A memetic random-key genetic algorithm for a symmetric multi-objective traveling salesman problem

This paper proposes a methodology to find weakly Pareto optimal solutions to a symmetric multi-objective traveling salesman problem using a memetic random-key genetic algorithm that has been augmented by a 2-opt local search. The methodology uses a “target-vector approach” in which the evaluation function is a weighted Tchebycheff metric with an ideal point and the local search is randomly guided by either a weighted sum of the objectives or a weighted Tchebycheff metric. The memetic algorithm has several advantages including the fact that the random keys representation ensures that feasible tours are maintained during the application of genetic operators. To illustrate the quality of the methodology, experiments are conducted using Euclidean TSP examples and a comparison is made to one example found in the literature.