Temperature parallel simulated annealing with adaptive neighborhood for continuous optimization problem
Mitsunori Miki, Tomoyuki Hiroyasu, Masayuki Kasai, Keiko Ono, Takeshi Jitta · 2002
this paper, we propose Temperature Parallel Simulated Annealing with Adaptive Neighborhood(TPSA/AN) which is the extension of TPSA by using the Corana's SA[9] for continuous optimization problems. The di#erence between the conventional sequential SA for combinatorial optimization problems and TPSA/AN is that TPSA/AN has a procedure for exchanging solutions between di#erent constant temperatures and a procedure for adjusting the neighborhood range. The exchange of solutions and the adjustment of the neighborhood range are executed at certain transitions. In this algorithm, the distribution for generating a next point x' from current point x is as follows: x i # = x i + rm (3) where r is a random number generated in the range [-1, 1]; m is the neighborhood range. The algorithm in this paper has the same parameter m for each design values, while Corana's SA has a di#erent parameter for each design value. If the next point x' lies outside the definition domain of an objective function, our algorithm will generate a new point again. The neighborhood range m is varied for adaptive search using equations (4), (5), (6) and (7): m new = m old g(p)(4) g(p)=1+c 0.6 , if p>0.6(5) g(p)= 1+c -1 , if p<0.4(6) g(p)=1 , otherwise (7) where c is a multiplying factor for adjusting the neighborhood range ; p is a rate between accepted and rejected moves, and it is calculated from the following equation: p = n/N (8) where N is a given number of transitions; n is the number of accepted moves in interval N. In this paper, parameter c is set to 2, following the Corana's paper