Download e-book for iPad: Sequential Approximate Multiobjective Optimization Using by Hirotaka Nakayama

Download e-book for iPad: Sequential Approximate Multiobjective Optimization Using by Hirotaka Nakayama

By Hirotaka Nakayama

This publication highlights a brand new course of multiobjective optimzation, which hasn't ever been taken care of in earlier guides. whilst the functionality kind of aim services isn't really recognized explicitly as encountered in lots of functional difficulties, sequential approximate optimization in accordance with metamodels is a good device from a realistic perspective. numerous refined tools for sequential approximate multiobjective optimization utilizing computational intelligence are brought besides genuine purposes, generally engineering difficulties, during this ebook.

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Specification of bond lj Lk xj uj , j = 1, . . , n1 Xk Uk , k = 1, . . , n2 For this kind of problem, the satisficing trade-off method can be effectively applied. Then we have to solve a linear fractional min–max problem. In the following section, we shall give a brief review of the method for solving it. An Algorithm for Linear Fractional Min–Max Problems Let each objective function in our bond trading problem be of the form Fi (x) = pi (x)/qi (x), i = 1, . . , r where pi and qi are linear in x.

In the satisficing trade-off method, the objective function with target such as f1 → f 1 is usually treated as two objective functions, f1 → max and f1 → min. Under this circumstance, suppose that for f1 → max we set the ideal value f1∗ = f 1 , the nadir value f1∗ = f 1 − ε and the aspiration level f 1 − ε, and for f1 → min we set the ideal value f1∗ = f 1 , the nadir value f1∗ = f 1 + ε and the aspiration level f 1 + ε. Then the treatment of f1 is the same between the above formulation and the satisficing trade-off method.

1) From the above, it can be known that all nondominated (Pareto optimal) individuals are assigned the rank = 1. The ranking method based on the Pareto optimality among individuals has a merit to be computationally simple. Originally, the concept of rank was introduced by Goldberg [49]. In the ranking method of Goldberg, all nondominated individuals are assigned the rank = 1 first. Then the individuals with rank = 1 are removed from the population. All nondominated individuals in the remained individuals are assigned 1 In this book, the fitness evaluation based on the Pareto optimality or Pareto ordering is called the ranking method or rank-based method.

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