optimization of combinatorial problems with parallel hybrid evolutionary algorithms tansel...
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optimization of combinatorial problemswith parallel hybrid evolutionary algorithms
Tansel Dökeroğlu, Ph.D.July, 2015
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• 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
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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
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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
3
4
Factory 1Factory 2
Factory 3
Factory 4
The Quadratic Assignment Problem (QAP)
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Formal Definition of the QAP
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NP-Hard problems and metaheuristics
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Genetic Algorithms
Generations(iterations)
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Crossover and Mutation Operators
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Generations :
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• 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
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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
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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
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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.
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The communication topology of the proposed algorithm
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Proposed Algorithm
Genetic Algorithm Phase(at each slave processor)
Robust Tabu Engine(at each slave processor)
Master Nodemigrate individuals
population
best individual
Global best
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Experimental Setup and Performance Evaluation
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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
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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.
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Setting parameters for # of individuals and generations
in order to prevent stagnation to local optima
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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
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improvement of the solution quality of as the number of generations, populations, and processors are increased
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Comparing the results with the state-of-the-art parallel algorithms
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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.
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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
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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.
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• 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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Thank You
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