A Set of Greedy Randomized Adaptive Local Search Procedure (GRASP) Implementations for the Multidimensional Assignment Problem

The focal problem for centralized multisensor multitarget tracking is the data association problem of partitioning the observations into tracks and false alarms so that an accurate estimate of the true tracks can be recovered. Large classes of these association problems can be formulated as multidimensional assignment problems, which are known to be NP-hard for three dimensions or more. The assignment problems that result from tracking are large scale, sparse and noisy. Solution methods must execute in real-time. The Greedy Randomized Adaptive Local Search Procedure (GRASP) has proven highly effective for solving many classes NP-hard optimization problems. This paper introduces four GRASP implementations for the multidimensional assignment problem, which are combinations of two constructive methods (randomized reduced cost greedy and randomized max regret) and two local search methods (two-assignment-exchange and variable depth exchange). Numerical results are shown for a two random problem classes and one tracking problem class.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

Global optimization of a class of nonconvex quadratically constrained quadratic programming problems

In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.     

地震期间应急资源调度方案的优化选取

应急资源的调度是地震救援工作的重点,为解决这个难题,本文构建了以时效性、伤亡性和经济性为三大分量的多目标函数,然后经过无量纲和Delphi加权处理,将其转化为单目标函数,并将其中的决策效用函数看成运筹学中指派问题的效率函数,最后运用匈牙利法计算出最大的目标函数值,从而得出最优的资源调度方案.与其他多目标的应急资源调度方法相比,本文构建的这种算法具有简易、实用的优点,可以说为地震期间应急资源调度方案的优化选取工作提供了一种切实、可行的途径.     

指派问题匈牙利解法的又两个注记

本文就指派问题匈牙利解法中的一些方法提出两个注记，且为此提供一个较为简单的解法。     

群体决策的偏好协调性检验

对于一类群体决策问题，本文引进群体的偏好协调性指标，并且给出了偏好协调性指标的统计检验．在此基础上，还提出一个求该类群体决策问题的方法，以及讨论了群体的偏好快调性指标和群体决策结果间的关系．     

Enumerating typical abelian prime-fold coverings of a circulant graph

Enumerating the isomorphism classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory (see [R. Feng, J.H. Kwak, J. Kim, J. Lee, Isomorphism classes of concrete graph coverings, SIAM J. Discrete Math. 11 (1998) 265-272; R. Feng, J.H. Kwak, Typical circulant double coverings of a circulant graph, Discrete Math. 277 (2004) 73-85; R. Feng, J.H. Kwak, Y.S. Kwon, Enumerating typical circulant covering projections onto a circulant graph, SIAM J. Discrete Math. 19 (2005) 196-207; SIAM J. Discrete Math. 21 (2007) 548-550 (erratum); M. Hofmeister, Graph covering projections arising from finite vector spaces over finite fields, Discrete Math. 143 (1995) 87-97; M. Hofmeister, Enumeration of concrete regular covering projections, SIAM J. Discrete Math. 8 (1995) 51-61; M. Hofmeister, A note on counting connected graph covering projections, SIAM J. Discrete Math. 11 (1998) 286-292; J.H. Kwak, J. Chun, J. Lee, Enumeration of regular graph coverings having finite abelian covering transformation groups, SIAM J. Discrete Math. 11 (1998) 273-285; J.H. Kwak, J. Lee, Isomorphism classes of graph bundles, Canad. J. Math. XLII (1990) 747-761]). A covering is called abelian (or circulant, respectively) if its covering graph is a Cayley graph on an abelian (or a cyclic, respectively) group. A covering p from a Cayley graph onto another Cay (Q,Y) is called typical if the map p:A→Q on the vertex sets is a group epimorphism. Recently, the isomorphism classes of connected typical circulant r-fold coverings of a circulant graph are enumerated in [R. Feng, J.H. Kwak, Typical circulant double coverings of a circulant graph, Discrete Math. 277 (2004) 73-85] for r=2 and in [R. Feng, J.H. Kwak, Y.S. Kwon, Enumerating typical circulant covering projections onto a circulant graph, SIAM J. Discrete Math. 19 (2005) 196-207; SIAM J. Discrete Math. 21 (2007) 548-550 (erratum)] for any r. As a continuation of these works, we enumerate in this paper the isomorphism classes of typical abelian prime-fold coverings of a circulant graph.     

Efficient algorithms for wavelength assignment on trees of rings

A fundamental problem in communication networks is wavelength assignment (WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree using at most 3L wavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3L upper bound is tight since there are instances of the WA problem that require 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation (resp. 2.5-approximation) algorithm for the WA problem on a tree of rings with degree at most six (resp. eight). Previous results include: 4L (resp. 3L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).     

Labeling bipartite permutation graphs with a condition at distance two

An L(p,q)-labeling of a graph G is an assignment f from vertices of G to the set of non-negative integers {0,1,…,λ} such that |f(u)−f(v)|≥p if u and v are adjacent, and |f(u)−f(v)|≥q if u and v are at distance 2 apart. The minimum value of λ for which G has L(p,q)-labeling is denoted by λ_p,q(G). The L(p,q)-labeling problem is related to the channel assignment problem for wireless networks.In this paper, we present a polynomial time algorithm for computing L(p,q)-labeling of a bipartite permutation graph G such that the largest label is at most (2p−1)+q(bc(G)−2), where bc(G) is the biclique number of G. Since λ_p,q(G)≥p+q(bc(G)−2) for any bipartite graph G, the upper bound is at most p−1 far from optimal.     

Towards auction algorithms for large dense assignment problems

In this paper, we focus on the problem of solving large-scale instances of the linear sum assignment problem by auction algorithms. We introduce a modified auction algorithm, called look-back auction algorithm, which extends the forward auction algorithm by the ability of reusing information from previous bids. We show that it is able to reuse information from the previous bids with high efficiency for all tested types of input instances. We discuss then the design and implementation of a suite of sequential and distributed memory auction algorithms on a Linux cluster with the evaluation on several types of input instances of the linear sum assignment problem. Our results show that the look-back auction algorithm solves sequentially nearly all types of dense instances faster than other evaluated algorithms and it is more stable than the forward-reverse auction algorithm for sparse instances. Our distributed memory auction algorithms are fully memory scalable. This research has been supported by IGA CTU under grant CTU0308013 and under research program MSMT 6840770014.