A Genetic Algorithm With Projection Operator for the Traveling Salesman Problem

The traveling salesman problem is a NP-hard combinatorial optimization problem. So far, many algorithms are proposed for the problem. However, exact algorithms are time-consuming, while heuristic approaches may not obtain a global optimum. In fact, the genetic algorithm based on edge assembly crossover shows it good performance. Nevertheless, a drawback of the algorithm is that the algorithm may not work well for instances with cities produced by lattice, such as the instances coming from VLSI. In this paper, we propose projection operator for the algorithm to overcome the drawback. Under the control of the operator, when the state of trapped into local optimum is detected, individuals are projected and leave the neighborhood of the local optimum. Experimental results show that our projection operator can improve solution of the instances coming from the field of VLSI application.