1. A cooperative parallel tabu search algorithm for the quadratic assignment problem Ya-Tzu, Chiang

2. Introduction Quadratic Assignment Problem (QAP) is a combinatorial optimization problem. The problem consists of assigning n facilities to n locations with the objective of minimizing the costs. The QAP can be formulated as a permutation problem as follows: A permutation s can be illustrated as :

3. Introduction The exact solution for even small problems (20<n<30) is considered computationally nontrivial. To obtain optimal solutions for modest size (30<n<40) QAP instances a massively parallel computing environment is required.

4. References review Many sequential metaheuristic approaches have been applied to the QAP. TSTaillard(1991), Misevicius(2005) GA/TSMisevicius(2003, 2004), Drezner(2003, 2005) ACOStutzle and Dorigo(1999), Gambardella, Taillard and Dorigo(1997) Path-relinkingJames, arego and Glover(2005) GRASPLi, Pardalos and Resende(1994)

5. Introduction QAP make the application of parallel computing to this problem incredibly attractive. The current study proposes a cooperative parallel tabu search for the QAP that provide exceptional results for 41 QAPLIB test instances in reasonable computational times.

6. Parallel Metaheuristics for the QAP Crainic and Toulouse(2003) group strategies for parallel heuristic methods into three categories. Type1 : a low-level parallelization strategy Type2 : Decomposition Type3 : multi-heuristic

7. Type1 : a low-level parallelization strategy A master process is responsible for controlling the assignment of work to each processor and collection the results. Taillard(1991), Chakrapani and Skorin- Kapov(1993), James, Rego and Glover(2005),

8. Type2 : Decomposition Decomposition strategies consist of the division of the decision variables among processors. TSP : Felten, Karlin and Otto(1985), Fiechter(1994)

9. Type3 : multi-heuristic The model comprises two variants of parallel designs: independent search strategies and cooperative multi-thread strategies. Taillard(1991), Pardalos, Pitsoulis and Resende(1995), Battiti and Tecchiolli(1992), Talbi, Hafidi and Geib(1997) The algorithm proposed in the current study is a cooperative multi-thread (Type 3 ) tabu search algorithm.

10. Cooperative Parallel Tabu Search for the QAP The CPTS algorithm developed in the current study consists of the parallel execution of several TS operators on multiple processors. Each processor change the stopping criterion and the tabu tenure parameters. The TS operators share search information by means of a global memory which holds a reference set of solutions.

11. Cooperative Parallel Tabu Search for the QAP (Con.) The main feature of the CPTS is to take advantage of parallel computing in the implementation of adaptive memory. Short term memory Longer term memory

12. Cooperative Parallel Tabu Search Pseudocode (initializing the reference set) The algorithm considers as many reference set solutions as the number of the processors available.

14. The Tabu Search The classical two-exchange (swap) neighborhood is employed.

15. The Diversification Operator

16. Reference Set Management The reference set define a global memory used by CPTS to manage and allow the exchange of search information between the processors. Reference set : 1. reference set index 2. one permutation 3. objective function value 4. update flag

17. Reference Set Management Reference set management in the initialization. Reference set management in the cooperative parallel search. -- Only one processor at a time may update the reference set.

18. Platform Design Considerations — Memory Management and Algorithm Design Considerations In CPTS, there are three types of memory stores that need to be handled. First data type -- only read by the processors. Second data type -- local variables (private to each processor) Third data type -- the shared reference set

19. Parallel Search Synchronous Parallel Search -- In the initialization phase, each processor runs a tabu search algorithm concurrently. The synchronization is accomplished by performing the initialization phase. Asynchronous Parallel Search -- The critical sections do not enforce any type of synchronization in the cooperative parallel search. The execution time of the TS operator running on any processor is variable.

20. Load Balancing Considerations Not enforcing synchronous access to the reference set was done purposefully. This helps maximize the processors utilization since all processors can be busy except when waiting to update the reference set. Good solutions enter the reference set more slowly. (controlling the maximum failure parameter)

21. Load Balancing Considerations Static scheduling -- If some processors run longer than others, static scheduling will cause the wall clock time to increase. Dynamic scheduling -- Apply in the cooperative parallel search so that each processor was assigned smaller chunks of work.

22. Scalability CPTS is scalable in two ways if more processors are available. The number of iterations of the cooperative parallel search could be increased. The maximum failure parameter could be increased.

23. Computational Analysis of the CPTS Algorithm

24. Computational Analysis of the CPTS Algorithm (con.)

25. Comparative Analysis with Alternative Sequential and Parallel Algorithms

29. Conclusions A CPTS for the QAP provides exceedingly high quality results for a large set of benchmark instances from QAPLIB. Outcomes can be enhanced in settings where additional processors are available or improved by incorporating more sophisticated adaptive memory components.