New Mutation Operator for Multiobjective Optimization with Differential Evolution

Transcription

1 TIEJ601, Postgraduate Seminar in Information Technology New Mutation Operator for Multiobjective Optimization with Differential Evolution by Karthik Sindhya Doctoral Student Industrial Optimization Group

2 Overview Status of my PhD Thesis in a nutshell Background Polynomial mutation operator Tests Conclusion and future work

3 Status of my PhD 3

4 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. 3

5 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. 3

6 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. Collection of Papers 3

7 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. Collection of Papers 3

8 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. Collection of Papers Prof. Kaisa Miettinen Prof. Kalyanmoy Deb 3

9 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. Collection of Papers Prof. Kaisa Miettinen Prof. Kalyanmoy Deb Past Two conference publications Two journal articles in review Present One article Future One article by June

10 Status of my PhD Guaranteed Convergence and Distribution in Evolutionary Multiobjective Optimization via Achievement Scalarizing Function. Collection of Papers Prof. Kaisa Miettinen Prof. Kalyanmoy Deb Past Two conference publications Two journal articles in review Present One article by December 2010 Future One article by June

11 Thesis in a Nutshell

12 Thesis in a Nutshell

13 Thesis in a Nutshell Principle Background: Use MCDM techniques to speed up EMO algorithms without compromising on diversity.

14 Thesis in a Nutshell Principle Background: Use MCDM techniques to speed up EMO algorithms without compromising on diversity.

15 Thesis in a Nutshell Principle Background: Use MCDM techniques to speed up EMO algorithms without compromising on diversity. Contribution/Outcome: Hybrid EMO algorithm Enhanced convergence Good lateral diversity preservation Stopping criteria Wide applicability

16 Thesis in a Nutshell Principle Background: Use MCDM techniques to speed up EMO algorithms without compromising on diversity. Contribution/Outcome: Hybrid EMO algorithm Enhanced convergence Good lateral diversity preservation Stopping criteria Wide applicability

17 Thesis in a Nutshell Principle Background: Use MCDM techniques to speed up EMO algorithms without compromising on diversity. Hybrid Algorithm: Efficient operators Good diversity preservation Efficient local search procedure Contribution/Outcome: Hybrid EMO algorithm Enhanced convergence Good lateral diversity preservation Stopping criteria Wide applicability

18 Background

19 Background EMO Algorithm: Initialize population Fitness evaluations Recombination Mutation Selection Evolutionary Multi-objective Optimization (EMO) algorithms - widely used in multi-objective optimization. Numerous versions of different EMO algorithms have been proposed. Fewer research on operators for EMO algorithms. Single objective operators usually borrowed as such in multi-objective algorithms.

20 Background EMO Algorithm: Initialize population Fitness evaluations Recombination Mutation Selection Evolutionary Multi-objective Optimization (EMO) algorithms - widely used in multi-objective optimization. Numerous versions of different EMO algorithms have been proposed. Fewer research on operators for EMO algorithms. Single objective operators usually borrowed as such in multi-objective algorithms.

21 Background EMO algorithm - Differential Evolution Widely used algorithm in the field of single and multi-objective optimization. Simple, self-adapting mutation operator. Trial vector is generated by adding scaled random vector difference to a third vector. Exploits linear dependencies between decision variables. Real-life multi-objective problems may not necessarily have linear dependencies in decision variables.

22 Background EMO algorithm - Differential Evolution Widely used algorithm in the field of single and multi-objective optimization. y Simple, self-adapting mutation operator. Nonlinear Trial vector is generated by adding scaled random vector difference to a third vector. Linear Exploits linear dependencies between decision variables. x Real-life multi-objective problems may not necessarily have linear dependencies in decision variables.

23 Background EMO algorithm - Differential Evolution Widely used algorithm in the field of single and multi-objective optimization. Simple, self-adapting mutation operator. Trial vector is generated by adding scaled random vector difference to a third vector. Exploits linear dependencies between decision variables. Real-life multi-objective problems may not necessarily have linear dependencies in decision variables.

24 Polynomial Mutation Operator (POMO) Operator based on polynomials: P1,P2,P3 Chosen set of vectors C1 Trial vector from linear mutation C2 Trial vector from polynomial mutation Pareto set Decision space C1 x2 P1 Linear mutation C2 P2 P3 Original DE mutation operator: Polynomial mutation x1

25 Tests 5 True Pareto set t = 4.0 (POMO) EMO algorithm - GDE3 Test problems - OKA2 x3 0 Bi-objective, 3 variables x2 5 4 x1 Polynomial mutation 2 4 x3 5 0 True Pareto set F = 0.1 F = 0.2 F = 0.3 F = 0.4 F = 0.5 F = 0.6 F = 0.7 F = 0.8 F = 0.9 F = x x Linear mutation

26 Tests

27 Tests

28 Tests

29 Tests

30 Tests Linear mutation works better on problems with linear dependencies. Polynomial mutation handles problems with nonlinear dependencies better.

31 Conclusion & Future Work Conclusion Polynomial operator demonstrates the need for a better operator to handle non-linear variable dependencies. Future Work Choice of t-value requires further study. Hybrid algorithm of linear and non-linear mutation operators.

32 Colleagues Tomi Haanpää Sauli Ruuska

33

34 Thank you