1. Ant Colony Optimization to Resource Allocation Problems Peng-Yeng Yin and Ching-Yu Wang Department of Information Management National Chi Nan University

2. Resource Allocation Problems (RAP) What is single-objective “RAP”? minimize subject to 0 ≦ a i ≦ x i ≦ b i ≦ Q i=1, 2…T

3. Existing Methods to solve RAP Mathematical Programming Dynamic programming, linear programming Hybrid method: Fuzzy dynamic programming Providing exact solutions but could be extremely time-consuming for solving large- scaled problems Meta-heuristics : eg. GA Providing approximate solutions in reasonable time

4. Our Objective Single-objective RAP Using customized ant colony optimization with constructive heuristic

5. The ACO Algorithm

6. Our ACO for solving RAP The ant allocates the resources by constructing a tour from start to sink … … … …

7. Constructive Heuristic A heuristic for constructing feasible tours check whether the feasible solutions exist or not When ( ) or ( ), there is no feasible solutions

8. Constructive Heuristic Dynamically recompute the new lower- bound & upper-bound for allocating resources to the next factory –Guarantee a feasible solution is eventually constructed –Compress the searching space –Decrease the computational time

9. Constructive Heuristic suppose that an artificial ant has allocated resources to the first i factories, the allowable resource quantity range [ ] to be allocated to factory i+1 is leaveQ is the remaining resource quantity after having allocating resources to the first i factories

10. Our ACO for solving RAP State Transition rule Assume that the ant has allocating j resources to factory i, the probability for allocating k resources to factory i+1 is defined as Pheromone τ ijk Visibility … … … …

11. Our ACO for solving RAP pheromone updating rule :

12. Experimental result Existing GA approach Coding Handling of infeasible solution Disadvantages  Initial population is hard to generate  Likely produce infeasible solutions  Infeasibility-handling is time-consuming

13. Experimental result mini

14. Convergence analysis Global best solution observed so-far vs. number of ACO iterations

15. Convergence analysis Branch Entropy Assume that the ant has allocating j resources to factory i, the branch entropy for allocating resources to factory i+1 is defined as The smaller the entropy value is, the higher the probability with which the ant will move to a specific unit of resource for allocation, that is to say the ACO algorithm is bound to converge

16. Convergence analysis Branch Entropy vs. number of ACO iterations

17. Conclusion A constructive heuristic for guaranteeing feasible solutions A customized ACO is devised such that the performance is significantly better than other meta-heuristics like GA