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Approaches to the Travelling Salesman Problem Using Evolutionary Computing Algorithms

Genetic algorithms (GAs) were developed as problem independent search algorithms (Goldberg, 1989; Holland, 1975; Man et al., 1999), which simulate the biological evolution to search for an optimal solution to a problem. Figure 1(a) shows the main processes of genetic algorithms. When developing a genetic algorithm, we analyze the properties of the problem and determine the “gene encoding” policy -- Several parameters are chosen as genes and the parameter set is regarded as a chromosome, which reflects an individual. Following the gene encoding policy, we scatter many individuals in a population, and then repeatedly evaluate the individuals' fitness values and select the fittest ones to reproduce the offspring by crossover and mutation operators. Genetic algorithms follow the criterion of “survival of the fittest” to develop increasingly fit individuals. Hybrid with local search heuristics, Genetic Local Search (GLS) is an upgraded version that replaces each individual with its local optimal neighbour. As shown in Fig. 1(b), a local search process is launched in evaluation. GLS is thereby regarded as a method to mimic the cultural evolution instead of biological evolution, and also referred to as Mimetic Algorithm (MA) or Lamarckian Evolutionary Algorithm (Digalakis & Margaritis, 2004). Using these “evolutionary computing algorithms” for combinatorial optimization problems has been a well-studied problem-solving approach. The benefit of evolutionary computing is not only its simplicity but also its ability to obtain global optima. Many research findings have indicated that a well-adapted genetic local search algorithm can acquire a near-optimal solution better than those found by simply local searching algorithms (Goldberg, 1989; Pham & Karaboga, 2000). Therefore, numerous results on evolutionary optimization have been published in recent years (Larranaga et al., 1999; Man et al., 1999; Mohammadian et al., 2002). Using genetic algorithms to solve the travelling salesman problem (TSP) is one of the popular approaches (Larranaga et al., 1999). The TSP is a classical NP-hard combinatorial optimization problem which has been extensively studied. Given