Changing the QAP's hard definition such that the facilities M are allowed to be mapped by a (single-valued, not necessarily injective) function π into the set of possible locations Y subject to a relation Π, π ⊆ Π, it arises the Semi-QAP that might be regarded as a relaxation of the QAP. In contrast to the Tree-QAP (flow graph F is a tree) the corresponding Semi-Tree-QAP is solvable in polynomi...

In this paper we present the problem of designing a three level hub center network. In our network, the top level consists of a complete network where a direct link is between all central hubs.  The second and third levels consist of star networks that connect the hubs to central hubs and the demand nodes to hubs and thus to central hubs, respectively. We model this problem in an incomplete net...

Task assignment problem (TAP) involves assigning a number of tasks to a number of processors in distributed computing systems and its objective is to minimize the sum of the total execution and communication costs, subject to all of the resource constraints. TAP is a combinatorial optimization problem and NP-complete. This paper proposes a hybrid meta-heuristic algorithm for solving TAP in a ...

In this brief note we consider rank aggregation, a popular method in voting theory, social choice, business decisions etc. Mathematically the problem is to find a permutation – viewed as a vector – that minimizes the sum of the `1-distances to a given family of permutations. The problem may be solved as an assignment problem and we establish several properties of optimal solutions in this problem.

Proof of Theorem 3.3: The proof of the first part of the theorem is similar to that of Theorem 3.1, and is omitted. Next, we prove the second part of the theorem. Suppose that the state estimator (5) with 1G given by (6) is a nonfragile quadratic guaranteed cost estimator with cost matrix Q 0 , then from Lemma 3E, (31) and (44) hold for some

In this paper we prove a very general theorem and establish related results about the existence of robust multivalued solutions for assignment problems. Indian Institute of Management Ahmedabad-380 015 India and ERSA University of the Witwatersrand

We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G. Parisi for the minimum matching problem in the pseudo-dimension d mean field model for d ≥ 1. The case d = 1 corresponds to the π2/6-limit for the assignment problem proved by D. Aldous in 2001. We introduce a game-theoretical framework by which we establish the analogous limit also for d > 1.