Search results for "Generalized assignment problem"
showing 3 items of 3 documents
An Exact Algorithm for the Quadratic Assignment Problem on a Tree
1989
The Tree QAP is a special case of the Quadratic Assignment Problem (QAP) where the nonzero flows form a tree. No condition is required for the distance matrix. This problem is NP-complete and is also a generalization of the Traveling Salesman Problem. In this paper, we present a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem. The bounds are computed using a Lagrangian relaxation of this formulation. To solve the relaxed problem, we present a Dynamic Programming algorithm which is polynomially bounded. The obtained lower bound is very sharp and equals the optimum in many cases. This fact allows us to employ a redu…
The minimal cost maximum matching of a graph (supplementary remarks)
1971
In addition to the preceding paper, it will be shown that (1) the matching problem is closely related to the linear assignment problem and how (2) this property can be taken advantage of for solving the matching problem.
A genetic algorithm for the minimum generating set problem
2016
Graphical abstractDisplay Omitted HighlightsWe propose a novel formulation for the MGS problem based on multiple knapsack.The so-conceived MGS problem is solved by a novel GA.The GA embeds an intelligent construction method and specialized crossover operators.We perform a thorough comparison with regards to state-of-the-art algorithms.The proposal proves to be very competitive, specially for large and hard instances. Given a set of positive integers S, the minimum generating set problem consists in finding a set of positive integers T with a minimum cardinality such that every element of S can be expressed as the sum of a subset of elements in T. It constitutes a natural problem in combinat…