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By Christophe Dabancourt

Apprendre à programmer : Algorithmes et perception objet

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Maximum difference is about 4%) is smaller than any other algorithm. In case of 30 nodes, for instance, the proposed GA is faster than Inagaki’s GA and Munetomo’s GA with prob. 2. Performance comparison on the rate of convergence. 0 15 20 25 30 35 40 45 50 Number of nodes Fig. 9. Computation time between Dijkstra’s and the proposed algorithms. 87 and prob. 92 times), respectively. 2. , 80% route optimality) in about 122 fitness function evaluations. The convergence speed of the proposed GA is superior to that of Inagaki’s GA and Munetomo’s GA with prob.

2). Consequently, random initialization is effected so that initial population is generated with the encoding method already explained in Sect. 1. , nodes) 28 3 Real-World Application: Routing Problem from the topological information database in a random manner during the encoding process. It is possible that the algorithm encounters a node for which all of whose neighboring nodes have already been visited. In this case, the defective chromosome is refreshed and reinitialized. This may induce a subtle bias in which some partial paths are more likely to be generated.

It can be defined as follows: Iij = 1, 0, if the link (i, j) exists in the routing path otherwise. 1) It is obvious that all the diagonal elements of I must be zero. Using the above definitions, the SP routing problem can be formulated as a combinatorial optimization problem minimizing the objective function (Eq. 2a) i=S j=S j=i subject to    1, Iij − Iji = −1,   j=S j=S 0, j=i j=i D D if i = S if i = D otherwise and D Iij j=S j=i ≤ 1, = 0, if i = D if i = D Iij ∈ {0, 1}, for all i. 2b) The constraint (Eq.

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