多目标优化与决策的基本方法.pptVIP

多目标优化与决策的基本方法基于Matlab的一种现代方法 单元讨论目标Unit Object 教科书 多目标优化问题非劣解及约束法 目标规划法 扩展到工程领域与非线性优化 Matlab R14 SP1的Optimization Toolbox 详细讲解fgoalattain，大致对应目标规划法，但是扩展到非线性 多目标优化的数学描述Multiobjective optimization model 多目标优化的非劣解集Noninferior solution for the model 约束法Constraint Method 目标规划法Goal Attainment Method Matlab优化工具箱Matlab Optimization Toolbox 优化工具箱提供了一般和大型的非线性优化函数，同时还提供了线性规划，二次规划，非线性最小二乘以及非线性方程求解的工具。 主要特性： 无约束非线性极小化问题 约束性线性极小化、极大极小、多目标优化，半无穷极小化问题。 二次规划和线性规划问题 非线性最小二乘和边界曲线拟合问题 非线性系统方程求解问题 约束线性最小二乘问题 大型问题的特殊算法 fgoalattain一般用法Solve multiobjective goal attainment problem fgoalattain实例线性系统输出反馈极点配置 Practical fgoalattain seeking K A [ -0.5 0 0; 0 -2 10; 0 1 -2 ]; B [ 1 0; -2 2; 0 1 ]; C [ 1 0 0; 0 0 1 ]; %% % Suppose we wish to design an output feedback controller, x, to have % poles to the left of the location [-5, -3, -1] in the complex plane. % The controller must not have any gain element exceeding an absolute % value of 4. goal [-5, -3, -1] %% % Set the weights equal to the goals to ensure same percentage % under- or over-attainment in the goals. weight abs goal %% % Initialize output feedback controller x0 [ -1 -1; -1 -1]; %% % Set upper and lower bounds on the controller lb repmat -4,size x0 ub repmat 4,size x0 %% % Create a vector-valued function eigfun that returns the eigenvalues of the % closed loop system. This function requires additional parameters namely, % the matrices A, B, and C ; the most convenient way to pass these is through % an anonymous function: eigfun @ x sort eig A+B*x*C %% % To begin the optimization we call FGOALATTAIN: [x,fval,attainfactor,exitflag,output,lambda] ... fgoalattain eigfun,x0,goal,weight,[],[],[],[],lb,ub,[],options ; %% % The attainment factor indicates the level of goal achievement. % A negative attainment factor indicates over-achievement, positive % indicates under-achievement. The value attainfactor we obtained in % this run indicates tha