1. Resource Allocation Problem Reporter: Wang Ching Yu Date: 2005/04/07

2. Resource Allocation Problem Single Objective RAP

3. Methods to Single objective RAP Traditional methods –Dynamic Programming –Branch & Bound Meta-heuristics –GA

4. Methods to Single objective RAP Existing GA approach Coding Handling of infeasible solution Disadvantages  Initial population is hard to generate  Likely produce infeasible solutions  Infeasibility-handling is time-consuming

5. Resource Allocation Problem Multi Objective RAP

6. Multi objective RAP Has n objectives, n≥2, these objectives are always “conflict” Usually has more than one solution, in this solution set, none solution could be better than any others in all objectives, this solution set is called “Pareto-optimal solution”

7. Multi objective RAP There are two difficulties in searching solutions: –There are many objective function n, the searching space is huge and complicated –How to design a efficient algorithm to find the Pareto-optimal solution

8. Multi objective RAP In traditional, the way to solve the above difficulties is: –Simplify the problem EP (Expected Priority) approach in AHP –Heuristics

9. Multi objective RAP Optimization methods –Simulated Annealing –Tabu Search –Genetic algorithm –Random search

10. Multi objective RAP –The Complex method

11. Pareto Optimal If there are two solutions (a, b), the multi- objective RAP want to maximize n objectives, if we say a dominate b ( ) and a is a non- dominated solution.

12. Pareto Optimal In traditional, according to the evaluation of fitness function, there are two mechanism: Pareto-based: –Goldberg: non-dominated sorting to rank a search population according to Pareto optimality.

13. Pareto Optimal

14. –Foseca and Fleming: each individual is ranked according to their degree of dominance

15. Pareto Optimal Zitzler and Thiele: SPEA (Strengthen Pareto Evolutionary Algorithm) –Use tow populations, P and P ’ –The fitness of the members of P ’ is calculated as a function of how many individuals in P they dominate

16. Pareto Optimal ● : P ×: P’

17. Pareto Optimal Non-Pareto based: –weighted-sum EP (Expected Priority) approach in AHP Disadvantage 1.how to design the weighted-sum? 2.subjective solutions