A worst-case analysis of two approximate algorithms for the asymmetric travelling salesman problem

Article Abstract:

The asymmetric travelling salesman problem (ATSP) is examined through the application of approximate algorithms. The algorithms offer worst case ratio performance and are bound by data dependent variables. A minimum spanning tree that eliminates ambiguity from quantity dependence on arc weights is then constructed. Bounds generated offer bad results for the ATSP. Greater difficulty in obtaining solutions is observed when weights are distributed over larger ranges.

Numerical analysis, Traveling sales personnel, Traveling salespeople

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A double annealing algorithm for discrete location/allocation problems

Article Abstract:

A double annealing algorithm for solving discrete location/allocation problems characterized by two mutually dependent groups of binary variables is introduced. The algorithm, which was applied to the vertex-constrained multi-site location problems on graphs known as the P-median problem, involves two, synchronized annealing processes. It also requires deannealing to drive the concurrent annealing of the two sets of variables.

Industrial locations, Industrial location, Resource allocation, Simulated annealing (Mathematics)

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A note of the approximation of the asymmetric traveling salesman problem

Article Abstract:

Some asymmetric traveling salesman problem (ATSP) instances are approximable within bounds equal to 3 and 9/5. Two preprocessing linear programs to reformulate ATSP instances into equivalent ones achieving data-dependent bounds by the same approximation algorithms are discussed.

Analysis, Linear programming, Usage, Algorithm, Asynchronous communications, Asynchronous transfer mode, ATM

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