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Extra info for A bad network problem for the simplex method and other minimum cost flow algorithms

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The process of generating new solutions and updating the probability vector is repeated until some termination criteria are met; for instance, the run can be terminated if all probability-vector entries are close to either 0 or 1. 02, the first iteration of PBIL could proceed as follows. 5) are 10010, 11010, 00101, and 10111. The last solution has the highest fitness and is used to update the probability vector. 51). PBIL was also referred to as the hill climbing with learning (HCwL) [95] and the incremental univariate marginal distribution algorithm (IUMDA) [113].

5 with the building-block partitions specified by the MPM. To decide between alternative MPMs, ECGA uses a variant of the minimum description length (MDL) metric [149, 150, 151], which favors models that allow higher compression of data (in this case, the selected set of promising solutions). More specifically, the Bayesian information criterion (BIC) [164] is used. To find a good model, ECGA uses a greedy algorithm that starts with each variable forming one partition (like in probabilistic uniform crossover).

To visualize the model used in PIPE, see Fig. 10. The model is updated by adapting the probabilities based on the population of selected solutions. 1 x x x Fig. 10. This figure shows an example probabilistic model of a program with no interactions covered used in PIPE and a candidate solution (mathematic expression) generated by the model. Each node in the model stores the probabilities of functions and terminal symbols. The sampling proceeds recursively in a top-down fashion. If a terminal is generated in a node, the generation along this branch is terminated.

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A bad network problem for the simplex method and other minimum cost flow algorithms by Zadeh N.


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