In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3-SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomial-time hierarchy based on superconcentrator graphs. This resolves an open question of Ko and Lin (1995) and should be useful in deriving ...

Performance comparisons between algorithms have a long tradition in metaheuristic research. An early example are comparisons between Tabu Search (TS) and Simulated Annealing (SA) algorithms for tackling the Quadratic Assignment Problem (QAP). The results of these comparisons are to a certain extent inconclusive, even when focusing on only these two types of algorithms. While comparisons of SA a...

We propose the adoption of a vector extrapolation technique to accelerate convergence of correspondence problems under the quadratic assignment formulation for attributed graph matching (QAP). In order to capture a broad range of matching scenarios, we provide a class of relaxations of the QAP under elastic net constraints. This allows us to regulate the sparsity/complexity trade-off which is i...

In this paper we study two formulation reductions for the quadratic assignment problem (QAP). In particular we apply these reductions to the well known Adams and Johnson [2] integer linear programming formulation of the QAP, which we call formulation IPQAP-I. We analyze two cases: In the first case, we study the effect of constraint reduction. In the second case, we study the effect of variable...

We present a coarse-grain (outer-loop) parallel implementation of RLT1/2/3 (Level 1, 2, and 3 Reformulation and Linearization Technique—in that order) bound calculations for the QAP within a branch-and-bound procedure. For a search tree node of size S, each RLT3 and RLT2 bound calculation iteration is parallelized S ways, with each of S processors performing O(S) and O(S) linear assignment prob...

The Birkhoff polytope is defined to be the convex hull of permutation matrices, Pσ ∀σ ∈ Sn. We define a second-order permutation matrix P [2] σ in R ×n corresponding to a permutation σ as (P [2] σ )ij,kl = (Pσ)ij(Pσ)kl. We call the convex hull of the second-order permutation matrices, the second-order Birkhoff polytope and denote it by B. It can be seen that B is isomorphic to the QAP-polytope,...

Many methods currently used in combinatorial optimization are inspired by adaptative natural behaviors or natural systems, e.g. hill-climbing local search, genetic algorithms, simulated annealing, : : : These heuristics provide some very good results, even when the problem size makes it impossible to use more traditional exact methods (such as branch and bound, ...). Ants system algorithms belo...

This paper proposes an optimization algorithm for the Quadratic Assignment Problem (QAP) based on replicator equations. If the growth rate of a replicator equation is composed of the performance index and the constraints of the QAP suitably, by increasing the value of the control parameter in the growth rate, the equilibrium solutions which correspond to the feasible solutions of the QAP become...

A merge process is proposed to engineer a multi-spin flip in an Ising machine. The deforms the Hamiltonian (energy function) of model. We prove theorem for and show that single-spin deformed equivalent original Hamiltonian. induces transition within subspace feasible solutions. propose hybrid simulated annealing (SA) algorithm with process. outperforms conventional SA algorithm, genetic tabu se...

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...