Presentation is loading. Please wait.

Presentation is loading. Please wait.

Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Multi-Objective Dynamic Optimization using Evolutionary Algorithms by Udaya Bhaskara.

Published byAlexandra Curtis Modified over 9 years ago

Similar presentations

Presentation on theme: "Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Multi-Objective Dynamic Optimization using Evolutionary Algorithms by Udaya Bhaskara."— Presentation transcript:

1 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Multi-Objective Dynamic Optimization using Evolutionary Algorithms by Udaya Bhaskara Rao N. under the guidance of Dr. Kalyanmoy Deb Professor Department of Mechanical Engineering

2 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Birds view  Introduction to DMO.  Test problems in DMO.  NSGA-II application in DMO.  Introduction to hydrothermal scheduling problem.  NSGA-II application on hydrothermal scheduling problem.  Hydrothermal scheduling problem formulation as DMO.  Modifications in the proposed algorithm.  Results and discussion.  Conclusions.  Future scope of work.

3 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introduction to DMO  Dynamic optimization is optimization in dynamic environment.  i.e. either objective function or constraints are time dependent.  The dynamic multi-objective optimization (DMO) is multi- objective optimization in dynamic environment.  Classification in DMOs : POF POS No changeChange No changeType IVType I ChangeType IIIType II

4 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introduction to DMO  It is better to go for DMO, whenever the problem is time dependent. Advantages in using DMO: 1. By relating time with generation number, number of variables reduce i.e. the dimension of problem reduces. 2. Whenever problem changes, the new problem adopts the old solution, which helps in faster convergence. 3. Results for all the problems can be found in one run.

5 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO  The following test problems are formulated by Farina et. al. (2004). FDA 1 : Constant convex Pareto-optimal front in objective space and linear change in solution space. FDA 2 : Pareto-optimal front changes from convex to non convex and no change in solution space. FDA 3 : Change in Pareto-optimal front but all convex and linear change in solution space. FDA 4 : Constant non convex Pareto-optimal front and linear change in solution space which is three Dimensional space. FDA 5 : Change in Pareto-optimal front but all non convex and linear change in solution space which is three dimensional space.

6 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO FDA 1: Type I

7 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO FDA 2: Type III

8 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO FDA 3: Type II

9 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO FDA 4: Type I

10 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Test problems in DMO FDA 5: Type II

11 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) NSGA-II application in DMO  Present algorithm is developed based on NSGA-II.  NSGA-ll algorithm can not be applied straightaway on DMO problems.  Elitism, restricts the upward movement of Pareto-optimal front in NSGA-II and hence removed.  The term time is correlated with generation number.

12 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Elitism removed Modified NSGA-II algorithm-I

13 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Elitism introduced interactively Modified NSGA-II algorithm-II

14 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) FDA 2 simulation

15 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) FDA 3 simulation

16 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) FDA 5 simulation

17 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introduction to hydrothermal scheduling problem  In hydrothermal systems both hydroelectric and thermal generating units are to be utilized together to meet the total power demand.  The hydrothermal problem here consists of N s number of thermal and N h number of hydroelectric generating units sharing the total power demand.  Minimizing both fuel cost and emission of nitrogen oxides from the thermal generating units.  The static problem formulation is taken from the work done by M. Basu (2005). (Weighted sum approach using simulated annealing)

18 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introduction to hydrothermal scheduling problem  In this present work the problem is formulated for two hydraulic units and four thermal units.  Problem is defined for four timeslots of each 12 hours.  So the total number of variables are 24.  The demand values for these four time slots are as follows:

19 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Objective functions Economy: Emission:

20 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Constraints Power balance constraints: Water availability constraints:

21 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Constraint handling Step 1 : The procedure is to be started with the two water available constraints, as they are independent of variables related to thermal units. Step 2 : Constraint equation can be written as,

22 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Constraint handling Step 3 : Start with h = 1, m = 1  For finding P hm value from constraint equation, first rewrite the equation in terms of P hm by taking all four P h values of the present hydro unit from GA solution and finding out the ratios with respect to P hm.  The obtained quadratic equation in terms of P hm is solved algebraically to get P hm value. Subsequently the positive value is chosen, so that the lower limit is satisfied automatically. If it is also satisfied the upper limit go to Step 5, else go to Step 4.

23 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Constraint handling Step 4 : m = m + 1, and if m ≤ 4 repeat Step 3 else go to Step 6. Step 5 : Change all four P h value by using previously calculated ratios and h = h + 1, if h ≤ 2 repeat Step 3, else Exit. Step 6 : The constraint is not satisfied, so for the present variable values, the fitness function is to be penalized with the constraint violation.  If both water availability constraints are satisfied through the above process, similar analysis is to be done on power balance constraints

24 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) NSGA-II application on hydrothermal scheduling problem Population size = 240 Number of generations = 1000 Crossover probability = 0.9 Mutation probability = 0.04 Distribution index for crossover = 20 Distribution index for mutation = 50 Input parameters :

25 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Analysis of obtained results P h1 vs. F 1 P h2 vs. F 1

26 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Analysis of obtained results P s1 vs. F 1 P s2 vs. F 1

27 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Analysis of obtained results P s3 vs. F 1 P s4 vs. F 1

28 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Hydrothermal scheduling problem reformulation as DMO  As the problem parameters change with time, this problem comes under DMO.  Few modifications required in problem formulation, they are as follows: 1. Term time should be removed as a variable. 2. All time variable parameters should be directly related with generation number.  The dimension of problem has reduced from 24 to 6.

29 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Modifications in the proposed algorithm  The proposed algorithm can handle the changes occurring after every 12 hours.  The algorithm is further modified to handle frequent changes.  The main modifications are as follows: 1. Introducing new solutions at change by generating random solutions. 2. Introducing new solutions at change by mutating old solutions.

30 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introducing new random solutions at change First modification

31 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Introducing new mutated solutions at change Second modification

32 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Interpolation

33 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion Comparison among three modified algorithms : 4 timeslots8 timeslots

34 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion Comparison among three modified algorithms : 16 timeslots48 timeslots

35 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion Comparison among three modified algorithms : 96 timeslots 192 timeslots

36 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 4 timeslots8 timeslots Percentage of random new solutions verses performance index :

37 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 16 timeslots48 timeslots Percentage of random new solutions verses performance index :

38 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 96 timeslots 192 timeslots Percentage of random new solutions verses performance index :

39 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 4 timeslots8 timeslots Percentage of mutated new solutions verses performance index :

40 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 16 timeslots48 timeslots Percentage of mutated new solutions verses performance index :

41 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Results and discussion 96 timeslots 192 timeslots Percentage of mutated new solutions verses performance index :

42 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Conclusions 1. Static to dynamic conversion of the problem, increases its convergence rate and simultaneously there also exists a possibility for dimensionality reduction. 2. Modified NSGA-II algorithms, has yielded better results for all test problems. 3. The reformulated hydrothermal scheduling problem has been solved efficiently. 4. The static analysis of hydrothermal scheduling problem with modified NSGA-II produced better results compared to previous works.

43 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Conclusions 5. Best results are produced when the hydrothermal scheduling problem is formulated into DMO problem, with considerable reduction in computational time over static problems. 6. The final proposed algorithm has increased the possibility in achieving Pareto-optimal front within short time period and performs best up to one hour time slot.

44 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Future scope of work 1. Generalization of the proposed algorithm, would make it user friendly. 2. The hydrothermal scheduling problem defined for individual hydro units, can be extended for cascaded hydro units. 3. The present algorithm is used to search for Pareto-optimal front, this algorithm can be slightly modified to get reliable and robust Pareto-optimal solutions also.

45

46 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Back up slides

47 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Parameter Analysis

48 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Nomenclature

49 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Input parameters

50 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Input parameters

51 Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Pareto front  Non-dominated front is Pareto-optimal front.  Trade-off of optimal solutions on F 1 vs F 2 plot.

Download ppt "Kanpur Genetic Algorithms Laboratory IIT Kanpur 25, July 2006 (11:00 AM) Multi-Objective Dynamic Optimization using Evolutionary Algorithms by Udaya Bhaskara."

Similar presentations

Crew Pairing Optimization with Genetic Algorithms

Crew Pairing Optimization with Genetic Algorithms
Topic Outline ? Black-Box Optimization Optimization Algorithm: only allowed to evaluate f (direct search) decision vector x objective vector f(x) objective.

Topic Outline ? Black-Box Optimization Optimization Algorithm: only allowed to evaluate f (direct search) decision vector x objective vector f(x) objective.
Constraint Optimization We are interested in the general non-linear programming problem like the following Find x which optimizes f(x) subject to gi(x)

Constraint Optimization We are interested in the general non-linear programming problem like the following Find x which optimizes f(x) subject to gi(x)
MOEAs University of Missouri - Rolla Dr. T’s Course in Evolutionary Computation Matt D. Johnson November 6, 2006.

MOEAs University of Missouri - Rolla Dr. T’s Course in Evolutionary Computation Matt D. Johnson November 6, 2006.
1 An Adaptive GA for Multi Objective Flexible Manufacturing Systems A. Younes, H. Ghenniwa, S. Areibi uoguelph.ca.

1 An Adaptive GA for Multi Objective Flexible Manufacturing Systems A. Younes, H. Ghenniwa, S. Areibi uoguelph.ca.
Using Parallel Genetic Algorithm in a Predictive Job Scheduling

Using Parallel Genetic Algorithm in a Predictive Job Scheduling
Multi-Objective Optimization NP-Hard Conflicting objectives – Flow shop with both minimum makespan and tardiness objective – TSP problem with minimum distance,

Multi-Objective Optimization NP-Hard Conflicting objectives – Flow shop with both minimum makespan and tardiness objective – TSP problem with minimum distance,
Elitist Non-dominated Sorting Genetic Algorithm: NSGA-II

Elitist Non-dominated Sorting Genetic Algorithm: NSGA-II
Comparison of Genetic Algorithm and WASAM Model for Real Time Water Allocation: A Case Study of Song Phi Nong Irrigation Project Bhaktikul, K, Mahidol.

Comparison of Genetic Algorithm and WASAM Model for Real Time Water Allocation: A Case Study of Song Phi Nong Irrigation Project Bhaktikul, K, Mahidol.
Optimal Design Laboratory | University of Michigan, Ann Arbor 2011 Design Preference Elicitation Using Efficient Global Optimization Yi Ren Panos Y. Papalambros.

Optimal Design Laboratory | University of Michigan, Ann Arbor 2011 Design Preference Elicitation Using Efficient Global Optimization Yi Ren Panos Y. Papalambros.
Particle Swarm Optimization (PSO)

Particle Swarm Optimization (PSO)
PROCESS INTEGRATED DESIGN WITHIN A MODEL PREDICTIVE CONTROL FRAMEWORK Mario Francisco, Pastora Vega, Omar Pérez University of Salamanca – Spain University.

PROCESS INTEGRATED DESIGN WITHIN A MODEL PREDICTIVE CONTROL FRAMEWORK Mario Francisco, Pastora Vega, Omar Pérez University of Salamanca – Spain University.
2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003 Application of Multi-objective Optimization in Food Refrigeration Processes.

2003 International Congress of Refrigeration, Washington, D.C., August 17-22, 2003 Application of Multi-objective Optimization in Food Refrigeration Processes.
Non-Linear Problems General approach. Non-linear Optimization Many objective functions, tend to be non-linear. Design problems for which the objective.

Non-Linear Problems General approach. Non-linear Optimization Many objective functions, tend to be non-linear. Design problems for which the objective.
INTEGRATED DESIGN OF WASTEWATER TREATMENT PROCESSES USING MODEL PREDICTIVE CONTROL Mario Francisco, Pastora Vega University of Salamanca – Spain European.

INTEGRATED DESIGN OF WASTEWATER TREATMENT PROCESSES USING MODEL PREDICTIVE CONTROL Mario Francisco, Pastora Vega University of Salamanca – Spain European.
Multi-Objective Evolutionary Algorithms Matt D. Johnson April 19, 2007.

Multi-Objective Evolutionary Algorithms Matt D. Johnson April 19, 2007.
Data classification based on tolerant rough set reporter: yanan yean.

Data classification based on tolerant rough set reporter: yanan yean.
NORM BASED APPROACHES FOR AUTOMATIC TUNING OF MODEL BASED PREDICTIVE CONTROL Pastora Vega, Mario Francisco, Eladio Sanz University of Salamanca – Spain.

NORM BASED APPROACHES FOR AUTOMATIC TUNING OF MODEL BASED PREDICTIVE CONTROL Pastora Vega, Mario Francisco, Eladio Sanz University of Salamanca – Spain.
Genetic Algorithms in Materials Processing N. Chakraborti Department of Metallurgical & Materials Engineering Indian Institute of Technology Kharagpur.

Genetic Algorithms in Materials Processing N. Chakraborti Department of Metallurgical & Materials Engineering Indian Institute of Technology Kharagpur.
Handling Constraints 報告者 : 王敬育. Many researchers investigated Gas based on floating point representation but the optimization problems they considered.

Handling Constraints 報告者 : 王敬育. Many researchers investigated Gas based on floating point representation but the optimization problems they considered.

Similar presentations

Ads by Google