Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Stochastic analysis of the quadratic assignment problem
Mathematics of Operations Research
Constructive bounds and exact expectation for the random assignment problem
Random Structures & Algorithms
The ζ (2) limit in the random assignment problem
Random Structures & Algorithms
A note on the asymptotic behaviour of bottleneck problems
Operations Research Letters
| Hi-index | 0.00 |
The analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study. Simulated annealing, a metaheuristic for combinatorial optimization problems, is based on this analogy. In this paper we show how a statistical mechanics formalism can be utilized to analyze the asymptotic behavior of combinatorial optimization problems with sum objective function and provide an alternative proof for the following result: Under a certain combinatorial condition and some natural probabilistic assumptions on the coefficients of the problem, the ratio between the optimal solution and an arbitrary feasible solution tends to one almost surely, as the size of the problem tends to infinity, so that the problem of optimization becomes trivial in some sense. Whereas this result can also be proven by purely probabilistic techniques, the above approach allows one to understand why the assumed combinatorial condition is essential for such a type of asymptotic behavior.