A compressed-annealing heuristic for the traveling salesman problem with time windows

This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling-salesman problem with time windows (TSPTW). Augmenting temperature from traditional simulated annealing with the concept of pressure (analogous to the value of the penalty multiplier), compressed annealing relaxes the time-window constraints by integrating a penalty method within a stochastic search procedure. Computational results validate the value of a variable-penalty method versus a static-penalty approach. Compressed annealing compares favorably with benchmark results in the literature, obtaining best known results for numerous instances.