1. Handling Constraints 報告者 : 王敬育

2. Many researchers investigated Gas based on floating point representation but the optimization problems they considered were defined on a search space: i.e., each variable X k was restricted to a given interval The domain D is defined by ranges of variables for a given

3. Example: p123

4. We consider a particular class of optimization problems which are defined on a convex domain; these can be formulated as follows: Optimize a function f(X 1,X 2 …X q ), subject to the following sets of linear constraints:

5. The developed system (GENOCOP for GEenetic algorithm for Numerical Optimization for COnstrained Problems) It combines some of the ideas seen in the previous approaches, but in a totally new context. The main idea behind this approach lies in: (1)An elimination of the equalities present in the set of constraints (2) Careful design of special genetic operators, which guarantee to keep all chromosomes within the constrained solution space.

9. Operators We describe six genetic operators based on floating point representation, which were used in modified version of the GENOCOP system. The first three are unary operators. The other three are binary.

10. Boundary mutation This operator requires also a single parent X and produces a single offspring X’. The operator is a variation of the uniform mutation with where being either left(k) or right(k), each with equal probability.

11. Non-uniform mutation

12. Arithmetical crossover

13. 1

15. Testing GENOCOP See p130 ~ p133 following parameters for all experiments: pop_sizes = 70 k = 28(number of parents in each generation ; classification step) b = 2(coefficient for non-uniform mutation)

22. Denote the GENOCOP II system as the method #4

24. GENOCOP III This method incorporates the original GENOCOP system, but also extends it by maintaining two separate populations. The first population P s consists of so-called search points which satisfy linear constraints of the problem. The second population P r consists of so-called reference points; these points are fully feasible, they satisfy all constraints.