论文部分内容阅读
动态规划是解决多阶段决策问题的一种最优化方法。无论优化问题是线性的还是非线性的,只要能分解成一系列的单阶段决策问题,则可采用动态规划寻求其最优解。对于离散型问题、目标函数的一阶导数(梯度)▽~Tf(X)、二阶导数(海森阵)H(X)不连续或其表达式很复杂时,动态规划法具有突出的优点。目前,动态规划已广泛应用于解决许多实际工程问题。 动态规划的最优顺序,有从n阶段算到第1阶段,也有从第1阶段算到n阶段,最后得出最优策略的。应用时可视具体问题的要求及处理方便而定。现研究后一种情况,而且是极小化目标函数值问题。对前一种情况,解决方法与此类似,对极大化目标函数问题,将目标函数反号即变为极小化问题。
Dynamic programming is an optimization method to solve the multi-stage decision problem. Regardless of whether the optimization problem is linear or non-linear, dynamic programming can be used to find the optimal solution as long as it can be decomposed into a series of single-stage decision problems. For the discrete problem, the dynamic programming method has outstanding advantages when the first derivative (gradient) ▽ ~ Tf (X) of the objective function and the second derivative (Hessian matrix) H (X) are discontinuous or their expressions are complex . At present, dynamic programming has been widely used to solve many practical engineering problems. The optimal order of dynamic programming, from the n stage to the first stage, but also from the first stage to the n stage, and finally come to the optimal strategy. Applications can be specific to the requirements of the problem and easy to handle. Now the latter case, but also to minimize the objective function value problem. In the former case, the solution is the same. For the problem of maximizing the objective function, the inverse of the objective function becomes the minimization problem.