A Formalism for Dynamic Programming
نویسندگان
چکیده
We introduce a formal structure for dynamic programming that associates a unique dynamic programming functional equation to every deterministic, separable decision tree representation of the underlying problem. Since, in general, the computational complexity of the resulting functional equation depends on the decision tree chosen, the art of dynamic programming is shown to lie in the choice of decision tree to model the problem. The development is illustrated with alternative formulations of the classic knapsack problem.
منابع مشابه
A dynamic programming approach for solving nonlinear knapsack problems
Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...
متن کاملStochastic Dynamic Programming with Markov Chains for Optimal Sustainable Control of the Forest Sector with Continuous Cover Forestry
We present a stochastic dynamic programming approach with Markov chains for optimal control of the forest sector. The forest is managed via continuous cover forestry and the complete system is sustainable. Forest industry production, logistic solutions and harvest levels are optimized based on the sequentially revealed states of the markets. Adaptive full system optimization is necessary for co...
متن کاملA dynamic bi-objective model for after disaster blood supply chain network design; a robust possibilistic programming approach
Health service management plays a crucial role in human life. Blood related operations are considered as one of the important components of the health services. This paper presents a bi-objective mixed integer linear programming model for dynamic location-allocation of blood facilities that integrates strategic and tactical decisions. Due to the epistemic uncertain nature of ...
متن کاملModeling and Evaluation of Stochastic Discrete-Event Systems with RayLang Formalism
In recent years, formal methods have been used as an important tool for performance evaluation and verification of a wide range of systems. In the view points of engineers and practitioners, however, there are still some major difficulties in using formal methods. In this paper, we introduce a new formal modeling language to fill the gaps between object-oriented programming languages (OOPLs) us...
متن کاملExtracting Dynamics Matrix of Alignment Process for a Gimbaled Inertial Navigation System Using Heuristic Dynamic Programming Method
In this paper, with the aim of estimating internal dynamics matrix of a gimbaled Inertial Navigation system (as a discrete Linear system), the discretetime Hamilton-Jacobi-Bellman (HJB) equation for optimal control has been extracted. Heuristic Dynamic Programming algorithm (HDP) for solving equation has been presented and then a neural network approximation for cost function and control input ...
متن کاملA numerical approach for optimal control model of the convex semi-infinite programming
In this paper, convex semi-infinite programming is converted to an optimal control model of neural networks and the optimal control model is solved by iterative dynamic programming method. In final, numerical examples are provided for illustration of the purposed method.
متن کامل