Permutation is a fundamental operator for array data, with applications in, for example, changing matrix layouts and reorganizing data cubes. We consider the problem of permuting large quantities of data stored on secondary storage that supports fast random block accesses, such as solid state drives and distributed key-value stores. Faster random accesses open up interesting new opportunities f...

This paper proposes an effective multi-objective differential evolution algorithm (MDES) to solve a permutation flow shop scheduling problem (PFSSP) with modified Dejong's learning effect. The proposed algorithm combines the basic differential evolution (DE) with local search and borrows the selection operator from NSGA-II to improve the general performance.  First the problem is encoded with a...

After reviewing the group structure and representation theory for dihedral $$D_{2n},$$ we consider an intertwining operator $$\varPhi _\rho $$ from algebra $$\mathbb {C}[D_{2n}]$$ into a corresponding space of semi-magic matrices. From this operator, one obtains generating function enumerating associated squares with fixed line sum extending circulant While work complements approach to $$D_{2n}...

In this paper, we consider the permutation representation of genetic algorithms, and more generally, local search algorithms. We use a variety of permutation distance measures to profile the behavior of the most commonly used mutation operators for permutation-based genetic algorithms. Our operator profiles are also applicable to other local search algorithms, such as simulated annealing, as th...

Based on one-dimensional single-electron infinite periodic models of transpolyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, although preserved in bound-state molecular systems, no longer generally held in periodic systems. The overall permutation symmetry breakdown provides a natural explanation of the widely observed large devia...

The generating functions for a large class of combinatorial problems involving the enumeration of permutations may be expressed as solutions to matrix Riccati equations. We show that the generating functions for the permutation problem in which the number of inversions is also preserved form a system of matrix Riccati equations in which the differential operator is the Eulerian differential ope...

We establish finiteand infinite-dimensional versions of the following assertion. If M is a matrix with the property that whenever P and Q are diagonal projections with P ≤ Q, the spectrum of PMP (considered as an operator on the range of P ) is contained in that of QMQ (considered as an operator on the range of Q), then there is a permutation matrix U such that U−1MU is triangular.