移动目标点的思想可以被认为是线性规划单纯形法的自然推广 ,在单纯形法中 ,目标点从一个顶点移到另一个顶点。

Convex Quadratic Programming Approach to the Maximum Matching Problem

The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented.

Quadratic programming versus second order con programming in portfolio optimization

Despite the extensive literature in finding new models to replace the Markowitz model or trying to increase the accuracy of its input estimations, there is less studies about the impact on the results of using different optimization algorithms. This paper aims to add some research to this field by comparing the performance of two optimization algorithms in drawing the Markowitz Efficient Frontier and in real world investment strategies. Second order cone programming is a faster algorithm, appears to be more efficient, but is impossible to assert which algorithm is better. Quadratic Programming often shows superior performance in real investment strategies.

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

Investigation of methods for increasing the energy efficiency on unmanned aerial vehicles (UAVS)

In recent years, development of Unmanned Aerial Vehicles (UAV) has become a significant growing segment of the global aviation industry. These vehicles are developed with the intention of operating in regions where the presence of onboard human pilots is either too risky or unnecessary. Their popularity with both the military and civilian sectors have seen the use of UAVs in a diverse range of applications, from reconnaissance and surveillance tasks for the military, to civilian uses such as aid relief and monitoring tasks. Efficient energy utilisation on an UAV is essential to its functioning, often to achieve the operational goals of range, endurance and other specific mission requirements. Due to the limitations of the space available and the mass budget on the UAV, it is often a delicate balance between the onboard energy available (i.e. fuel) and achieving the operational goals. This thesis presents an investigation of methods for increasing the energy efficiency on UAVs. One method is via the development of a Mission Waypoint Optimisation (MWO) procedure for a small fixed-wing UAV, focusing on improving the onboard fuel economy. MWO deals with a pre-specified set of waypoints by modifying the given waypoints within certain limits to achieve its optimisation objectives of minimising/maximising specific parameters. A simulation model of a UAV was developed in the MATLAB Simulink environment, utilising the AeroSim Blockset and the in-built Aerosonde UAV block and its parameters. This simulation model was separately integrated with a multi-objective Evolutionary Algorithm (MOEA) optimiser and a Sequential Quadratic Programming (SQP) solver to perform single-objective and multi-objective optimisation procedures of a set of real-world waypoints in order to minimise the onboard fuel consumption. The results of both procedures show potential in reducing fuel consumption on a UAV in a ight mission. Additionally, a parallel Hybrid-Electric Propulsion System (HEPS) on a small fixedwing UAV incorporating an Ideal Operating Line (IOL) control strategy was developed. An IOL analysis of an Aerosonde engine was performed, and the most efficient (i.e. provides greatest torque output at the least fuel consumption) points of operation for this engine was determined. Simulation models of the components in a HEPS were designed and constructed in the MATLAB Simulink environment. It was demonstrated through simulation that an UAV with the current HEPS configuration was capable of achieving a fuel saving of 6.5%, compared to the ICE-only configuration. These components form the basis for the development of a complete simulation model of a Hybrid-Electric UAV (HEUAV).

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

基于SQP算法的7000m载人潜水器有约束非线性控制分配研究

以7000m载人潜水器为研究对象,分析了潜水器的推进系统,并给出了6自由度推力转换模型,重点讨论了载人潜水器控制分配的优化问题.结合7000m载人潜水器的推进器布置和推进器特点,设计了优化准则代价函数,采用序列二次规划(sequential quadratic programm ing,SQP)算法求解了载人潜水器的非线性控制分配问题,通过半物理仿真平台实验验证了本文提出的控制分配算法的正确性和有效性.yh

Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Surrogate-based-optimization methods provide a means to achieve high-fidelity design optimization at reduced computational cost by using a high-fidelity model in combination with lower-fidelity models that are less expensive to evaluate. This paper presents a provably convergent trust-region model-management methodology for variableparameterization design models: that is, models for which the design parameters are defined over different spaces. Corrected space mapping is introduced as a method to map between the variable-parameterization design spaces. It is then used with a sequential-quadratic-programming-like trust-region method for two aerospace-related design optimization problems. Results for a wing design problem and a flapping-flight problem show that the method outperforms direct optimization in the high-fidelity space. On the wing design problem, the new method achieves 76% savings in high-fidelity function calls. On a bat-flight design problem, it achieves approximately 45% time savings, although it converges to a different local minimum than did the benchmark.

A nonlinear model for the long-term hydro-thermal generation scheduling problem over multiple areas with transmission constraints

This paper presents a nonlinear model with individual representation of plants for the centralized long-term hydrothermal scheduling problem over multiple areas. In addition to common aspects of long-term scheduling, this model takes transmission constraints into account. The ability to optimize hydropower exchange among multiple areas is important because it enables further minimization of complementary thermal generation costs. Also, by considering transmission constraints for long-term scheduling, a more precise coupling with shorter horizon schedules can be expected. This is an important characteristic from both operational and economic viewpoints. The proposed model is solved by a sequential quadratic programming approach in the form of a prototype system for different case studies. An analysis of the benefits provided by the model is also presented. ©2009 IEEE.