An approximation algorithm for multidimensional assignment problems minimizing the sum of squared errors

Local search heuristics for the multidimensional assignment problem

“…-A host of local search procedures and construction heuristics which often have some approximation guarantee (Bandelt et al 2004;Burkard et al 1996b;Crama and Spieksma 1992;Isler et al 2005;Kuroki and Matsui 2007;Murphey et al 1998 and some others) are proposed for special cases of MAP (usually with decomposable weights, see Sect. 3.2) and exploit the specifics of these instances.…”

“…The question of selecting proper test bed is one of the most important questions in heuristic experimental evaluation (Rardin and Uzsoy 2001). While many researchers focused on instances with random independent weights (Andrijich and Caccetta 2001;Balas and Saltzman 1991;Krokhmal et al 2007;Pasiliao et al 2005 and some others) and random instances with predefined solutions (Clemons et al 2004;Grundel and Pardalos 2005;Karapetyan et al 2009), several more sophisticated models are of greater practical interest (Bandelt et al 2004;Burkard et al 1996b;Crama and Spieksma 1992;Frieze and Yadegar 1981;Kuroki and Matsui 2007). There is also a number of papers which consider real-world and pseudo real-world instances (Bekker et al 2005;Murphey et al 1998; but the authors of this paper suppose that these instances do not well represent all the instance classes and building a proper benchmark with the real-world instances is a subject for another research.…”

“…Several special cases of the problem were intensively studied in the literature (see Kuroki and Matsui 2007 and references there) and for few classes of instances polynomial time exact algorithms were found, see, e.g., Burkard et al (1996aBurkard et al ( , 1996b, Isler et al (2005). In many cases MAP remains hard to solve (Kuroki and Matsui 2007;Spieksma and Woeginger 1996). For example, if there are three sets of points of size n on a Euclidean plain and the objective is to find n triples of points, one from each set, such that the total circumference or area of the corresponding triangles is minimal, the corresponding 3-AP is still NPhard (Spieksma and Woeginger 1996).…”

“…As regards the solution methods, apart from exact and approximation algorithms (Balas and Saltzman 1991;Crama and Spieksma 1992;Kuroki and Matsui 2007;Pasiliao et al 2005;Pierskalla 1968), several heuristics including construction heuristics (Balas and Saltzman 1991;Karapetyan et al 2009;Oliveira and Pardalos 2004), greedy randomized adaptive search procedures (Aiex et al 2005;Murphey et al 1998;Oliveira and Pardalos 2004;Robertson 2001), metaheuristics (Clemons et al 2004;Huang and Lim 2006) and parallel heuristics are presented in the literature. Several local search procedures are proposed and discussed in Aiex et al (2005), Balas and Saltzman (1991), Bandelt et al (2004), Burkard et al (1996b), Clemons et al (2004), Huang and Lim (2006), Oliveira and Pardalos (2004), Robertson (2001).…”

Heuristic Approach to Multidimensional Temporal Assignment of Spatial Grid Points for Effective Vegetation Monitoring and Land Use in East Africa

“…Approximations to the multi-dimensional assignment problem were generated by Kuroki & Matsui (2007), Gutin, …”