Efficient approximation of melting temperature in simulated annealing algorithms applied to Chebyshev travelling salesman problem

Simulated annealing algorithms are widely used for solving NP-hard combinatorial optimisation problems including the travelling salesman problem (TSP). This article presents results of an empirical investigation for estimating the melting temperature for the simulated annealing algorithm based on the objective function value. We limit our search to Chebyshev order-picking systems with unequal horizontal and vertical speeds. The article utilises 90 randomly generated order-picking problems with densities ranging from 10 to 800 stops per tour. For each investigated problem, we utilise different seed values to generate and to solve ten replicates of the problem. Results show that quality melting temperature values can be estimated based on the statistical characteristics of the search space. This study helps to arrive at quality solutions with significantly fewer re-evaluations of the objective function.