Two hybrid genetic algorithms for the continuous p -centre problem

This article proposes two novel hybrid genetic algorithms, GLAA1 and GLAA2, for the continuous p-centre problem. The two meta-heuristics employ different encoding schemes: GLAA1 uses float encoding based on facility locations, while GLAA2 adopts integer encoding where each integer represents the facility index associated with a demand point. Instead of the crossover operator in standard genetic algorithms, a location-allocation operator, which is one step of the iterative location-allocation approach H1, is introduced. In this way, the gradient descent is integrated into the genetic algorithm framework. As part of the location-allocation operator, the smallest circle calculation is also enhanced using the convex hull concept. Moreover, a distance-based individual initialization, an elitist selection operator and a single-gene mutation operator are designed for both algorithms. The parameter settings of each algorithm are analysed, and several experiments are conducted on the TSP-Lib datasets. The results show that the proposed meta-heuristics are effective and efficient.