Searching for Backbones--a high-performance parallel algorithm for solving combinatorial optimization problems

Abstract A highly efficient parallel algorithm called Searching for Backbones (SfB) is proposed: based on the finding, that many parts of a good configuration for a given optimization problem are the same in all other good solutions, SfB reduces the complexity of this problem by determining these “backbones” and eliminating them in order to get even better solutions in a very short time. Applications and results are presented for the Traveling Salesman Problem and the Vehicle Routing Problem.

[1]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[2]  K. Binder,et al.  Monte Carlo Simulation in Statistical Physics , 1992, Graduate Texts in Physics.

[3]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[4]  P. Stadler,et al.  The landscape of the traveling salesman problem , 1992 .

[5]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[8]  C. Darwin.  On the Origin of Species by Means of Natural Selection: Or, The Preservation of Favoured Races in the Struggle for Life , 2019 .

[9]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[10]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[11]  Leslie E. Trotter,et al.  On the capacitated vehicle routing problem , 2003, Math. Program..

[12]  Ingo Morgenstern,et al.  OPTIMIZATION OF PRODUCTION PLANNING PROBLEMS A CASE STUDY FOR ASSEMBLY LINES , 2000 .

[13]  Martin Grötschel,et al.  Polyedrische Kombinatorik und Schnittebenenverfahren , 1984 .

[14]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[15]  Juraj Hromkovic,et al.  Algorithmics for Hard Problems , 2002, Texts in Theoretical Computer Science An EATCS Series.

[16]  J. M. Singer,et al.  Searching for backbones — an efficient parallel algorithm for the traveling salesman problem , 1996 .

[17]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[18]  Martin Grötschel,et al.  Solution of large-scale symmetric travelling salesman problems , 1991, Math. Program..

[19]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[20]  J. Fontanari,et al.  Stochastic versus deterministic update in simulated annealing , 1990 .