OBJECTIVE FUNCTION AND CONSTRAINT DESIGN EXAMPLES
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Dr. Anuja Arora, Jaypee Institute of Information Technology OBJECTIVE FUNCTION AND CONSTRAINT DESIGN EXAMPLES
Transcript of OBJECTIVE FUNCTION AND CONSTRAINT DESIGN EXAMPLES
Dr. Anuja Arora, Jaypee Institute of Information Technology
OBJECTIVE FUNCTION AND CONSTRAINT
DESIGN
EXAMPLES
Dr. Anuja Arora, Jaypee Institute of Information Technology
Encode the objective or cost function.
•The formulation of a fitness function, the use of population size, the choice of important parameters such as the rate of mutation and crossover, and the selection criteria of the new population should be carried out carefully.
RIVER
Field
Example1:
Farmer has to put 2400 m of fencing. They want to face off rectangle field which borders a
straight river. No fencing is needed along with river.
Design Objective Function and Constraint function for the above problem statement. Solve this
using optimization algorithm to reduce cost of material used.
Dr. Anuja Arora, Jaypee Institute of Information Technology
Encode the objective or cost function.
•The formulation of a fitness function, the use of population size, the choice of important parameters such as the rate of mutation and crossover, and the selection criteria of the new population should be carried out carefully.
Example1:
Three Farmer has to put 2400 m of fencing of a field. They want to face off rectangle field which
borders a straight river. No fencing is needed along with river.
Design Objective Function and Constraint function for the above problem statement. Solve this
using optimization algorithm to reduce cost of material used.
Area of rectangular region
Objective Function
f(x,y) =>min (lb) Quadratic Objective Function
Constraint => Perimeter should not be exceeded by 2400 m.
l l+2b<=2400 (equality/ inequality) Linear Constraint
Dr. Anuja Arora, Jaypee Institute of Information Technology
Encode the objective or cost function.
•The formulation of a fitness function, the use of population size, the choice of important parameters such as the rate of mutation and crossover, and the selection criteria of the new population should be carried out carefully.
Example2: A farm uses atleast 800 kg of special feed daily. Special feed is mixture of corn and
soyabean. Dietary requirement of special feed are atleast 30% protein and 5% fiber.
Determine the daily minimum cost of feed.
Objective Function f(X1,X2)=min(Z)= 0.3*X1+0.9*X2
Constraint function X1+X2>=800 Daily demand
0.09*X1+0.6*X2>=0.3 Protein Intake
0.02*X1+0.06*X2 <= 0.05 Intake
Per Kg. Cost/kg (in $)
Protein Fiber
Corn (X1) 0.09 0.02 0.3
Soya bean(X2) 0.6 0.06 0.9
Atleast 30% Atmost 5%
Dr. Anuja Arora, Jaypee Institute of Information Technology
Encode the objective or cost function.
•The formulation of a fitness function, the use of population size, the choice of important parameters such as the rate of mutation and crossover, and the selection criteria of the new population should be carried out carefully.
Example3: Asian Paint company produces interior and exterior paints from raw material
Material1 and Material 2.
- Daily demand for interior paint can’t exceed that of exterior paint by more than 1 unit
-Daily demand for interior paint is 2 unit
Determine optimum quantity of interior and exterior paint that company should get maximum
profit daily
Exterior
Paint/ unit
Interior
Paint/unit
Availability/
unit
Material 1 6 4 24
Material 2 1 2 6
Profit $5 $4
Dr. Anuja Arora, Jaypee Institute of Information Technology
Encode the objective or cost function.
•The formulation of a fitness function, the use of population size, the choice of important parameters such as the rate of mutation and crossover, and the selection criteria of the new population should be carried out carefully.
Example3: Asian Paint company produces interior and exterior paints from raw material
Material1 and Material 2.
- Daily demand for interior paint can’t exceed that of exterior paint by more than 1 unit
-Daily demand for interior paint is max 2 unit
Determine optimum quantity of interior and exterior paint that company should get maximum
profit daily
M1= units of exterior paint produced daily
M2= units of interior paint produced daily
Objective Function=> f(M1,M2)= Max(z)= 5M1+4M2
s.t. 6M1+4M2<=24 Constarin1 for material 1
M1+2M2<=6 Constarin2 for material 2
M2<=M1+1 M2<=2 additional contarint, M1, M2>=0
Exterior
Paint/ unit
Interior
Paint/unit
Availability
/ unit
Material 1 6 4 24
Material 2 1 2 6
Profit $5 $4
LECTURE 7 Extended
Topic Coverage Tags: GA problems
Problem1: 0-1 Knapsack problem
A bag can contain Maximum 80 kg weight and item list is as follows.
Items Qty weight
X 2 3
Y 3 4
Z 4 5
A 5 7
B 2 10
C 3 3
W 1 8
Write objective function/ cost function to keep maximum number of items in bag
with 50 kg constraint and every item should be in bag. Use binary encoding to
design chromosome.
Problem2:
Maximize
Subject to
and ,
Problem3: Travel salesman problem: To find the tour with minimum cost.
Constraints: 1. Cover all cities;
2. One city will visit only once
Hint: Euclidean function can be considered to measure the route cost.
Anuja
aro
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