Difference between revisions of "Eight step procedures"

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'''Step 5: Define the boundary conditions''' <br />
 
'''Step 5: Define the boundary conditions''' <br />
• This helps create a starting point to finding a solution to the problem. First, we set <math>f^{*}_{n+1}(s) = 0</math> for all values of <math>s</math>. Here, we can note that <math>s = 0,,C</math> <br />
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• This helps create a starting point to finding a solution to the problem. First, we set <math>f^{*}_{n+1}(s) = 0</math> for all values of <math>s</math>. Here, we can note that <math> s=0,...,C </math> <br />
 
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'''Step 6: Define the recurrence relation''' <br />
 
'''Step 6: Define the recurrence relation''' <br />
 
• During this step, we make an allowable decision involving <math>j</math> items for the remaining capacity <math>s</math> for items <math>n</math>. We can write this statement as: <br />
 
• During this step, we make an allowable decision involving <math>j</math> items for the remaining capacity <math>s</math> for items <math>n</math>. We can write this statement as: <br />
o f*n(s) = max j=0,1,,min{a[n], floor(s/w[n]0} {b[n,j]+f*n+a(s-j*w[n])} <br />
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o <math> f^{*}_{n}(s)= \overset{max}{j=0,1,...,min\left \{ a[n],\left \lfloor \frac{s}{w[n]} \right \rfloor \right \}} \left \{ b[n,j]+ f^{*}_{n+1}(s-j*w[n]) \right \} </math> <br />
 
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'''Step 7: Compute the optimal value from the bottom-up''' <br />
 
'''Step 7: Compute the optimal value from the bottom-up''' <br />

Revision as of 18:40, 20 November 2020

Author: Eljona Pushaj, Diana Bogdanowich, Stephanie Keomany
Steward: Fengqi You

Introduction

Theory, Methodology, and/or Algorithmic Discussion

Definition

To solve a problem using the 8-step procedure, one must follow the following steps:

Step 1: Specify the stages of the problem
• The stages of a dynamic programming problem can be defined as points where decisions are made. These are often denoted with the variable .

Step 2: Specify the states for each stage
• The states of a problem are defined as the knowledge necessary to make a decision, or . We set equal to the maximum value of .

Step 3: Specify the allowable actions for each state in each stage
• This can be defined as:
o

Step 4: Describe the optimization function using an English-language description.
• In this sentence, we describe the optimization function for each state, or , and each stage, or . This can also be called

Step 5: Define the boundary conditions
• This helps create a starting point to finding a solution to the problem. First, we set for all values of . Here, we can note that

Step 6: Define the recurrence relation
• During this step, we make an allowable decision involving items for the remaining capacity for items . We can write this statement as:
o

Step 7: Compute the optimal value from the bottom-up
• In this step, a table is made

Numerical Example

Applications

Conclusion

References