Greedy Like Algorithms for the Traveling Salesman and Multidimensional Assignment Problems

2010

J Heuristics

Self Cite

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components.

Section: Pure Local Search Experimentsmentioning

confidence: 95%

Local search heuristics for the multidimensional assignment problem

2010

J Heuristics

Self Cite

“…Greedy heuristic was discussed in many papers, see, e.g. [4,9,16,17,18,23]. It was proven [16] that in the worst case Greedy produces the unique worst solution; however, it was shown [17] that in some cases Greedy may be a good selection as a fast and simple heuristic.…”

mentioning

confidence: 99%

Local Search Heuristics for the Multidimensional Assignment Problem

Graph Theory, Computational Intelligence and Thought

2009

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate a combination of two neighborhoods may yield a heuristics which is superior to both of its components. 1 Burkard et al. show it for a special case of 3-AP and since 3-AP is a special case of s-AP the result can be extended to the general MAP

“…The proofs of this theorem for TSP [6] and for MAP [27] are not constructive and use the main result of [6].…”

Section: All Maximal Sets Of F Are Called Bases (Or Feasible Solutiomentioning

confidence: 97%

A selection of useful theoretical tools for the design and analysis of optimization heuristics

2008

Memetic Comp.

An intensive practical experimentation is certainly required for the purpose of heuristics design and evaluation, however a theoretical approach is also important in this area of research. This paper gives a brief description of a selection of theoretical tools that can be used for designing and analyzing various heuristics. For design and evaluation, we consider several examples of preprocessing procedures and probabilistic instance analysis methods. We also discuss some attempts at the theoretical explanation of successes and failures of certain heuristics.