Memory-based statistical learning for the travelling salesman problem

The travelling salesman problem is a well known combinatorial optimization problem and evolutionary computation methods are one of the important methods to solve it. A difficult issue for evolutionary computation methods is to identify good edges that belong to the global optimum during the search progress. To address this issue, this paper proposes a tour construction algorithm, which is based on a memory-based statistical learning mechanism. A probability matrix is created according to the edge distribution in a memory population, which stores the best solution found by every individual. For each individual, a tour is constructed according to its local personal best solution found so far and the global probability matrix. Two variants of ant colony optimization are chosen to test the effectiveness of the proposed algorithm. The result show that the proposed algorithm is an efficient learning algorithm for the travelling salesman problem.