Lake-Energy Optimization Algorithm for Travelling Salesman Problem

Lake freezing is a common natural phenomenon in winter. Inspired by this phenomenon, a novel intelligent and parallel algorithm, lake-energy optimization algorithm (LEO), is proposed in this paper. The LEO algorithm simulates the process of lake freezing. With the temperature of lake reducing, the water loses energy to the environment and starts to precipitate and freeze when its energy is below the threshold of freezing point. The LEO approach consists of two major models: the lake energy model and the wind-blow model. For the lake energy model, the center energy of lake, atmospheric energy, molecular energy of lake, as well as the wind are the main factors that affect the energy of lake with different weights under each stage of freezing. Meanwhile, the wind-blow model, as a supportive role, is responsible for agitating after freezing to prevent the solution from local optimum. Furthermore, the properties of the approach, including the correctness, convergence and effectiveness of the algorithm, are verified theoretically through the Convergent Theorem and the Lyapunov Second Theorem on stability. Via numerous simulations of TSPLIB and comparison with other classical algorithms, the characters of high efficiency, low computational complexity and strong convergence of the LEO algorithm are illustrated, which are especially crucial for the functioning of large-scale distribution problems.