Statistical mechanics analysis of generalized multi-dimensional knapsack problems

Multi-dimensional Knapsack Problems

This chapter reviews our recent work on applying hybrid collaborative techniques that integrate Branch and Bound (B&B) and Memetic Algorithms (MAs) in order design effective heuristics for the Multidimensional Knapsack Problem (MKP). To this end, let us recall that Branch and Bound (B&B) [1] is an exact algorithm for finding optimal solutions to combinatorial problems, that, basically works by ...

Statistical mechanics of the multi-constraint continuous knapsack problem

Abstract. We apply the replica analysis established by Gardner to the multiconstraint continuous knapsack problem, which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the ...

Generalized ®nite element methods for three-dimensional structural mechanics problems

The present paper summarizes the generalized ®nite element method formulation and demonstrates some of its advantages over traditional ®nite element methods to solve complex, three-dimensional (3D) structural mechanics problems. The structure of the sti€ness matrix in the GFEM is compared to the corresponding FEM matrix. The performance of the GFEM and FEM in the solution of a 3D elasticity pro...

Probability Densities for Some One-Dimensional Problems in Statistical Mechanics

Generalized statistical mechanics of cosmic rays

We consider a generalized statistical mechanics model for the creation process of cosmic rays which takes into account local temperature fluctuations. This model yields Tsallis statistics for the cosmic ray spectrum. It predicts an entropic index q given by q = 11/9 at largest energies (equivalent to a spectral index of α = 5/2), and an effective temperature given by 59TH , where kTH ≈ 180 MeV ...