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CHAPTER 2 MOP Evolutionary Algorithm Approaches Cont.

Development of Multiobjective GAs:The 1st generation: Vector Evaluation approachVector Evaluated Genetic Algorithm (VEGA: Schaffer, 1985)J. D. Schaffer:

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CHAPTER 2 MOP Evolutionary Algorithm Approaches Cont.

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    2. Development of Multiobjective GAs: The 1st generation: Vector Evaluation approach Vector Evaluated Genetic Algorithm (VEGA: Schaffer, 1985) J. D. Schaffer: “Multiple objective optimization with vector evaluated genetic algorithms”, Proc. of 1st Inter. Conf. on GAs and Their Applic., pp.93-100, 1985. The 2nd generation: Pareto ranking + Diversity Multiobjective Genetic Algorithm (MOGA: Fonseca & Fleming, 1993) Fonseca, C. M. & Fleming, P. J: “Genetic algorithms for multiobjective optimization: formulation, discussion and generalization”, Proc. of the 5th Inter. Conf. on GAs, pp. 416-423, 1993. Non-dominated Sorting Genetic Algorithm (NSGA: K. Deb, 1995) Srinivas, N. & Deb, K.: “Multiobjective function optimization using nondominated sorting genetic algorithms”, Evolutionary Computation, vol. 3, pp. 221-248, 1995.

    3. The 3rd generation: Weighted Sum + Elitist Preserve Random-weight Approach (RWA: Ishibuchi et al., 1998) Ishibuchi, H & T. Murata: “A multiobjective genetic local search algorithm and its application to flowshop scheduling”, IEEE Trans. on Sys., Man & Cyber., vol. 28, no. 3, pp. 392-403, 1998. Strength Pareto Evolutionary Algorithm (SPEA: E. Zitzler et al., 1999) E. Zitzler & L. Thiele: “Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach”, IEEE Trans. on Evolutionary Comput., vol.3, no.4, pp.257-271, 1999. Adaptive Weight Approach (AWA: Gen & Cheng, 2000) Gen M,. & Cheng, R. : Genetic Algorithms and Engineering Optimization, John Wiley & Sons, New York, 2000. Non-dominated Sorting Genetic Algorithm ? (NSGAII K. Deb, 2002) Deb, K., A. Pratap, S. Agarwal & T. Meyarivan: “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II.” IEEE Trans. on Evolutionary Comput., vol. 6, no. 2, pp.182-197, 2002

    4. Vector evaluation approach Vector Evaluated Genetic Algorithms (VEGA: Schaffer, 1985) VEGA is the first notable work to solve MOP problems in which it uses a vector fitness measure to create the next generation. The selection step in each generation becomes a loop. Each time through the loop the appropriate fraction of the next generation, or subpopulation, is selected on the basis of each objective. The entire population is shuffled thoroughly to apply crossover and mutation operators. This is performed to achieve the mating of individuals of different subpopulations.

    5. Divide population into M equal blocks for M objectives at every generation Each block is reproduced with one objective function Complete population participates in crossover and mutation Proportionate selection operator is used In order to reduce the positional bias in the population, it is better to shuffle the population before it is partitioned.

    8. Pareto Ranking Approach Pareto Ranking Approach Pareto ranking approach consists of assigning rank 1 to nondominated chromosomes and removing them from contention, then finding the nondominated chromosomes among the remaining ones, rank 2; and so on. This approach assigns all nondominated solutions in identical fitness value in order to give them an equal probability of reproduction. A Pareto ranking-based fitness assignment method was first suggested by Goldberg. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.

    10. Multiobjective Genetic Algorithm (MOGA: Fonseca & Fleming, 1993) The method proceeds by sorting the population according to the ranks, and ties may be broken by random choice.

    15. Non-dominated Sorting Genetic Algorithm (NSGA: K. Deb, 1995) The population is ranked based on Goldberg’s Pareto ranking method. A stochastic remainder proportionate selection is used to reproduce a new generation. Brindle, A.: Genetic algorithms for function optimization, Ph.D. dissertation, Univ. of Alberta-Edmondton, 1981.

    25. Random-weighted Approach (RWA: Murata et al., 1998) Murata, Ishibuchi & Tanaka (1998) proposed a Random-Weight Approach (RWA) to obtaining a variable search direction toward the Pareto frontier. Gen, M. & R. Cheng: Genetic Algorithms and Engineering Optimization, John Wiley & Sons, New York, 2000. Ishibuchi, H., T. Yoshida and T. Murata: “Balance Between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling”, IEEE Trans. on Evolutionary Comput., vol.7, no.2, pp.204-223, 2003. Fixed-weight approach gives the GAs a tendency to sample the area toward a fixed point in the criterion space. Random-weight approach gives the GAs a tendency to demonstrate a variable search direction, therefore, the ability to sample the area uniformly over the entire frontier. Weighted-sum Approach

    26. Weighted-sum Approach

    27. For a problem to maximize q objective functions, weighted-sum objective is given as the follows: Random-weight wk is calculated by the following equation: where rj are non-negative random number between [0, 1]. Before selecting a pair of parents for crossover operation, a new set of random weights is specified. The selection probability pi for individual i is then defined by the following linear scaling function: where zmin is the worst fitness value in the current population.

    29. Strength Pareto Evolutionary Algorithm (SPEA: E. Zitzler et al., 1999) E. Zitzler & L. Thiele (1999) proposed a new evolutionary approach to multicriteria optimization, the Strength Pareto Evolutionary Algorithm (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. E. Zitzler & L. Thiele: “Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach”, IEEE Trans. on Evolutionary Comput., vol.3, no.4, pp.257-271, 1999. It is characterized by: Storing nondominated solutions externally in a second, continuously updated population. Evaluating an individual’s fitness dependent on the number of external nondominated points that dominate it. Preserving population diversity using the Pareto dominance relationship. Incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. Elitist Preserve Approach

    30. SPEA (E. Zitzler et al., 1999) The fitness assignment procedure is a two-stage process. First, the individuals in the external nondominated set P' are ranked. where si is proportional to the number of population members j?P for which i ? j. n is the number of individuals in P that are covered by i and N is the size of P.

    31. Afterwards, the individuals in the population P are evaluated. where the fitness of an individual j?P is calculated by summing the strengths of all external nondominated solutions i?P’ that cover j. Elitist Preserve Approach

    41. A: Non-dominated sorting

    42. A: Non-dominated sorting

    43. B: Crowding distance sorting

    44. B: Crowding distance sorting

    46. B: Crowding distance sorting

    50. Pseudo Code NPGA

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