An efficient hybrid genetic algorithm for the quadratic traveling salesman problem - PHAM, Quang Anh (Institutional Knowledge at Singapore Management University, 2023)
The traveling salesman problem (TSP) is the most well-known problem in combinatorial optimization which hasbeen studied for many decades. This paper focuses on dealing with one of the most difficult TSP variants named thequadratic traveling salesman problem (QTSP) that has numerous planning applications in robotics and bioinformatics.The goal of QTSP is similar to TSP which finds a cycle visiting all nodes exactly once with minimum total costs. However, the costs in QTSP are associated with three vertices traversed in succession (instead of two like in TSP). This leadsto a quadratic objective function that is much harder to solve.To efficiently solve the problem, we propose a hybrid geneticalgorithm including a local search procedure for intensification and a new mutation operator for diversification. The local search is composed of a restricted double-bridge move(a variant of 4-Opt); and we show the neighborhood can beevaluated in O(n2), the same complexity as for the classicalTSP. The mutation phase is inspired by a ruin-and-recreatescheme. Experimental results conducted on benchmark instances show that our method significantly outperforms state-of-the-art algorithms in terms of solution quality. Out of the800 instances tested, it finds 437 new best-known solutions.