| Summary: | In this work, the Traveling Salesman Problem (TSP) is discussed. The Hybrid Genetic Algorithm for solving the TSP is presented. The traveling salesman problem is formulated as follows: given matrix D=(dij)nxn of distances between n objects and the set P of permutations of the integers from 1 to n, find a permutation p=(p(1), p(2), ..., p(n)) P that minimizes. Many heuristic algorithms can be applied for the TSP. Recently, genetic algorithms (GAs) are among the advanced heuristic techniques for the combinatorial problems, like the TSP. genetic algorithms are based on the biological process of natural selection. The original concepts of GAs were developed in 1970s. Many simulations have demonstrated the efficiency of GAs on different optimization problems, among them, bin–packing, generalized assignment problem, graph partitioning, job–shop scheduling problem, set covering problem, vehicle routing. One of the main operators in GAs is the crossover (i.e. solution recombination). This operator plays a very important role by constructing competitive GAs. In this work, we investigate several crossover operators for the TSP, among them, CX (cycle crossover), PMX (partialy mapped crossover), POS (position based crossover), ER (edge recombination crossover), edge-NN (edge recombination crossover, nearest neighbour) and AP (alternating-positions crossover). Comparison of these crossover operators was performed. The results show high efficiency of the edge-NN, ER and PMX crossovers.
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