Optimization Methods: Dynamic Programming
- Learning Objectives
Module 5: Dynamic Programming
Learning Objectives
It was discussed in modules 3 and 4 that most widely used optimization method is linear
programming technique. But this technique is not flex
Optimization Methods: Dynamic Programming Applications Water Allocation
1
Module - 6 Lecture Notes 4
Water Allocation as a Sequential Process Numerical Example
Introduction
In the previous lecture, recursive equations for a basic water allocation problem
Optimization Methods: Dynamic Programming Applications Design of Continuous
Beam
1
Module 6 Lecture Notes 1
Design of Continuous Beam
Introduction
In the previous lectures, the development of recursive equations and computational procedure
were discussed.
Optimization Methods: Dynamic Programming Applications Capacity Expansion
1
Module 6 Lecture Notes 5
Capacity Expansion
Introduction
The most common applications of dynamic programming in water resources include water
allocation, capacity expansion of inf
Dynamic Programming
Applications
Design of
Continuous Beam
1
D Nagesh Kumar, IISc
Optimization Methods: M6L1
Objectives
To discuss the design of continuous beams
To formulate the optimization problem as a dynamic
programming model
2
D Nagesh Kumar, IISc
O
Optimization Methods: Dynamic Programming Applications Water Allocation
1
Module 6 Lecture Notes 3
Water Allocation as a Sequential Process Recursive Equations
Introduction
As discussed in previous lecture notes, in dynamic programming, a problem is handl
Dynamic Programming
Applications
Water Allocation
1
D Nagesh Kumar, IISc
Optimization Methods: M6L3
Introduction and Objectives
Dynamic Programming : Sequential or multistage
decision making process
Water Allocation problem is solved as a sequential
proce
Optimization Methods: Dynamic Programming Applications Reservoir Operation
1
Module 6 Lecture Notes 6
Reservoir Operation
Introduction
In the previous lectures, we discussed about the application of dynamic programming in
water allocation and capacity exp
Dynamic Programming
Applications
Water Allocation
Numerical Example
1
D Nagesh Kumar, IISc
Optimization Methods: M6L4
Objectives
To demonstrate the water allocation problem
through a numerical example using
Backward approach
Forward approach
2
D Nagesh K
Dynamic Programming
Applications
Optimum Geometric
Layout of Truss
1
D Nagesh Kumar, IISc
Optimization Methods: M6L2
Objectives
To discuss the design of elastic trusses
To formulate the optimization problem as a
dynamic programming model
2
D Nagesh Kumar,
Optimization Methods: Dynamic Programming Applications Optimum Geometric
Layout of Truss
1
Module 6 Lecture Notes 2
Optimum Geometric Layout of Truss
Introduction
In this lecture, the optimal design of elastic trusses is discussed from a dynamic programmi
Optimization Methods: Dynamic Programming Applications
- Learning Objectives
Module 6: Dynamic Programming Applications
Learning Objectives
The basic concepts of dynamic programming like concept of sub-optimization and principle
of optimality were discuss
Optimization Methods: Dynamic Programming Recursive Equations
1
Module 5 Lecture Notes 2
Recursive Equations
Introduction
In the previous lecture, we have seen how to represent a multistage decision process and also
the concept of suboptimization. In orde
Optimization Methods: Dynamic Programming - Introduction
1
Module 5 Lecture Notes 1
Introduction
Introduction
In some complex problems, it will be advisable to approach the problem in a sequential
manner in order to find the solution quickly. The solution
Optimization Methods: Dynamic Programming Other Topics
1
Module 5 Lecture Notes 4
Other Topics
Introduction
In the previous lectures we discussed about problems with a single state variable or input
variable St which takes only some range of values. In th
Dynamic Programming
Recursive Equations
1
D Nagesh Kumar, IISc
Optimization Methods: M5L2
Introduction and Objectives
Introduction
Recursive equations are used to solve a problem in sequence
These equations are fundamental to the dynamic programming
Objec
Dynamic Programming
Other Topics
1
D Nagesh Kumar, IISc
Optimization Methods: M5L4
Objectives
To explain the difference between discrete and
continuous dynamic programming
To discuss about multiple state variables
To discuss the curse of dimensionality in
Dynamic Programming
Computational
Procedure in Dynamic
Programming
1
D Nagesh Kumar, IISc
Optimization Methods: M5L3
Objectives
To explain the computational procedure of solving
the multistage decision process using recursive
equations for backward approa
Dynamic Programming
Introduction
1
D Nagesh Kumar, IISc
Optimization Methods: M5L1
Introduction and Objectives
Introduction
Complex problems are sometimes solved quickly if approached in a
sequential manner
Dynamic Programming : Sequential or multistage d
Optimization Methods: Dynamic Programming Computational Procedure
1
Module 5 Lecture Notes 3
Computational Procedure in Dynamic Programming
Introduction
The construction of recursive equations for a multistage program was discussed in the
previous lecture
Dynamic Programming
Applications
Reservoir Operation
1
D Nagesh Kumar, IISc
Optimization Methods: M6L6
Objectives
To develop the steady state operational
policy of a single reservoir
To develop backward recursive equations for
this operational policy
To d
Dynamic Programming
Applications
Capacity Expansion
1
D Nagesh Kumar, IISc
Optimization Methods: M6L5
Objectives
To discuss the Capacity Expansion Problem
To explain and develop recursive equations
for both backward approach and forward
approach
To demons
Optimization Methods: Advanced Topics in Optimization - Evolutionary Algorithms for
Optimization and Search
1
Lecture Notes 5
Evolutionary Algorithms for Optimization and Search
Introduction
Most real world optimization problems involve complexities like
Advanced Topics in Optimization
Piecewise Linear
Approximation of a
Nonlinear Function
1
D Nagesh Kumar, IISc
Optimization Methods: M8L1
Introduction and Objectives
Introduction
There exists no general algorithm for nonlinear programming due to its
irregu
Optimization Methods: Advanced Topics in Optimization - Multi-objective Optimization
1
Module 8 Lecture Notes 2
Multi-objective Optimization
Introduction
In a real world problem it is very unlikely that we will meet the situation of single objective
and m
Optimization Methods: Advanced Topics in Optimization
- Learning Objectives
Module 8: Advanced Topics in Optimization
Learning Objectives
In the previous modules, we discussed about almost all the major techniques used for
optimization. This module gives
Optimization Methods: Advanced Topics in Optimization - Multilevel Optimization
1
Module 8 Lecture Notes 3
Multilevel Optimization
Introduction
The example problems discussed in the previous modules consist of very few decision
variables and constraints.
Advanced Topics in Optimization
Evolutionary Algorithms for
Optimization and Search
1
D Nagesh Kumar, IISc
Optimization Methods: M8L5
Introduction
Real world optimization problems mostly involve complexities like
discrete-continuous or mixed variables, mu
Optimization Methods: Advanced Topics in Optimization - Piecewise linear
approximation of a nonlinear function
1
Module 8 Lecture Notes 1
Piecewise Linear Approximation of a Nonlinear Function
Introduction
In the previous lectures, we have learned how to
Advanced Topics in Optimization
Multilevel
Optimization
1
D Nagesh Kumar, IISc
Optimization Methods: M8L3
Objectives
To discuss about Multilevel Optimization
To describe a decomposition method for nonlinear
optimization problems, known as model-coordinati