Dynamic programming is a powerful technique for efficiently solving recursive problems, but it’s hardly the end of the story. In many cases, once we have a basic dynamic programming algorithm in place, we can make further improvements to bring down the running time or the space usage. We saw one example in the Fibonacci number algorithm. Buried inside the naïve iterative Fibonacci algorithm is ...

Dynamic programming is a powerful technique for efficiently solving recursive problems, but it’s hardly the end of the story. In many cases, once we have a basic dynamic programming algorithm in place, we can make further improvements to bring down the running time or the space usage. We saw one example in the Fibonacci number algorithm. Buried inside the naïve iterative Fibonacci algorithm is ...

We propose a new hybrid approach to solve the unbounded integer knapsack problem (UKP), where valid inequalities are generated based on intermediate solutions of an equivalent forward dynamic programming formulation. These inequalities help tighten the initial LP relaxation of the UKP, and therefore improve the overall computational efficiency. We also extended this approach to solve the multi-...

one major branch in mathematical sciences, which recently has been given especial attention, is optimization, including various methods such as linear programming, integer programming, and dynamic programming. due to the unique characteristics of air treatment systems, specifically multistage nature of such systems, dynamic programming has been widely applied. the purpose of this paper is to fi...

This paper proposes a k-group alignment algorithm for multiple alignment as a practical method. In iterative improvement methods for multiple alignment, the so-called group-togroup two-dimensional dynamic programming has been used, and in this respect our proposal is to extend the ordinary two-group dynamic programming to a k-group alignment programming. This extension is conceptually straightf...

In this paper, a new formulation along with numerical solution for the problem of finding a point-to-point trajectory with maximum load carrying capacities for flexible manipulators is proposed. For rigid manipulators, the major limiting factor in determining the Dynamic Load Carrying Capacity (DLCC) is the joint actuator capacity. The flexibility exhibited by light weight robots or by robots o...

In this paper, a method for solving a class of nonlinear optimal control problems is presented. The method is based on replacing the dynamic nonlinear optimal control problem by a sequence of quadratic programming problems. To this end, the iterative technique developed by Banks is used to replace the original nonlinear dynamic system by a sequence of linear time-varying dynamic systems, then e...