The New theory, solution for the traveling salesman problem.

A new theory on what may be a significant advance in mathematics
was introduced. During a two-hour presentation by Dr. Anang Z. Gani, a
senior lecturer in the Departement of Industrial Engineering at Bandung
Institute of Technology (ITB). Dr. Gani's theory which he calls the
"interaction" theory was introduced before an inter-disciplinary audience of
ITB's faculty members, students and journalists. The presentations was held
in a seminar room in the building housing the ITB Departement of Industrial
Engineering.

Dr. Gani claims that his new theory will permit the development of much more
efficient algorithms for solving combinatorial optimization problems, which
are problems where the number of possible solutions increases in proportion
to the number of possible combinations of the values of the variables concerned.

Operations Research
These problems pose serious computational difficulties because even small
problems can possess a very large number of possible solutions. The result
is that great deal of valueable computer time used up in determining the
optimum answer, despite the fact that all combinatorial optimization
techniques eximine only a small fraction of all feasible solutions. If the
interaction theory does stand up under critical appraisal, it will
revolutionize the mathematical field known as operations research. Operation
research is the colective name for a group of mathematical optimization
techniques, that are extensively utilized by companies all over the world,
if Dr. Gani's claims can be subtantisted, the potential savings run into the
tens of millions of dolars.

Traveling Salesman Problem
Particularly interesting is Dr. Gani's claims that the interaction theory
guarantees an optimal solution to the traveling salesman problem, a problem
that has defied solution until now. Stated briefly, the traveling salesman
problem concern itself with attemting to find a route that enables each node
(city, building, area etc.) in a network to be visited exactly once, with
the provision that we start and end the route at the same node. All attempt
to find an algorithm that guarantees an optimum solutions have until now
failed, despite years of sustained effort by many brilliant researchers.
Existing methods for solving the TSP produce solutions that are only
approximately optimal. To disaapointment of the present, Dr Gani's
presentations did not discuses the theoretica basis of his theory. Turning
aside requests for a rigorous mathematical proof, Dr. Gani hinted the he
would provide detailed justification of his theory is based on a special
project that Dr. Gani undertook as a student at the Georgia Institute of
Thechnology in 1965. The project was attempt to develop a mathematical model
that could help engineers trying solve material handling problems
encountered during the design of plant layouts. The final verdict on the
interaction theory is not in yet.
Academic debate about the virtues and the shortcomings of this new theory
will have to await Dr. Gani's release of its theoritical justifications.

Source : The Jakarta Post