Adaptive Temperature Schedule Determined by Genetic Algorithm for Parallel Simulated Annealing Mitsunori Miki Knowledge Engineering Dept., Doshisha University 1-3 Tatara Miyakodani Kyotanabe, Kyoto 610-0394 mmiki@mail.doshisha.ac.jp Tomoyuki Hiroyasu Knowledge Engineering Dept., Doshisha University 1-3 Tatara Miyakodani Kyotanabe, Kyoto 610-0394 tomo@is.doshisha.ac.jp Jun’ya Wako Graduate School of Engineering, Doshisha University Takeshi Yoshida Graduate School of Engineering, Doshisha University Abstract- Simulated annealing (SA) is an effec- tive general heuristic method for solving many combinatorial optimization problems. This pa- per deals with two problems in SA. One is the long computational time of the numerical an- nealings, and the solution to it is the parallel processing of SA. The other one is the determi- nation of the appropriate temperature schedule in SA, and the solution to it is the introduc- tion of an adaptive mechanism for changing the temperature. The multiple SA processes are performed in multiple processors, and the tem- peratures in the SA processes are determined by a genetic algorithms. The proposed method is applied to solve many TSPs (Traveling Sales- man Problems) and JSPs (Jobshop Scheduling Problems), and it is found that the method is very useful and effective. Key Words : Simulated Annealing, Genetic Algorithm, Adaptive Temperature, Traveling Salesman Problems, Jobshop Scheduling Prob- lems 1 Introduction There is a strong incentive to parallelize the compu- tation for solving optimization problems since it re- quires many iterations of analysis. Especially, sim- ulated annealing, which are very effective for solv- ing complicated optimization problems with many op- tima, requires tremendous computational power. Con- sequently, parallelization of the method is very impor- tant. It was Kirkpatrick et al. who first proposed sim- ulated annealing, SA, as a method for solving combi- natorial optimization problems[1]. It is reported that SA is very useful for several types of combinatorial op- timization problems. However, the most remarkable disadvantages are that it needs a lot of time to find the optimum solution and it is very difficult to determine the proper cooling schedule. Because of the progress of parallel computers, there are several studies on SA using parallel computers[2, 3]. Among these studies, the temperature parallel simu- lated annealing (TPSA), which was called the time- homogenous parallel annealing[4] before, is one of the algorithms that can overcome the cooling schedule problem, and that can reduce the computation time also. However, the higher temperatures assigned to some of the processors of a parallel computer can be consid- ered to be too high as the annealing proceeds since the annealing at the higher temperature does not yield the convergence of solutions. Therefore, the effectiveness of multiple processors is somewhat reduced in TPSA. In order to overcome this problem, we propose a new method for determining the temperature adaptively as the multiple annealings proceed. The temperatures as- signed to all the processors of a parallel computer are determined by a genetic algorithm(GA)[5]. The tem- peratures are dynamically changed to appropriate val- ues during the annealing process. 2 Important Temperature Region for TSP 2.1 Important Temperature Region There is an important temperature region in a temper- ature schedule of SA, where the search is carried out very efficiently. Harry[6] found that a specific constant temperature in SA yields good solutions for TSPs, and Mark[7] obtained the similar results for quadratic as- signment problems. Such specific constant temperatures are called the important temperature regions in SA in this paper, and our proposed method is based on the important temperature region.