optimization of combinatorial problemswith parallel hybrid evolutionary algorithms

Tansel Dökeroğlu, Ph.D.July, 2015

• Problem definition

• Metahueristics

• Genetic Algorithms and Tabu Search

• Parallel Algorithms and Message Passing Interface

• Proposed Parallel Hybrid Algorithm

• Experimental Setup and Results

• Conclusion and Future Work

Content

Combinatorial optimization is an area of research at the intersection of computer science, applied mathematics, and operations research.

The most widely studied problems of this area are:

• The Traveling Salesman• Bin Packing • Data Allocation• The Facility Layout Problem• Quadratic Assignment Problem

Problem Definition

This assignment can be written as a permutation such that p={2,1,4,3}.

The exact solution of the QAP problem for size 35 is peformed with hundreds of processors by working for months.

Large QAP instances are still optimally unsolvable.

1 2

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Factory 1Factory 2

Factory 3

Factory 4

The Quadratic Assignment Problem (QAP)

Formal Definition of the QAP

NP-Hard problems and metaheuristics

Genetic Algorithms

Generations(iterations)

Crossover and Mutation Operators

Generations :

10

• A neighborhood is constructed to identify adjacent solutions that can be reached from current solution.

• Classifies a subset of the moves as forbidden (or tabu).

• The classification depends on the history of the search, and particularly on the frequency that certain move or solution components, called attributes, have participated in generating past solutions.

• With an attractive evaluation where it would result in a solution better than any visited so far, its tabu classification may be overridden, aspiration criterion.

Tabu Search Algorithm

11

Parameters of Tabu Search

• Neighborhood structure• Local search procedure• Aspiration conditions• Form of tabu moves• Addition of a tabu move• Maximum size of tabu list• Number of failures

Why do we need parallel programs?(from the perspective of Moore’s law)

the # of transistors in an integrated circuit has doubled every two years

Message Passing Interface

Message Passing Interface (MPI) is a standard and portable message-passing system designed to function on a wide variety of parallel computers.

There are several well-tested and efficient implementations of MPI which are portable and scalable for large-scale parallel applications.

The standard defines the syntax and semantics of a core of library routines useful to a wide range of users writing portable message-passing programs in different computer programming languages such as Fortran, C, C++ and Java.

The communication topology of the proposed algorithm

Proposed Algorithm

Genetic Algorithm Phase(at each slave processor)

Robust Tabu Engine(at each slave processor)

Master Nodemigrate individuals

population

best individual

Global best

Experimental Setup and Performance Evaluation

QAP Benchmark Instanceshttp://www.opt.math.tu-graz.ac.at/qaplib/inst.html

There exist problem instances having size 12 ≤ n ≤ 256136 problem instances and 111 solutions

46 nodes, each with two CPUs, giving 92 CPUs.

Intel Xeon 5110 Dual-Core CPU (1.60 GHz, 4 MB L2 Cache, 1066 MHz FSB)

Each CPU has four cores gıvıng a total number of 368 processors.

Each node has 16 GB of RAM giving 736 GB of total memory

high-bandwidth communication among the HPC nodes, Gigabit Ethernet Switches, and Infiniband switch.

Setting parameters for # of individuals and generations

in order to prevent stagnation to local optima

Parameters settings for Tabu Search Algorithm Phase

For small problem instances, the small parameter settings are used,while the larger parameter settings are used for harder/larger problems

improvement of the solution quality of as the number of generations, populations, and processors are increased

Comparing the results with the state-of-the-art parallel algorithms

Conclusion

• A robust algorithm is developed with 0.049 % error deviation for hard/large problem instances of the QAP.

• A wider fitness landscape analysis is enabled with parallel computation for the QAP.

• Execution time of the proposed algorithm is reasonable (it can find (near-) optimal solutions in minutes rather than days or months).

• The proposed algorithm is reported to be among the best performing ones in the literature.

• The hybridization of metaheuristics is proved to be an efficient approach for the solution of the QAP.

Future work

• Enhancing with machine learning techniques such as reinforcement learning.

• Hyper-heuristics that execute several heuristics on the problem will be implemented .

• Migrating the existing code to CUDA platform. A more cost-effective way of solution.

CUDA is a parallel computing platform and programming model that enables dramatic increases in computing performance by harnessing the power of the graphics processing unit (GPU).

GeForce GTX 760: A Mid-Range GPU with 1152 CUDA cores

Journal papers• Dokeroglu T., (2015) Hybrid teaching-learning-based optimization algorithms for the Quadratic

Assignment Problem, Computers and Industrial Engineering. 85 (2015): 86-101.

• Dokeroglu T., Bayir M.A., Coşar A., (2015) Robust algorithms for exploiting the common tasks of relational cloud databases, Applied Soft Computing, Vol 30 : 72-82.

• Dokeroglu, Tansel, and Ahmet Cosar. (2014) Optimization of one-dimensional Bin Packing Problem with island parallel grouping genetic algorithms. Computers & Industrial Engineering 75 (2014): 176-186.

• Dokeroglu, T., Sert, S.A., and Cinar, M.S. (2014) Evolutionary multiobjective query workload optimization of Cloud data warehouses, The Scientific World Journal.

• Tosun, U., Dokeroglu, T., & Cosar, A. (2013). A robust island parallel genetic algorithm for the quadratic assignment problem. International Journal of Production Research, 51(14), 4117-4133.

• Dokeroglu, T., Ozal, S., Bayir, M. A., Cinar, M. S., & Cosar, A. (2014). Improving the performance of Hadoop Hive by sharing scan and computation tasks. Journal of Cloud Computing, 3(1), 1-11.

• Dokeroglu, T., Cosar, A. (2014), "Integer Linear Programming Solution Model for the Multiple Query Optimization Problem" ISCIS October 27-28th, 2014, Krakow, Poland.

• Dokeroglu, T., Sert, S.A., Cinar, M.S., and Cosar, A. (2014). Designing Cloud Data Warehouses using Multiobjective Evolutionary Algorithms, ACM International Conference on Agents and Artificial Intelligence (ICAART) Eseo, Angers, Loire Valley, France.

• Dokeroglu, T. (supervised by Ahmet Cosar) (2012). Parallel Genetic Algorithms for the Optimization of Multi-Way Chain Join Queries of Distributed Databases 38th VLDB Ph.D. Workshop, August 27-31, Istanbul/TURKEY.

• Dokeroglu, T., Tosun, U., and Cosar, A. (2012). Particle Swarm Intelligence as a Novel Heuristic for the Optimization of Distributed Database Queries, The 6th International Conference on Application of Information and Communication Technologies AICT2012 Georgia, Tbilisi, 17-19 .

• Dokeroglu, T and Cosar, A. (2011). Dynamic Programming with Ant Colony Optimization Metaheuristic for The Optimization of Distributed Database Queries, Proceedings of the 26th ISCIS, London, UK.

• Dokeroglu,T., Tosun, U., and Cosar, A. (2013). Evaluating the Performance of Recombination Operators with Island Parallel Genetic Algorithms, International Federation of Automatic Control (IFAC), Saint Petersburg, Russia.

• Dokeroglu, T. Tosun, U., and Cosar, A. (2012). Parallel Optimization with Mutation Operator for the Quadratic Assignment Problem Proceedings of WIVACE, Italian Workshop on Artificial Life and Evolutionary Computation, Parma/Italy.

Proceeding papers

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