A branch‐and‐bound‐based heuristic for solving the quadratic assignment problem

Abstract

In this article a branch-and-bound algorithm is proposed for solving the quadratic assignment problem. Using symmetric properties of the problem, the algorithm eliminates "mirror image" branches, thus reducing the search effort. Several routines that transform the procedure into an efficient heuristic are also implemented. These include certain 2-way and 4-way exchanges, selective branching rules, and the use of variable upperbounding techniques for enhancing the speed of fathoming. The computational results are quite encouraging. As an exact scheme, the algorithm solved the 12-facility problem of Nugent et al. and the 19-facility problem of Elshafei. More importantly, as a heuristic, the procedure produced the best known solutions for all well-known problems in the literature, and produced improved solutions in several cases.

Symmetry in Integer Linear Programming

“…Related but simpler and less efficient algorithms for solving quadratic assignment problems can be found in [8,76]. They essentially just avoid the creation of isomorphic subproblems from the same parent node.…”

Uma revisão comentada das abordagens do problema quadrático de alocação

“…A formulação booleana foi proposta inicialmente por Koopmans & Beckmann (1957), sendo depois utilizada em diversos trabalhos, tais como Steinberg (1961), Lawer (1963), Gavett & Plyter (1966), Elshafei (1977), Bazaraa & Kirca (1983), Christofides & Benavent (1989), Bos (1993), Mans et al (1995), Jünger & Kaibel (1996a, 2001) e mais recentemente por Liang (1996), Torki et al (1996), Tsuchiya et al (1996Tsuchiya et al ( , 2001), Maniezzo (1997) …”

Machine layout: an optimization and knowledge-based approach

“…Examine Figure 13: Maximum spanning tree for data in natrix (7) tree Tt is as folLows: Step 3. Step 3.…”

“…Constraint (7) ensures that each facility is assigned to exactly one location and constraint (8) (Bazaraa , 1975 …”