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## Network Crossover on GAs

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**Network Crossover on GAs**2011.05.09 Tsung-Yu Ho present**Reference Paper**• ‘’Network Crossover Performance on NK Landscapes and Deceptive Problems’’ • GECCO, 2010 • Mark Hauschild and Martin Pelikan**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**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.**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 ?**Methodology**Prior knowledge Clear Problem Information Matrix GAs Network Crossover The advantages as last slide mentions**Goal & Test Problems**• Test Algorthms • GAs with network crossover • ... uniform crossover • ... 2-points crossover • hBOA (outperform ?) • Test problems • Trap-5 • NK Landscapes (overlapping problem)**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. ’’**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.**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.**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**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**Test Problems**• 5-bit trap problem • NK Landscapes problem • Unrestriced NK landscapes. • Nearest neighbor NK landscapes.**NK Landscapes**• NK Landscapes problem • Unrestriced NK landscapes. • Nearest neighbor NK landscapes. : Number of neighbors per bit : the set of neighbors for bit**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**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**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**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.**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.**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.**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.**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’’.