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Enhancing Genetic Algorithms with Network Crossover for Efficient Problem Solving

This paper presents a detailed analysis of the network crossover operator, highlighting its benefits in solving challenging problems efficiently. By incorporating user-specified network structures, the network crossover offers a competitive advantage over traditional operators like uniform crossover. The method reduces model-building costs compared to Estimation of Distribution Algorithms (EDAs) and demonstrates improved performance over Simple Genetic Algorithms (SGAs). The text discusses the importance of prior knowledge and clear problem information matrix in implementing network crossover, along with practical algorithms and test problems for validation. Additionally, it explores the use of Probability Coincidence Matrix (PCM) in optimizing probabilistic models for enhanced problem-solving capabilities.

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Enhancing Genetic Algorithms with Network Crossover for Efficient Problem Solving

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  1. Network Crossover on GAs 2011.05.09 Tsung-Yu Ho present

  2. Reference Paper • ‘’Network Crossover Performance on NK Landscapes and Deceptive Problems’’ • GECCO, 2010 • Mark Hauschild and Martin Pelikan

  3. Motivation • GAs with uniform crossover • Break up too much linkages for tight linkage problems. • Need a problem-specified crossover operator • EDAs • Highly cost on model building • Specify the crossover operator according to model building

  4. Goal • GAs with network crossover • Can solve hard problems than SGA • Reduce the model-building cost than EDAs • A general crossover-form without specification for problems.

  5. Goal • GAs with network crossover • Can solve hard problems than SGA • Reduce the model-building cost than EDAs • A general crossover-form without specification for problems. Is it possible ?

  6. Methodology Prior knowledge Clear Problem Information Matrix GAs Network Crossover The advantages as last slide mentions

  7. Goal & Test Problems • Test Algorthms • GAs with network crossover • ... uniform crossover • ... 2-points crossover • hBOA (outperform ?) • Test problems • Trap-5 • NK Landscapes (overlapping problem)

  8. Some Question about this paper • Page1,’’... This paper discusses a network crossover operator that works with a user-specified network graph to determine which bits are exchanged. In addition, due to not requiring a costly model building phase, it might be able to outpeform EDAs.’’ • Page2.’’...For those problems without an implict graph, it is possible to run an EDA on trial instances of the problems to learn a network structure. ’’

  9. Network Crossover • Network crossover operator needs prior knowledge of structure information. • Graph for network crossover • Node (gene) , Edge(gen’s linkage) • Need an N x N matrix to record the relation • How to get this structure information? • Clear graph definition (edge between nodes) • Without an implicit graph problems • Run EDAs to get this graph.

  10. Information Matrix • An N x N matrix G is given • For reducing information, only spedify the strongestconnection • Do not require the strength of each interaction • Only 0 or 1 in each entry • How to decide the strongest connection (G)? • Papers ‘’Using previous models to bias structural Learning in the hierarchical BOA’’, M. Hauschild, M. Pelikan, K. Sastry, and D. E. Goldberg, GECCO’2008.

  11. Network Crossover Algorithm • Pick up n/2 mask for crossover in length n • Randomly choose one bit as start point. • From start point, use breadth first search to add the point

  12. Network Crossover Algorithm

  13. Network Crossover Algorithm 0 0 0 0 0 0 0 0 3 0 0 1 0 0 0 0 0 6 3 0 1 1 0 0 1 0 0 2 0 1 1 0 0 1 1 0 6 3 7 2

  14. Network Crossover Algorithm

  15. Test Problems • 5-bit trap problem • NK Landscapes problem • Unrestriced NK landscapes. • Nearest neighbor NK landscapes.

  16. NK Landscapes • NK Landscapes problem • Unrestriced NK landscapes. • Nearest neighbor NK landscapes. : Number of neighbors per bit : the set of neighbors for bit

  17. NK Landscapes • Unrestriced NK landscapes • Each position i, choose a random set of k neighbors with equality probability • A lookup table defining fi from the uniforn distribution over [0,1) • k = 5, in this test

  18. NK Landscapes • Nearest neighbor NK landscapes • Bits are arange as a circle • k bits follow the i th bit K = 3 step = 1 step = k

  19. Test Problems • 5-bit trap problem (k = 5) • NK Landscapes problem • Unrestriced NK landscapes (k = 5) • Nearest neighbor NK landscapes (k = 5, step = 1) • Nearest neighbor NK landscapes (k = 5, step = 5) • RTR & elitism to compare

  20. Deterministic Hill Climber • Deterministic Hill Climber • Take a candidate solution • Performs one-bit changes on this solution that lead to maxmum improvement • Terminated until no improvement.

  21. Result

  22. Result

  23. Result

  24. Information Matrix • Papers ‘’Using previous models to bias structural Learning in the hierarchical BOA’’, M. Hauschild, M. Pelikan, K. Sastry, and D. E. Goldberg, GECCO’2008. • Generally speaking,if the structure information are not fully correct, it may lead to being unable sovle problem. • The paper give the strongest connection matrix, for network crossover.

  25. Probability Coincidence Matrix • Probability Coincidence Matrix (PCM) • For each pair (i,j), the value of Pi,j means the proportion of of probabilistic models in which ith and jth string position are connected. • Incremete the count by 1, if each models has a connection on i and j. • P = 0.25 • 25% of the available probabilistic models contains a connection between i and j. • Use the threshold Pmin to divide value into 1 or 0.

  26. Summary for PCM • EDAs provides a series of probabilistic models that hold a great deal of information about problems. • We can use these available probabilistic modelsas prior information to speed up model building on EDAs • The prior information can help network crossover.

  27. Conclusion • GAs with network crossover to solve overlapping problem without model building like EDAs • A general form, that do not be modified for specified problems. • The most big problems is ‘’How to get the strongest information matrix’’.

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