Hybridization of simulated annealing and D-numbers as a stochastic generator

Alireza Sotoudeh-Anvari*, Seyed Mojtaba Sajadi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Simulated annealing (SA) is one of the oldest and the most well-known metaheuristics for optimization problems. One exclusive merit of this algorithm is that it does not get stuck in any local optima. However, due to strictly random process and some unnecessary moves, the convergence speed of SA is relatively slow. To alleviate this weakness, in this paper, a hybrid metaheuristic algorithm, comprising SA and D-number to better explore the search space is introduced. Within this proposed framework, D-number is embedded in SA and works as a stochastic engine (random generator) to reduce redundant moves, particularly during high temperatures. Mathematically, in the new approach, the probability of accepting inferior solution can be checked by D-number instead of uniformly distributed random variable. The results derived from hybrid SA show this search mechanism allows some non-improving moves to be avoided. Consequently, D-number as a high quality random generator in SA results in a good performance with low implementation effort in some cases. Traveling salesman problem (TSP) as an illustrative application is selected to verify the performance of this hybrid SA. On the whole, the result derived from the combination of SA and D-numbers is relatively encouraging.

Original languageEnglish
Early online date7 May 2024
Publication statusE-pub ahead of print - 7 May 2024


  • D-numbers
  • Hybrid metaheuristic
  • Random generator
  • Simulated annealing
  • Traveling salesman problem


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