Cluster based branching for the asymmetric traveling salesman problem

Article Abstract:

A study has been conducted to investigate a branching scheme in which additional information on the problem structure is utilized. The cluster is the key concept of the new approach, which has been defined as a node set that can be visited consecutively in an optimal solution. Lower bounds have been generated in the overall composition of the resulting branch and bound algorithm. Findings have revealed that considerable savings in computing time can be obtained compared to previously published assignment based branch and bound algorithms for the asymmetric traveling salesman.

Operations research, Management science, Traveling-salesman problem, Transformations (Mathematics)

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A global optimization method for nonconvex separable programming problems

Article Abstract:

A new method was proposed to obtain the global optimum of a nonconvex separable programming (NSP) program. The proposed method, which utilizes less number 0-1 variables, involves conversion of a NSP problem into a linearly mixed 0-1 program after a separable function is expressed by a piecewise linear function. Conversion of a NSP problem leads to generation of a solution that is extremely close to the global optimum. The quality of such solution can be enhanced by adequately adding the break points and searching intervals.

Linear programming, Mathematical programming

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Comments on properties of the minmax solutions in goal programming

Article Abstract:

Research is presented concerning the use of compromise programming and goal programming minmax models to generate solutions. The efficiency of the solutions which are generated by the models is discussed.

Models, Industrial efficiency, Economic efficiency, Goal setting, Chebyshev approximation

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