Average value of solutions of the bipartite quadratic assignment problem and linkages to domination analysis

Abstract

In this paper we study the complexity and domination analysis in the context of the bipartite quadratic assignment problem. Two variants of the problem, denoted by BQAP1 and BQAP2, are investigated. A formula for calculating the average objective function value A of all solutions is presented whereas computing the median objective function value is shown to be NP-hard. We show that any heuristic algorithm that produces a solution with objective function value at most A has the domination ratio at least

Combinatorial optimization with interaction costs: Complexity and solvable cases

“…When F 1 and F 2 contain all subsets of [m] and [n] respectively, COPIC reduces to the bipartite unconstrained quadratic programming problem [23,47,35,39] studied in the literature by various authors and under different names. Also, when F 1 and F 2 are feasible solutions of generalized upper bound constraints on m and n variables, respectively, COPIC reduces to the bipartite quadratic assignment problem and its variations [21,48]. Most quadratic combinatorial optimization problems can also be viewed as special cases of COPIC, including the quadratic minimum spanning tree problem [4], quadratic set covering problem [5], quadratic travelling salesman problem [37], etc.…”