1. Ana Wu aw81212n@pace.edu Daniel A. Sabol ds11298w@pace.edu
A Novel Approach for Library Materials Acquisition using Discrete Particle Swarm Optimization
Ana Wu
Daniel A. Sabol

2. Content Problem Solutions Experiments Library Materials Acquisition
Discrete Particle Swarm Optimization (DPSO)
Simulated Annealing (SA)
Multi-threading
Experiments

3. Problem Acquire materials for multiple departments n materials
material 1, material 2, material 3, … , material n
Each material has its own cost
Each material belongs to a specific category
m departments
dept. 1, dept. 2, dept. 3, … , dept. m
Each department owns a budget
Each department has a preference value for each material (ranges from 0 to 1)

4. Problem Simple example Materials Book A Book B Book C Book D Book E
Cost
$100
$45
$70
$60
$38
Category
Science
Art
Social
Dept.
Computer Science
Business
Art
Budget
$550
$880
$660
Preference
Book A
Book B
Book C
Book D
Book E
Computer Science
0.7
0.4
0.5
Business
0.3 1
Art
0.6
0.9

5. Problem
If one material is acquired by more than one department, the cost will be apportioned by these departments in proportion to their preference values.
Book A
$100
Preference
Book A
Computer Science
0.7
Business
0.3
Art
Cost
100 * (0.7 / ( )) = 70
100 * (0.3 / ( )) = 30

6. Problem Constrains Purpose Objectives
Budget constrain: the expense can't exceed its budget
Category constrain: the number of materials in each category has an upper bound and a lower bound
Purpose
Determine which materials should be acquired under the budget constrain and category constrains
Objectives
Maximize the average preference and the budget execution rate
Higer objective value means better solution
To meet the requirement for various departments

7. Problem Library Materials Acquisition
A generalized version of the knapsack problem
NP-Hard problem
For larger scale instances, no algorithm can produce optimal solution within reasonable amount of time
When n = 100, we need 1010 years for a supercomputer to run all the solutions
Only heuristics optimization algorithm can help find a better solution.
Heuristics
Cannot make sure the solution is the optimal solution
Simulated Annealing, Tabu Search, DPSO.

8. Weighted sum of the average preference.
Objective function.
Objective is to maximize the combination of average preference and the budget execution rate.
Weighted sum of the average preference.
Symbol
Description n
Number of materials m
Number of departments q
Number of categories
pij
Preference value of department j for material i ci
Cost of material i Bj
Budget of department j
CUK
Upper bound of the amount of materials in category k
CLK
Lower bound of the amount of materials in category k
bik
1 indicates material i belongs to category k; 0 otherwise
xij
1 indicates material i is acquired by department j; 0 otherwise zi
1 indicates material i is acquired by at least one department; 0 otherwise
aij
Actual cost of department j for material i
Budget Execution Rate
Actual Expenses of all department divided by the budget of all department.

9. Solution-DPSO Discrete Particle Swarm Optimization
Proposed by Kennedy (a social psycholoist) & Eberhart (an electrical engineer) in 1995
Inspired by the observation on behavior of flocking birds and schooling fish

10. Solution-DPSO Flocking birds
In foraging, birds flock together and arrange themselves in specific shapes by sharing their information about food sources
Each bird is associated with a position, a velocity, and a fitness value (how far away from the destination)
The movement of each bird will be influenced by the experiences of itself and the peers
itself: remember the best position it has found so far (pbest)
peers: know the best position that one member of the flock has found so far (gbest)

11. Solution-DPSO Discrete Particle Swarm Optimization (DPSO)
The idea is similar to bird flocks
Particle: a bird
Solution: position of bird
pbest: the best position (nearest) a bird has achieved so far
gbest: the global best position of all birds within the swarm
All particles move toward to its pbest and gbest

12. Solution-DPSO Process
1.Initialize position and velocity for each particle randomly;
2.Loop
For each particle, evaluate the fitness value. If get a better solution, update pbest;
For each particle, update its velocity by pbest and gbest;
newV = w*V + c1r1(pbest-P) + c2r2(gbest - P)
For each particle, update the position
newP = P + newV
3.End loop when a criterion is met, such as the maximum number of iterations

13. Solution-DPSO Drawback of DPSO Our Improvement Premature convergence
All particles converge to current best solution
Experiment:
In case with 50 materials, all particles converge at around 200th iterations
Our Improvement
Simulated Annealing (neighbor solution)
Every time it converges, we add SA
To enhance the exploration range

14. Solution-DPSO+SA Detailed steps
When convergence occurs, use current solution as the initial solution for SA
Do SA algorithm
After SA ends, assign the result to the position of the first particle
Rest the positions and velocities by randomly generating positions and velocities for other particles

16. Solution-DPSO+SA+Multithreading
To improve the performance
One thread -> one particle self execution
Threads:
Generate and update velocity and position
Evaluate the fitness value
Calculate possibility
Send solution to main process

17. Solution-DPSO+SA+Multithreading
Main process:
Check whether the whole algorithm is converged
Run SA and dispatch particles when converged
Broadcast current best solution
Control the iterations

18. Experiments Setups Cases Intel Core i7-4810MQ 2.80GHz CPU and 16G RAM
50 particles, cognition learning rate: 2.0, social learning rate: 2.0, max velocity: 6.0
Cases
Case I
20 materials, 3 departments, 3 categories
Case II
50 materials, 3 departments, 3 categories
Case III
100 materials, 10 departments, 10 categories

19. Experiments
The comparison of DPSO and DPSO+SA

20. Experiments
The performance of DPSO+SA in single and multiple thread

21. Experiments
The execution time of DPSO+SA in single and multiple thread

22. Thank you!