A fast method for generalized starting temperature determination in homogeneous two-stage simulated annealing systems

Abstract

We propose a method for determining the starting temperature in two-stage simulated annealing systems utilizing traditional homogeneous temperature schedules. While most previous work in this area has focused on ad hoc experimentally derived constant starting temperatures for the low-temperature annealing phase, this investigation presents a method for generalized starting temperature determination for the aforementioned class of two-stage simulated annealing systems. We have tested our method on three NP-hard optimization problems using both classic and adaptive homogeneous cooling schedules. The experimental results have been consistently very good – on average the running time is halved when using an adaptive cooling schedule and reduced by a third in the case of the classic schedule – with no average loss in solution quality. Scope and purpose The homogeneous simulated annealing algorithm is a general-purpose optimization paradigm that has proven to be quite effective for finding high-quality solutions to a diverse range of NP-hard combinatorial optimization problems. These types of problems are quite common in the field of operations research, and indeed simulated annealing has been used quite extensively to produce high-quality solutions to many of these problems. Two common examples are the graph partitioning problem and the traveling salesperson problem. Although the efficacy and robustness of the simulated annealing heuristic has been thoroughly demonstrated in the literature, the main drawback to the algorithm is its sometimes prohibitive run times. Two-stage simulated annealing is a technique introduced in the literature as a method for decreasing the run times of simulated annealing while maintaining its exceptional solution quality for many problems. The main drawback to the two-stage simulated annealing technique is its problem- and formulation-dependent nature. To date, an effective general method for determining the starting temperature in two-stage simulated annealing systems that is fast and both problem- and formulation-independent has yet to be demonstrated. This investigation presents such a method.